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DENTSPLY SIRONA : Management's Discussion and Analysis of Financial Condition and Results of Operations (form 10-Q)
Information included in or incorporated by reference in this Form 10-Q, and
other filings with the U.S. Securities and Exchange Commission (the "SEC") and
the Company's press releases or other public statements, contains or may contain
forward-looking statements. Please refer to a discussion of the Company's
forward-looking statements and associated risks in Part I, "Forward-Looking
Statements," Part I, Item 1, "Business" and Part I, Item 1A, "Risk Factors" of
the Company's Form 10-K for the year ended December 31, 2020. See Part II, Item
1A, "Risk Factors" of this Form 10-Q for any updated risk factors.
DENTSPLY SIRONA Inc. ("Dentsply Sirona" or the "Company"), is the world's
largest manufacturer of professional dental products and technologies, with a
134-year history of innovation and service to the dental industry and patients
worldwide. Dentsply Sirona develops, manufactures, and markets a comprehensive
solutions offering including dental equipment and dental consumable products
under a strong portfolio of world class brands. The Company also manufactures
and markets healthcare consumable products. As The Dental Solutions Company,
Dentsply Sirona's products provide innovative, high-quality, and effective
solutions to advance patient care and deliver better, safer, and faster
dentistry. Dentsply Sirona's worldwide headquarters is located in Charlotte,
North Carolina. The Company's shares of common stock are listed in the United
States on Nasdaq under the symbol XRAY.
The Company operates in two operating segments, Technologies & Equipment and
Consumables.
The Technologies & Equipment segment is responsible for the design, manufacture,
sales and distribution of the Company's Dental Technology and Equipment Products
and Healthcare Consumable Products. These products include dental implants,
CAD/CAM systems, orthodontic clear aligner products, imaging systems, treatment
centers, instruments, as well as consumable medical device products.
The Consumables segment is responsible for the design, manufacture, sales and
distribution of the Company's Dental Consumable Products which include
preventive, restorative, endodontic, and dental laboratory products.
The impact of COVID-19 and the Company's response
Information pertaining to the impact of the COVID-19 pandemic on the Company's
operations and financial results during the course of 2020 as well as the
Company's overall response can be found in "Part II, Item 7. Management's
Discussion and Analysis of Financial Condition and Results of Operations"
included in the Company's Annual Report on Form 10-K for the year ended December
31, 2020. Updates to that summary of impact for the six months ended June 30,
2021 are as follows:
•Continuing the trend from the last three quarters, the Company has continued to
see demand improve and dental patient traffic normalize in major markets.
Certain markets including regions of Southeast Asia and South America have
experienced setbacks in demand in the second quarter as a result of renewed
COVID-19 infections from recent variants of the virus. While most government
authorities have lifted many of their restrictions, the end dates for all
restrictions being lifted are still unknown. It is also uncertain when customer
demand will fully return to pre-COVID-19 levels upon lifting these restrictions,
or whether a resurgence of the virus may have an impact on demand in affected
markets.
•The Company's COVID-19 infection crisis management process implemented in 2020
remains in effect, and there have been no significant disruptions to operations
as a result of infections. During the course of the pandemic, the Company has
utilized this process to manage several incidents of exposure at facilities. All
potential and actual cases have been reviewed to ensure that the Company managed
exposed employees appropriately, consistently and safely. None of these
incidents have resulted in a material loss of production or financial impact to
the results for the six months ended June 30, 2021.
•The Company previously undertook various initiatives during the second quarter
of 2020, to ensure its ongoing liquidity which included, among other actions,
entering into a $310 million revolving credit facility on April 9, 2020, a 40
million euro revolving credit on May 5, 2020, a 30 million euro revolving credit
facility on May 12, 2020 and 3.3 billion Japanese yen revolving credit facility
on June 11, 2020. These additional short-term facilities were entered into in an
abundance of caution and have all expired as planned as of June 30, 2021.
•During the second quarter the Company has continued to prioritize employee
safety and preventing the possible spread of COVID-19 by encouraging ongoing
work-from-home where possible and maintaining travel restrictions.
Up through the date of the filing of this Form 10-Q, the Company's principal
manufacturing facilities and other operations have remained operational at a
more normalized level than during the preceding year. The Company continues to
monitor the COVID-19 pandemic. As governmental authorities adjust restrictions
globally, the Company plans to appropriately staff sales, manufacturing, and
other functions to meet customer demand and deliver on continuing critical
projects while also complying with all government requirements.
Restructuring Announcement
In November 2018, the Board of Directors of the Company approved a plan to
restructure and simplify the Company's business. The goal of the restructuring
is to drive annualized net sales growth of 3% to 4% and adjusted operating
income margins of 22% by the end of 2022 as well as achieve net annual cost
savings of $200 million to $225 million by 2021. In July 2020, the Board of
Directors of the Company approved an expansion of this plan that is intended to
further optimize the Company's product portfolio and reduces operating expenses.
The product portfolio optimization has resulted in the divestiture or closure of
certain underperforming businesses. The operating expense reductions will come
as a result of additional leverage from continued integration and simplification
of the business. The Company had initially anticipated one-time expenditures and
charges of approximately $275 million yielding annual cost savings of $200
million to $225 million by 2021. The program expansion is expected to result in
total charges of approximately $375 million and annual cost savings of
approximately $250 million. The Company expects that these expanded actions will
result in incremental global headcount reductions of 6% to 7% in addition to the
original projections of 6% to 8%. Since November 2018, the Company has incurred
expenditures of approximately $321 million under this program, of which,
approximately $123 million were non-cash charges. These amounts include the
charges for the portfolio shaping initiatives announced on August 6, 2020 which
are further discussed below.
As part of this expanded plan, the Company announced on August 6, 2020 that it
will exit its traditional orthodontics business as well as both exit and
restructure certain portions of its laboratory business. The traditional
orthodontics business is part of the Technologies & Equipment segment and the
laboratory business is part of the Consumables segment. The Company is exiting
several of its facilities and reducing its workforce by approximately 4% to 5%.
The Company expects to record total restructuring charges in a range of $60
million to $70 million for inventory write-downs, severance costs, fixed asset
write-offs, and other facility closure costs related to these actions. The
Company estimates that $45 million to $55 million of these restructuring charges
will be non-cash charges related to inventory write-downs and fixed asset
write-offs. The Company has recorded expenses of approximately $57 million
related to these actions, of which approximately $47 million were non-cash
charges. For the six months ended June 30, 2021, the Company made a $3 million
adjustment related to inventory reserves and paid $1 million in severance costs.
The Company expects nearly all of the remaining restructuring charges to be
completed by the first quarter of 2022.
RESULTS OF OPERATIONS, THREE MONTHS ENDED JUNE 30, 2021 COMPARED TO THREE MONTHS
ENDED JUNE 30, 2020
The Company presents net sales comparing the current year periods to the prior
year periods. In addition, the Company also compares net sales on an organic
sales basis, which is a Non-GAAP measure.
The Company defines "organic sales" as net sales excluding: (1) net sales from
acquired and divested businesses recorded prior to the first anniversary of the
acquisition or divestiture, (2) net sales attributable to discontinued product
lines in both the current and prior year periods, and (3) the impact of foreign
currency translation, which is calculated by comparing current-period sales to
prior-period sales, with both periods converted to the U.S. dollar rate at local
currency foreign exchange rates for each month of the prior period.
The "organic sales" measure is not calculated in accordance with US GAAP;
therefore, this item represents a Non-GAAP measure. This Non-GAAP measure may
differ from those used by other companies and should not be considered in
isolation from, or as a substitute for, measures of financial performance
prepared in accordance with US GAAP. Organic sales is an important internal
measure for the Company. The Company's senior management receives a monthly
analysis of operating results that includes organic sales. The performance of
the Company is measured on this metric along with other performance metrics.
The Company discloses organic sales to allow investors to evaluate the
performance of the Company's operations exclusive of certain items that impact
the comparability of results from period to period and may not be indicative of
past or future performance of the normal operations of the Company. The Company
believes that this information is helpful in understanding underlying net sales
trends.
Three Months Ended June 30,
(in millions, except percentages)               2021              2020       $ Change       % Change
Net sales                              $     1,067               $ 491      $     576        117.3  %
Net sales for the three months ended June 30, 2021 were $1,067 million, an
increase of $576 million or 117.3% from the three months ended June 30, 2020.
The increase in net sales was attributable to increased volumes in both the
Technologies & Equipment and Consumables segments due to a recovery in demand
from the impact of the COVID-19 pandemic. As a result, organic sales increased
104.6% as compared to the same prior year period.
Net sales were also positively impacted by approximately 10.7% due to the
weakening of the U.S. dollar as compared to the same prior year period as well
as a benefit of 11.9% from acquisitions offset by a reduction of 9.9% due to
divestitures of non-strategic businesses and discontinued products.
Net Sales by Region
Net sales by geographic region were as follows:
United States                          $     366                 $ 131      $     235        179.4  %
Europe                                       431                   216            215         99.5  %
Rest of World                                270                   144            126         87.5  %
The increase in net sales was attributable to both the Technologies & Equipment
and the Consumables segments and resulted from the overall higher volumes during
the three months ended June 30, 2021 due to the recovery in demand from the
COVID-19 pandemic. As a result, organic sales increased by 145.8% as compared to
the same prior year period. The increase in net sales also included a benefit of
43.6% from acquisitions offset by a reduction of 11.8% due to divestitures of
non-strategic businesses and discontinued products.
COVID-19 pandemic. As a result, organic sales increased by 91.8% as compared to
the same prior year period. Net sales for the quarter ended June 30, 2021 was
also positively impacted by 15.6% due to the weakening of the U.S. dollar as
compared to the same prior year period, offset by a reduction of 7.9% due to
the three months ended June 30, 2021 due to a recovery in demand from the
the same prior year period. Net sales for three months ended June 30, 2021 was
compared to the same prior year period, as well as a benefit of 0.8% from
acquisitions offset by a reduction of 10.9% due to divestitures of non-strategic
businesses and discontinued products.
(in millions, except percentages)                     2021                2020             $ Change             % Change
Gross profit                                      $      598          $     176          $     422               239.8%
Gross profit as a percentage of net sales              56.0%
For the three months ended June 30, 2021, the increase in the gross profit rate
as a percentage of net sales was primarily driven by favorable mix including an
increase in net sales for higher margin products, as compared to the same period
ended June 30, 2020.
(in millions, except percentages)                      2021               2020             $ Change             % Change
("SG&A")                                           $     398           $    261          $     137                    52.5  %
Research and development expenses ("R&D")                 40                 18                 22                   122.2  %
Restructuring and other costs                              5                  1                  4                         NM
SG&A as a percentage of net sales                       37.3  %            53.2  %
R&D as a percentage of net sales                         3.7  %             3.7  %
NM - Not meaningful
SG&A Expenses
For the three months ended June 30, 2021, the decrease in SG&A expenses as a
percentage of net sales was primarily driven by greater absorption of expenses
due to higher sales as well as continued expense discipline, as compared to the
same period ended June 30, 2020.
R&D Expenses
For the three months ended June 30, 2021, the increase in R&D expenses from the
comparable quarter of the prior year was primarily driven by significant spend
controls put in place in 2020 in response to the COVID-19 pandemic. As a
percentage of sales, R&D expenses were flat year-over-year. The Company intends
to continue to increase its investment and the ratio of R&D expense to net sales
Restructuring and Other Costs
The Company recorded restructuring and other costs of $5 million for the three
months ended June 30, 2021 compared to $1 million for the three months ended
June 30, 2020.
In connection with the various restructuring initiatives, as described earlier,
the Company recorded $9 million of restructuring costs and a benefit of $4
million in other costs for the three months ended June 30, 2021. For the three
months ended June 30, 2020, the Company recorded $2 million of restructuring
costs and a benefit of $1 million in other costs.
Other Income and Expense
(in millions)                                            2021                  2020      $ Change
Net interest expense                         $        16                      $ 11      $       5
Other expense (income), net                            5                         5              -
Net interest and other expense (income)      $        21                      $ 16      $       5
Net Interest Expense
The increase in net interest expense was due to higher average debt levels
during for the three months ended June 30, 2021 compared to the prior year
Income Taxes and Net Income
(in millions, except percentages)                               2021                2020             $ Change
Provision (benefit) for income taxes                        $      35           $     (24)         $      59
Effective income tax rate                                        26.1   %           (20.0) %
Net income (loss) attributable to Dentsply Sirona           $      99
$ (95) $ 194
Provision (benefit) for income taxes
For the three months ended June 30, 2021, the provision for income taxes was $35
million as compared to a benefit of $24 million during the three months ended
During the three months ended June 30, 2021, the Company recorded $3 million of
tax expense for other discrete tax matters.
The increase in the effective tax rate is primarily from an increase in mix of
higher-taxed foreign income and additional U.S. tax on foreign income. The
Company continues to reassess the realizability of its deferred tax assets and,
after weighing all positive and negative evidence, continues to maintain a
valuation allowance on certain deferred tax assets.
Segment Results
Technologies & Equipment               $     622                 $ 304      $     318        104.6  %
Consumables                                  445                   187            258        138.0  %
Segment Adjusted Operating Income (a)
(in millions, except percentages)                2021                2020      $ Change       % Change
Technologies & Equipment (b)           $      135                   $ (4)     $     139               NM
Consumables (b)                               154                    (17)           171               NM
(a) See Note 6, Segment and Geographic Information, in the Notes to Consolidated
Financial Statements in Item 8 of this Form 10-Q for a reconciliation from
segment adjusted operating income to consolidated US GAAP income.
(b) Certain charges related to discontinuance of product lines which were
previously reported in adjusted operating income for the reportable segments, $7
million for the three months June 30, 2020, have been reclassified to the "All
other" category to conform to current year presentation and the Company's
internal reporting to the Chief Operating Decision Maker package. These amounts
are not material to the measure of segment results for the years presented.
Technologies & Equipment
The increase in net sales occurred across all dental businesses and resulted
from overall higher volumes during the three months ended June 30, 2021 due to a
recovery in demand from the COVID-19 pandemic. As a result, organic sales
increased 85.2% as compared to the same prior year period, driven primarily by
the Equipment & Instruments, Digital Dentistry, and Implants businesses. Net
sales were also positively impacted by approximately 10.4% due to the weakening
of the U.S. dollar over the prior year period, as well as a benefit of 19.0%
from acquisitions offset by a reduction of 10.0% due to divestitures of
The adjusted operating income increase was primarily driven by the increase in
net sales as well as continued expense discipline.
The increase in net sales occurred across all regions and resulted from overall
higher volumes during the three months ended June 30, 2021 due to a recovery in
demand from the COVID-19 pandemic. As a result, organic sales increased 135.3%
as compared to the same prior year period, primarily driven by the Endodontic,
Restorative, and Preventive businesses. Net sales were also positively impacted
by approximately 11.2% due to the weakening of the U.S. dollar as compared to
the same prior year period, offset by a reduction of 8.5% due to divestitures of
net sales as well as favorable mix including increased volumes for higher margin
products, and continued expense discipline.
RESULTS OF OPERATIONS, SIX MONTHS ENDED JUNE 30, 2021 COMPARED TO SIX MONTHS
Six Months Ended June 30,
(in millions, except percentages)            2021             2020        $ Change       % Change
Net sales                              $    2,094           $ 1,365      $     729         53.4  %
Net sales for the six months ended June 30, 2021 were $2,094 million, an
increase of $729 million or 53.4% from the six months ended June 30, 2020. The
increase in net sales was attributable to both the Technologies & Equipment and
Consumables segments which were affected by overall higher volumes primarily due
to a recovery in demand from the impact of the COVID-19 pandemic. During the six
months ended June 30, 2020, the Company saw normal sales levels for the months
of January and February and started to experience a decline in sales volume
beginning in March and extending through June due to the onset of the pandemic.
As a result, organic sales increased 45.3% in the first six months of 2021
relative to the comparative period.
Net sales were also positively impacted by approximately 7.2% due to the
as a benefit of 7.7% from acquisitions offset by a reduction of 6.8% due to
(in millions, except percentages)              2021             2020       $ Change       % Change
United States                          $     713               $ 431      $     282         65.4  %
Europe                                       849                 589            260         44.1  %
Rest of World                                532                 345            187         54.2  %
and the Consumables segments and was primarily due to overall higher volumes
during the six months ended June 30, 2021 following periods of lower demand
resulting from the COVID-19 pandemic. As a result, organic sales increased by
47.6% as compared to the same prior year period. The increase in net sales also
included a benefit of 23.6% from acquisitions offset by a reduction of 7.3% due
to divestitures of non-strategic businesses and discontinued products.
The increase in net sales was attributable to both the Consumables and the
Technologies & Equipment segments and was primarily due to overall higher
volumes during the six months ended June 30, 2021 following periods of lower
demand resulting from the COVID-19 pandemic. As a result, organic sales
increased by 38.9% as compared to the same prior year period. Net sales for the
quarter ended June 30, 2021 was also positively impacted by 11.1% due to the
weakening of the U.S. dollar as compared to the same prior year period, offset
by a reduction of 5.9% due to divestitures of non-strategic businesses and
resulting from the COVID-19 pandemic. During the six months ended June 30, 2020,
the Company experienced a decline in sales volume beginning in March and
extending through June due to the COVID-19 pandemic, particularly in China and
other Asian markets. As a result, organic sales increased by 53.5% as compared
to the same prior year period. Net sales for the six months ended June 30, 2021
was also positively impacted by 7.7% due to the weakening of the U.S. dollar as
acquisitions offset by a reduction of 7.8% due to divestitures of non-strategic
(in millions, except percentages)                      2021                   2020             $ Change             % Change
Gross profit                                      $    1,177               $    644          $     533                    82.8  %
Gross profit as a percentage of net sales               56.2  %
For the six months ended June 30, 2021, the increase in the gross profit rate as
a percentage of net sales was primarily driven by favorable mix including the
Research and development expenses ("R&D")                 77                 52                 25                    48.1  %
Goodwill impairment                                        -                157               (157)                        NM
Restructuring and other costs                              8                 44                (36)                        NM
For the six months ended June 30, 2021, the decrease in SG&A expenses as a
For the six months ended June 30, 2021, the increase in R&D expense from the
comparable six month period of the prior year was primarily driven by
significant spend controls put into place in 2020 in response to the COVID-19
pandemic, increased investment on product development initiatives particularly
in the Company's Technology & Equipment segment, and in research investments
specific to our recent acquisitions of Byte and Datum Dental. The Company
intends to continue to increase its investment and the ratio of R&D expense to
net sales over time.
Goodwill Impairment
There were no impairments recorded in the six months ended June 30, 2021. During
the six months ended June 30, 2020, as a result of updating the estimates and
assumptions pertaining to the impact of the ongoing COVID-19 pandemic the
Company determined that the goodwill associated with the Equipment & Instruments
reporting unit within the Technologies & Equipment segment was impaired. As a
result, the Company recorded a goodwill impairment charge of $157 million.
Restructuring and Other Cost
The Company recorded restructuring and other costs of $8 million for the six
months ended June 30, 2021 compared to $44 million for the six months ended
the Company recorded $12 million of restructuring costs and a benefit of $4
million in other costs for the six months ended June 30, 2021.
During the six months ended June 30, 2020, the Company recorded $5 million of
restructuring costs and $39 million in other costs, which consisted primarily of
impairment charges of $39 million related to indefinite-lived intangible assets
within the Technologies & Equipment segment driven by a decline in forecasted
sales as a result of the COVID-19 pandemic as well as an unfavorable change in
the discount rate.
(in millions)                                 2021                2020      Change
Net interest expense                $       30                   $ 18      $    12
Other expense (income), net                 (4)                     3           (7)
Net interest and other expense      $       26                   $ 21      $     5
during the six months ended June 30, 2021 compared to the prior year period. As
noted in Part I, Item 1, Note 15, Subsequent Events, in July 2021 the Company
entered into a cross currency basis swap which effectively converts a portion of
the Company's $750 million bond coupon from 3.3% to 1.7%. Also in July 2021, the
Company entered into variable interest rate swaps which convert a portion of the
$750 million Senior Notes from a fixed rate of 3.3% into a variable interest
rate. Together, these instruments are expected to result in a net reduction of
interest expense for the remainder of 2021.
Income Taxes and Net Income (Loss)
(in millions, except percentages)                               2021               2020             $ Change
Provision (benefit) for income taxes                        $      67           $    (14)         $      81
Effective income tax rate                                        23.7   %           (5.6) %
Net income (loss) attributable to Dentsply Sirona           $     216
$ (235) $ 451
For the six months ended June 30, 2021, the provision for income taxes was $67
million as compared to a tax benefit of $14 million during the six months ended
tax expense for other discrete tax matters. The Company also recorded a $4
million tax expense as a discrete item related to business divestitures.
tax expense for other discrete matters. The Company also recorded a $11 million
tax benefit as a discrete item related to the indefinite-lived intangible asset
impairment charge.
(in millions, except percentages)              2021              2020       $ Change       % Change
Technologies & Equipment               $     1,219              $ 824      $     395       47.9%
Consumables                                    875                541            334       61.7%
(in millions, except percentages)              2021              2020       $ Change        % Change
Technologies & Equipment (b)           $     261                $ 107      $     154       143.9%
Consumables (b)                              304                   45            259       575.6%
million for the six months June 30, 2020, have been reclassified to the "All
The increase in net sales occurred across all dental businesses and was the
result of overall higher volumes during the six months ended primarily due to
demand recovery from the impact of the COVID-19 pandemic. As a result, organic
sales increased 35.0% as compared to the same prior year period, driven
primarily by the Equipment & Instruments and Implants businesses. Net sales were
also positively impacted by approximately 7.4% due to the weakening of the U.S.
dollar over the prior year period, as well as a benefit of 12.7% from
The increase in net sales occurred across all regions and was the result of
overall higher volumes during the six months ended primarily due to demand
recovery from the impact of the COVID-19 pandemic. As a result, organic sales
increased 60.6% as compared to the same prior year period, primarily driven by
the Endodontic, Restorative, and Preventive businesses. Net sales were also
positively impacted by approximately 6.9% due to the weakening of the U.S.
dollar as compared to the same prior year period, offset by a reduction of 5.8%
due to divestitures of non-strategic businesses and discontinued products.
The adjusted operating income increase was primarily driven by favorable mix
including increased volumes for higher margin products, and continued expense
discipline.
There have been no changes to the critical accounting policies as disclosed in
the Company's Form 10-K for the year ended December 31, 2020 other than those
changes explained in Part I, Item 1, Note 1, Significant Accounting Policies, in
the Notes of the Unaudited Consolidated Financial Statements of this Form 10-Q.
Goodwill represents the excess cost over the fair value of the identifiable net
assets of business acquired. Goodwill is not amortized; instead, it is tested
for impairment annually or more frequently if events or circumstances indicate
that the carrying value of goodwill may be impaired. Judgment is involved in
determining if an indicator of impairment has occurred during the course of the
year. Such indicators may include a decline in expected cash flows,
unanticipated competition or slower growth rates, among others. When testing
goodwill for impairment, the Company may assess qualitative factors for its
reporting units to determine whether it is more likely than not that the fair
value of a reporting unit is less than its carrying amount including goodwill.
Alternatively, the Company may bypass this qualitative assessment and perform
the quantitative goodwill impairment test.
Goodwill is allocated among reporting units and evaluated for impairment at that
level. The Company's reporting units are either an operating segment or one
level below its operating segments, as determined in accordance with ASC 350.
Effective 2021 and prospectively, the Company will perform its required annual
goodwill impairment test as of April 1 rather than on April 30 which was the
Company's previous practice. The Company believes this change is preferable as
it more closely aligns with the timing of the Company's strategic business
planning process. The Company does not believe this change resulted in any
delay, acceleration or avoidance of impairment. Furthermore, a retrospective
application to prior periods is impracticable as the Company is unable to
objectively determine, without the use of hindsight, the assumptions which would
be used in earlier periods.
For the fiscal year 2021, the Company performed its goodwill impairment test as
of April 1, 2021 and elected to bypass the qualitative assessment and performed
a quantitative assessment. The Company did not record any goodwill impairment
during the first six months of 2021. During the comparative first six months of
2020, the Company recorded a goodwill impairment charge of $157 million
associated with one reporting unit within the Technologies & Equipment segment.
In conjunction with its annual goodwill impairment test, the Company applied a
hypothetical sensitivity analysis to each of its reporting units by increasing
the discount rate of these reporting units by 100 basis points and, in a
separate test, reducing by 10% the fair value of those reporting units. All of
the Company's reporting units passed the hypothetical tests without the fair
value being reduced below carrying value, and therefore it is noted that there
are currently no reporting units deemed at risk of being impaired based on the
sensitivity analysis.
To determine the fair value of the reporting units, the Company used a
discounted cash flow model which utilizes both internal and market-based data as
its valuation technique. The discounted cash flow model uses five-to-ten year
forecasted cash flows plus a terminal value based on a multiple of earnings or
by capitalizing the last period's cash flows using a perpetual growth rate. The
Company's significant assumptions in the discounted cash flow model include, but
are not limited to, the weighted average cost of capital, revenue growth rates
(including perpetual growth rates), and operating margin percentages of the
reporting unit's business. These assumptions were developed in consideration of
current market conditions. The Company reconciled the aggregate fair values of
its reporting units to its market capitalization, which included a reasonable
control premium based on market conditions.
Indefinite-Lived Intangible Asset Impairment
Indefinite-lived intangible assets consist of tradenames and trademarks and are
not subject to amortization; instead, tested for impairment annually or more
frequently if events or circumstances indicate that the carrying value of
indefinite-lived intangible assets may be impaired or if a decision is made to
sell a business. The Company performed this annual impairment test as of April
1, 2021 in conjunction with the goodwill impairment annual test.
The Company did not record any indefinite-lived intangible asset impairment
2020, the Company recorded an indefinite-lived intangible asset impairment
charge of $39 million within the Technologies & Equipment segment.
The fair value of acquired tradenames and trademarks is estimated by the use of
a relief from royalty method, which values an indefinite-lived intangible asset
by estimating the royalties saved through the ownership of an asset. Under this
method, an owner of an indefinite-lived intangible asset determines the arm's
length royalty that likely would have been charged if the owner had to license
the asset from a third party. The royalty rate, which is based on the estimated
rate applied against forecasted sales, is tax-effected and discounted at present
value using a discount rate commensurate with the relative risk of achieving the
cash flow attributable to the asset. Management judgment is necessary to
determine key assumptions, including revenue growth rates, perpetual revenue
growth rates, royalty rates, and discount rates. Other assumptions are
consistent with those applied to goodwill impairment testing.
The Company also applied a hypothetical sensitivity analysis as part of the
annual impairment test of indefinite-lived intangibles. It was noted that if the
fair value of each of these indefinite-lived intangibles assets had been
hypothetically reduced by 10% or the discount rate had been hypothetically
increased by 100 basis points as of April 1st, 2021, the fair value of these
assets would still exceed their book value and currently none of the
indefinite-lived intangible assets would be considered at risk based on the
The determination of fair value involves uncertainties around the forecasted
cash flows as it requires management to make assumptions and apply judgement to
estimate future business expectations. Those future expectations include, but
are not limited to, the current and ongoing impact of the COVID-19 pandemic and
new product development changes for these reporting units. The Company also
considers the current and projected market and economic conditions amid the
ongoing pandemic for the dental industry both in the U.S. and globally, when
determining its assumptions.
A change in any of these estimates and assumptions used in the annual test, as
well as unfavorable changes in the ongoing COVID-19 pandemic, or in the overall
markets served by these reporting units, among other factors, could have a
negative material impact to the fair value of the reporting units and the
indefinite-lived tangible assets and could result in a future impairment charge.
There can be no assurance that the Company's future goodwill and
indefinite-lived assets impairment testing will not result in a material adverse
impact to the Company's results of operations.
Refer to Part I, Item 1, Note 13, Goodwill and Intangible Assets, in the Notes
of the Unaudited Consolidated Financial Statements of this Form 10-Q for further
discussion of the Company's annual goodwill and indefinite-lived intangible
asset impairment testing.
Cash provided by operating activities during the six months ended June 30, 2021
was $263 million, an increase of $99 million as compared to $164 million during
the six months ended June 30, 2020. This increase was driven primarily by the
higher cash collections in the current period, offset by changes in working
capital including a build in inventory during the current period to meet
recovered demand.
For the six months ended June 30, 2021, on a constant currency basis, the number
of days of sales outstanding in accounts receivable increased by 2 day to 56
days as compared to 54 days at December 31, 2020. On a constant currency basis,
the number of days of sales in inventory increased by 11 days to 113 days at
June 30, 2021 as compared to 102 days at December 31, 2020. The Company
calculates "constant currency basis" by removing the impact of foreign currency
translation, which is calculated by comparing current-period sales, accounts
receivables, and inventory to prior-period sales, accounts receivable, and
inventory, with both periods converted to the U.S. dollar rate at local currency
foreign exchange rates for each month of the prior period.
Cash used in investing activities during the first six months of 2021 included
net cash paid for acquisitions of $241 million and capital expenditures of
$66 million, offset by the receipt of $27 million in net cash from the sale of a
non-core business. The Company expects critical capital expenditures to be in
the range of approximately $150 million to $170 million for the full year 2021.
Cash used in financing activities for the six months ended June 30, 2021 was
primarily related to net share repurchases of $90 million and dividend payments
of $44 million. Financing inflows consisted of proceeds from the exercise of
stock options of $45 million and additional borrowings of $19 million.
The Company's overall cash and cash equivalents decreased by $106 million to
$332 million during the six months ended June 30, 2021.
During the six months ended June 30, 2021, the Company repurchased approximately
1.5 million shares under its open market share repurchase plan for a cost of $90
million at a weighted average price of $60.62. Including prior year repurchases,
the total amount repurchased under this authorization is $740 million leaving
approximately $260 million available to be repurchased. Additional share
repurchases, if any, will be made through open market purchases, Rule 10b5-1
plans, accelerated share repurchases, privately negotiated transactions, or
other transactions in such amounts and at such times as the Company deems
appropriate based upon prevailing market and business conditions and other
factors.
The Company's total borrowings decreased by a net $26 million during the six
months ended June 30, 2021, driven by $45 million due to exchange rate
fluctuations on debt denominated in foreign currencies. At June 30, 2021 and
December 31, 2020, the Company's ratio of total net debt to total capitalization
was 27.4% and 27.0%, respectively. The Company defines net debt as total debt,
including current and long-term portions, less cash and cash equivalents, and
total capitalization as the sum of net debt plus equity.
In response to the COVID-19 pandemic, the Company previously took actions during
the course of 2020 to strengthen its liquidity and financial flexibility. See
the Company's most recently filed Form 10-K for more information.
At June 30, 2021, the Company had a borrowing capacity of $744 million available
under lines of credit, including lines available under its short-term
arrangements and revolving credit facility. Through the date of the filing of
this Form 10-Q, the Company has no outstanding borrowings under any of its
credit facilities.
These agreements are unsecured and contain certain affirmative and negative
covenants relating to the operations and financial condition of the Company. The
most restrictive of these covenants pertain to asset dispositions and prescribed
ratios of indebtedness to total capital and operating income, plus depreciation
and amortization to interest expense. At June 30, 2021, the Company was in
compliance with these covenants and expects to remain in compliance with all
covenants over the next twelve months.
At June 30, 2021, the Company held $52 million of precious metals on consignment
from several financial institutions. The consignment agreements allow the
Company to acquire the precious metals at market rates at a point in time which
is approximately the same time and for the same price as alloys are sold to the
Company's customers. In the event that the financial institutions would
discontinue offering these consignment arrangements, and if the Company could
not obtain other comparable arrangements, the Company may be required to obtain
third party financing to fund an ownership position in the required precious
metal inventory levels.
The cash held by foreign subsidiaries for permanent reinvestment is generally
used to finance the subsidiaries' operating activities and future foreign
investments. The Company has the ability to repatriate additional funds to the
U.S., which could result in an adjustment to the tax liability for foreign
withholding taxes, foreign and/or U.S. state income taxes, and the impact of
foreign currency movements. At June 30, 2021, management believed that
sufficient liquidity was available in the United States and expects this to
remain for the next twelve months. The Company has repatriated and expects to
continue repatriating certain funds from its non-U.S. subsidiaries that are not
needed to finance local operations, however, these particular repatriation
activities have not and are not expected to result in a significant incremental
tax liability to the Company.
Except as stated above, there have been no material changes to the Company's
scheduled contractual cash obligations disclosed in its Form 10-K for the year
ended December 31, 2020.
The Company continues to review its debt portfolio and may refinance additional
debt or add debt in the near-term as interest rates remain at historically low
levels. The Company believes there is sufficient liquidity available for the
next twelve months.
NEW ACCOUNTING PRONOUNCEMENTS
Refer to Part 1, Item 1, Note 1, Significant Accounting Policies, to the
Unaudited Interim Consolidated Financial Statements of this Form 10-Q for a
discussion of recent accounting pronouncements.
Challenge in memory of pioneering orthodontist boosts student research at WVU School of Dentistry | WVU Today
Aspen Dental Opens 8th Practice in California
Acknowledgments – GOV.UK
Gingival bleeding associated with COVID‐19 infection – Manzalawi – 2021 – Clinical Case Reports


Multiple properties being offered for the first time creating opportunity for potential drive through between two streets off Main St, yet frontage on Main St. Currently car wash, subway, 3 unit, night club and vacant building formerly a take out pizza with apartment. In the heart of busy activity including civic center, hotels, casino, waterfront concerts, and new bank facility to accommodate hundreds of employees. Specs here are including all frontages, maps and lots, taxes, etc. Can be purchased collectively. Also, listed separately.


The President today announced the nomination of Michael M. Reyna to serve as a Member of the Farm Credit Administration Board.
Mr. Michael M. Reyna, of Elk Grove, California, has extensive experience in agricultural finance and financial services regulation. Mr. Reyna currently serves as State Director for the United States Department of Agriculture (USDA), Office of Rural Development in California, a position he has held since 1993, which provides credit to rural communities and oversees a loan portfolio in excess of $2 billion. USDA Rural Development is responsible for providing community and economic development services to rural America. From 1989 to 1993, he was the principal committee consultant for the California State Assembly's Ways and Means Committee where he specialized in the areas of housing and economic development. From 1988 to 1989, Mr. Reyna was the principal committee consultant for the California State Legislature's Elections, Reapportionment and Constitutional Amendments Committee. From 1982 to 1988, he was the Senior Program Analyst for the California State Legislature's Legislative Analyst's Office.
Mr. Reyna received his B.A. in Business Administration from the University of Texas and a Master of Public Affairs from the University of Texas, LBJ School of Public Affairs.
The Farm Credit Administration (FCA) is a bipartisan, independent regulatory agency. Members of the Board are responsible for regulation and examination of the banks, associations and related entities that collectively comprise what is known as the Farm Credit System, including the Federal Agricultural Mortgage Corporation (Farmer Mac). Members of the Board are also responsible for protecting the interests of the public and those who borrow from farm credit institutions or invest in farm credit securities. Initially created by Executive Order of the President in 1933, the agency now derives its powers and authorities from the Farm Credit Act of 1971, as amended.


My good friend over at Pop Culture Nerd is at it again!
What an interesting meme! I don't know if I can participate but it's certainly fun to read your post, Michael. I love your 12th one, oh so true!!
It is a fun meme. And if you can, I'd love to read your answers, Ruth. Thanks.
p.s., #12 was the easiest to answer ;-).
Mine aren't better; yours are hilarious! I was laughing out loud at your boss being melodramatic, your ex being friends with the devil, and your getting the gold medal in the drunkard's walk. That takes mad skills.
Y'know, I get lucky with the book titles I acquire (perhaps, this is why I pick 'em). Thanks for doing this one again.
Welcome, Margot. And thanks very much for the kind words.
You're right on that, Jen. Time really does fly, sometimes. Especially, when you have good and creative friends like you and Elyse. Thanks so much.
I've been working on mine, and – LOL – we have the same #7.
Ha! Can't wait to see the rest of them, Naomi. Thanks.
Oh, good times! As soon as I get myself organized again (and, um, erm, another post written) I will play, too.
Oooh, I can't wait. Thanks, Rachel.
I love the one about the neighbor. Hilarious! I love this meme and your list.
Welcome, Jenn! Thanks very much, and I enjoyed your answers, too.
I like your answers (mainly because I've read a few of those books, haha).
I just love this meme, it's so much fun.
I hope you can add to this, Poncho. Thanks, cousin.
I have done something like this a year ago,but with music,here ( http://bokunosekai.wordpress.com/2010/10/05/lets-shuffle-the-music/ ) maybe you're interested.It was quite funny.
I will definitely check out your music meme answers, Novroz. And I can't wait for your book title answers to post! Thank you very much.


Side profile of Dr. Kellersberger's album before treatment.
In 2013, the Presbyterian Historical Society launched an Adopt-a-Document campaign to conserve the largest and most complex historical object it has ever restored: a 300-page, 5-inch-thick photograph album and scrapbook created by the trailblazing leprosy physician, Dr. Eugene Roland Kellersberger. Kellersberger was a Presbyterian Church in the United States medical missionary to the Congo from 1916 to 1940. During that time he documented his experiences treating leprosy and living in the Congo through photographs, notes, and sketches, all of which he kept in this oversized album.
Prior to its treatment, the album's spine was severely deteriorated—it was impossible to open without breaking the brittle pages, making its contents inaccessible. Conservators at the Conservation Center for Art and Historic Artifacts disbound the album, mended and reattached its photos, and placed each page inside a protective polyester enclosure.
Side profile of Dr. Kellersberger's album before and after treatment.
Now, each page can be handled and viewed without fear of damage, and the images can be safely digitized. Below, staff members take the first look at images previously impossible to view.
Bill Brock and Jenny Barr marvel at the restored album.
Because of our supporters, we were able to raise the funds required to conserve this unique artifact and make it accessible to researchers and scholars. Thank you for your support, donations, and interest in last year's Adopt-a-Document project! News about our 2014 Adopt-a-Document project will be coming soon.


text:
function ResolveLabVMDiskPath {
<#
    .SYNOPSIS
        Resolves the specified VM name to it's target VHDX path.
#>
    param (
        [Parameter(Mandatory)] [ValidateNotNullOrEmpty()] [System.String] $Name
    )
    process {
        $hostDefaults = GetConfigurationData -Configuration Host;
        $vhdName = '{0}.vhdx' -f $Name;
        $vhdPath = Join-Path -Path $hostDefaults.DifferencingVhdPath -ChildPath $vhdName;
        return $vhdPath;
    } #end process
} #end function ResolaveLabVMVhdPath

function GetLabVMDisk {
<#
    .SYNOPSIS
        Retrieves lab virtual machine disk (VHDX) is present.
    .DESCRIPTION
        Gets a VM disk configuration using the xVHD DSC resource.
#>
    [CmdletBinding()]
    param (
        [Parameter(Mandatory)] [System.String] $Name,
        [Parameter(Mandatory)] [System.String] $Media
    )
    process {
        $hostDefaults = GetConfigurationData -Configuration Host;
        $image = Get-LabImage -Id $Media;
        $vhd = @{
            Name = $Name;
            Path = $hostDefaults.DifferencingVhdPath;
            ParentPath = $image.ImagePath;
            Generation = 'VHDX';
        }
        ImportDscResource -ModuleName xHyper-V -ResourceName MSFT_xVHD -Prefix VHD;
        GetDscResource -ResourceName VHD -Parameters $vhd;
    } #end process
} #end GetLbVMDisk

function TestLabVMDisk {
<#
    .SYNOPSIS
        Checks whether the lab virtual machine disk (VHDX) is present.
#>
    [CmdletBinding()]
    param (
        [Parameter(Mandatory)] [System.String] $Name,
        [Parameter(Mandatory)] [System.String] $Media
    )
    process {
        $hostDefaults = GetConfigurationData -Configuration Host;
        $image = Get-LabImage -Id $Media;
        $vhd = @{
            Name = $Name;
            Path = $hostDefaults.DifferencingVhdPath;
            ParentPath = $image.ImagePath;
            Generation = 'VHDX';
        }
        ImportDscResource -ModuleName xHyper-V -ResourceName MSFT_xVHD -Prefix VHD;
        TestDscResource -ResourceName VHD -Parameters $vhd;
    } #end process
} #end function TestLabVMDisk

function SetLabVMDisk {
<#
    .SYNOPSIS
        Sets a lab VM disk file (VHDX) configuration.
    .DESCRIPTION
        Configures a VM disk configuration using the xVHD DSC resource.
#>
    [CmdletBinding()]
    param (
        [Parameter(Mandatory)] [System.String] $Name,
        [Parameter(Mandatory)] [System.String] $Media
    )
    process {
        $hostDefaults = GetConfigurationData -Configuration Host;
        $image = Get-LabImage -Id $Media -ErrorAction Stop;
        $vhd = @{
            Name = $Name;
            Path = $hostDefaults.DifferencingVhdPath;
            ParentPath = $image.ImagePath;
            Generation = 'VHDX';
        }
        ImportDscResource -ModuleName xHyper-V -ResourceName MSFT_xVHD -Prefix VHD;
        [ref] $null = InvokeDscResource -ResourceName VHD -Parameters $vhd;
    } #end process
} #end SetLabVMDisk

function RemoveLabVMDisk {
<#
    .SYNOPSIS
        Removes lab VM disk file (VHDX) configuration.
    .DESCRIPTION
        Configures a VM disk configuration using the xVHD DSC resource.
#>
    [CmdletBinding()]
    param (
        [Parameter(Mandatory)] [System.String] $Name,
        [Parameter(Mandatory)] [System.String] $Media
    )
    process {
        $hostDefaults = GetConfigurationData -Configuration Host;
        $image = Get-LabImage -Id $Media -ErrorAction Stop;
        if ($image) {
            ## If the parent image isn't there, the differencing VHD won't be either (and xVHD will throw)
            $vhd = @{
                Name = $Name;
                Path = $hostDefaults.DifferencingVhdPath;
                ParentPath = $image.ImagePath;
                Generation = 'VHDX';
                Ensure = 'Absent';
            }
            ImportDscResource -ModuleName xHyper-V -ResourceName MSFT_xVHD -Prefix VHD;
            [ref] $null = InvokeDscResource -ResourceName VHD -Parameters $vhd;
        }
    } #end process
} #end RemoveLabVMDisk

function ResetLabVMDisk {
<#
    .SYNOPSIS
        Removes and resets lab VM disk file (VHDX) configuration.
#>
    [CmdletBinding()]
    param (
        [Parameter(Mandatory)] [System.String] $Name,
        [Parameter(Mandatory)] [System.String] $Media
    )
    process {
        RemoveLabVMSnapshot -Name $Name;
        RemoveLabVMDisk @PSBoundParameters;
        SetLabVMDisk @PSBoundParameters;
    } #end process
} #end function ResetLabVMDisk

redpajama_set_name: RedPajamaGithub


text:
World U.S. Navy Intercepts Illegal Iranian Arms Ship in Arabian Sea
U.S. Navy Intercepts Illegal Iranian Arms Ship in Arabian Sea
By Hamodia Staff
Thursday, February 13, 2020 at 2:57 pm | י"ח שבט תש"פ
Arms cache seized by the US Navy from an Iranian ship. (U.S Navy)
U.S. Central Command reported today that on Feb. 9, 2020, members of the crew of the USS Normandy (CG 60), in accordance with international law, boarded a dhow and discovered a large cache of weapons. The US Navy ship was conducting maritime security operations in the U.S. Central Command area of operations at the time.
(U.S Navy)
The weapons seized include 150 Iranian-manufactured copies of Russian Kornet anti-tank guided missiles (ATGM), which are named 'Dehlavieh'. Other seized weapons components, including three Iranian surface-to-air missiles, Iranian thermal imaging weapon scopes, and Iranian components for unmanned aerial and surface vessels, as well as other munitions and advanced weapons parts, were of Iranian design and manufacture.
On Nov. 25, 2019, the guided-missile destroyer USS Forrest Sherman (DDG 98) seized identical weapons systems in the Arabian Sea. At the time, those weapons were determined to be of Iranian origin and assessed to be destined for the Houthis in Yemen. The attempted transfer would have been in violation of a UN Security Council Resolution that prohibits the direct or indirect supply, sale, or transfer of weapons to the Houthis.
The seized weapons are in U.S. custody awaiting final disposition, and the assessment of the materiel will be an interagency and international effort, and international partner nations and organizations were invited to inspect the cache.
Central Command stated that the operation is ongoing, and further information will be shared as it becomes available.
Protesters Flood Streets as Venezuela Opposition Leader Arrested
Pakistan Begins Drone Warfare On Its Own Soil
First Government Plane Carrying Refugees Arrives in Canada
U.S., Allies Conduct 18 Strikes Against IS
Earthquake-Hit Taiwan City Still on Edge as Rescuers Hunt Survivors

redpajama_set_name: RedPajamaCommonCrawl


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text:
Educational Policy Studies
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Bartlett, Lesley
Lesley Bartlett
lbartlett2@wisc.edu
235 Education Building
1000 Bascom Mall
Lesley Bartlett is a Professor in Educational Policy Studies. She is also affiliated with Anthropology, Curriculum and Instruction, and Latin American, Caribbean, and Iberian Studies (LACIS). An anthropologist by training who works in the field of International and Comparative Education, Professor Bartlett does research in literacy studies (including multilingual literacies), migration, and educator professional development. In 2019, Professor Bartlett was named Faculty Director of the Institute for Regional and International Studies at University of Wisconsin-Madison. She currently co-edits the Anthropology and Education Quarterly with her colleague, Professor Stacey Lee.
PhD Anthropology, University of North Carolina at Chapel Hill, 2001
Bartlett, L., & Dowd, A. J. (2019). The Need for Speed: Interrogating the Dominance of Oral Reading Fluency in International Reading Efforts. Comparative Education Review, 63(2), 189-212.
Bartlett, L., Oliveira, G., & Ungemah, L. (2018). Cruel Optimism: Migration and Schooling for Dominican Newcomer Immigrant Youth. Anthropology and Education Quarterly, 49(4), 444-461.
Bartlett, L., & Vavrus, F. (2017). Rethinking Case Study Research: A Comparative Approach. New York, NY: Routledge.
Bartlett, L., Dowd, A. J., & Jonason, C. (2015). Problematizing early grade reading: Should the post-2015 agenda treasure what is measured?. International Journal of Educational Development, 40(1), 308–314.
Bartlett, L., & Ghaffar-Kucher, A. (2013). Refugees, Immigrants, and Education in the Global South: Lives in Motion. New York: Routledge.
Vavrus, F., & Bartlett, L. (2013). Teaching in Tension: International Pedagogies, National Policies, and Teachers' Practices in Tanzania. Rotterdam: Sense Publishers.
Bartlett, L., & Garcia, O. (2011). Additive Schooling in Subtractive Times: Bilingual Education and Dominican Immigrant Youth in the Heights. Nashville: Vanderbilt University Press.
Bartlett, L., (2010). The Word and the World: The Cultural Politics of Literacy in Brazil. Creskill, NJ: Hampton Press.
Bartlett, L., (2008). Literacy's Verb: Exploring What Literacy Is and What Literacy Does. International Journal of Educational Development, 28(6), 737–753.
Bartlett, L., (2005). Dialogue, knowledge, and teacher-student relations: Freirean pedagogy in theory and practice. Comparative Education Review, 49(3), 344–364.
Select Awards and Honors
Editor, Anthropology and Education Quarterly, (2020, 2023)
Bereday Award for Best Article in Comparative Education Review, Comparative and International Education Society, 2020
Teaching Academy, University of Wisconsin-Madison, 2019
Fulbright Senior Scholar Award, Spain, 2018
Vilas Mid-Career Award, University of Wisconsin-Madison, (2016, 2018)
Spencer Mid-Career Fellow, Spencer Foundation, (2015, 2016)
Jackie Kirk National Book Award, Comparative and International Education Society, 2014
Fulbright-Hayes Faculty Fellowship Recipient, Dominican Republic, 2009
Fulbright Scholar, Dominican Republic, 2008
Mellon Post-doctoral, Center for Teaching, Learning and Writing, Duke University, 2001
Give to Department
Room 235, Education Building
Feedback, questions or accessibility issues: web@comms.education.wisc.edu.


By Swarovski, the modern Pure Crystalline watch will add a dose of feminine elegance to any outfit. This timepiece features a white silver-tone sunray dial surrounded by 850 sparkling crystals set in Swarovski's signature Crystalline technique. Completing the look is a stainless steel bracelet that easily combines with other Swarovski pieces for an on-trend look.


We fabricate and install custom mirrors for home and business.
We have installed mirrors in gyms, dance studios, theatres, bathrooms, backsplashes, mirrored doors and much more. Custom mirrors in your home makes for an aesthetically appealing and comfortable living environment. We specialize in both commercial and residential and can brighten and visually enlarge absolutely any room with our superior handcrafted mirror replacement expertise.


The Kenyan school year is more in line with the calendar year with children starting in a new grade or school in January. We're all aware of the transitions we see here in Canada when a child leaves elementary school behind and starts high school. This transition is even more significant for young people in Kenya. Throughout their grade eight year they studied for the entrance exams which took place in November and December. These marks determined if they can go to high school and the 'level' they can attend. Higher marks open up possibilities for better schools.
As well, these schools are most often residential schools. The young person goes away to live – often very far away from home and family.
This is also a very busy time for Kay and Ruth. Not only must they prepare the children (clothing, school supplies, school books, 'kits', basic supplies) but then bring the young person to their school. Last year one of our students was admitted to a school that was basically on the far side of Kenya!
Anastasia with some of her supplies, proudly and happily, heading off to school. The Probus Club of Brampton made a contribution that provided for her school year.
This year we are proud to announce that we have 19 children in high school!
Six are not sponsored but are supported through the fund raising of The Creation of Hope. They are either related to a sponsored child or were simply identified by the community or schools as having great potential but no financial ability.
Of these children the first, Faith Nthenge Muthini, is now in her last year of high school. While we have had one young lady graduate from trade school, Faith will be our first high school graduate in December.
Many of our sponsors provide funds for something extra for their child at Christmas. Others send over letters or parcels. Mail from Canada to Kenya is, well, somewhat adventurous, and often takes a long time. Many of these gifts were mailed in October and November just arrived and were presented to the children.
Muthina receiving a parcel from Barb Munich – Barb is one of a group of sponsors who will be joining us in Kenya this summer. One of my personal highlights will be introducing sponsors to their children!
Fatema – one of our youngest supporters – has made another $50.00 donation this month. Please thank Fatema again from all of us.
Steve, who lives in Canada, but is originally Nigerian visited the program. He left not only a positive impression on the children but a gift for them all.
53 children with 53 new pairs of shoes! Thanks Steve!
Eric and Barb and their Sunday school group at Emmanuel Baptist Church in Nova Scotia raised money to support all of Rolling Hills Residence for 4 days.
Here is our partial contribution for $2107.80 for your village. Please use a portion of this towards the purchase of goats for the families. If you recall that was Samantha Crawford's goal. The rest please use to take care of our foster child Mbithi Mutheu and the greatest needs of your community.
Emily Ross is a sponsor, a talented musician and a member of the Vanier Social Justice Club at Vanier Catholic Secondary School in Whitehorse Yukon. They raised and donated $500.00 for the program.
Contanza Leon has now sponsored Ezekiel Mwongela.
Here's a shot from last month's sponsorship.
These pictures mean a lot to the children – to see the real person who has changed their life.
With these sponsors added we are on the verge of closing off our sponsorship program to new children. This is a combination of factors – the neediest have been sponsored – and the simple limitations of our program. The Canadian component of our program is literally run off our dining room table by my wife, Anita, and I, while in Kenya it is Ruth and Kay.
We are cautious to not grow so big that we'll lose the ability to be personal and responsive. We also do not want to dilute the effectiveness of our service by stretching our limited man power and resources. The remaining children to be sponsored are on our webpage. Over time as new children are in need of sponsorship – or the emergence of children needing to be re-sponsored – we will have other opportunities.
We still need and welcome support for specific projects, for ongoing needs such as school uniforms and for supporting the entire Rolling Hills Residence ($50.00 per day).
We wish to extend our sincere condolences to our Program Director in Kikima, Ruth Kyatha and her entire family, on the death of Ruth's mother Serah Mbuve Kiundi on January 23 2012 who lived into her 95th year. The Walters family had the opportunity to meet and visit with Serah in 2008. She was a very strong woman of faith who believed in education for her daughters as well as her sons when she was a poor widow caring for 9 children decades ago. Such a commitment to education of females at that time was very unusual. Her character and strength is reflected as her legacy is carried on through her large and accomplished extended family including our incredible staff – Ruth Kyatha and Kay Mutinda.


Estroe started DJ-ing in 1998 and is regarded as one of the few international female DJs who made it to the top.
She has travelled to the USA, the Caribbeans, Russia, Canada, Japan and across Europe. Her list of venues and festivals is impressive: Berghain (Berlin), Watergate, (Berlin), Fuse (Brussel), Tresor (Berlin), Sub Club (Glasgow), Cocoon Club (Frankfurt), Rex Club (Paris), Origami Entertainment Club (Tokyo), Warehouse 702 (Tokyo), Harry Klein (Munchen), Q Club (Zurich), Awakenings (Amsterdam), Dave Clarke' White Noise (Amsterdam), Sonar (Barcelona), 5 Days Off (Amsterdam), Bergwacht (Cologne), DEMF (Detroit), Kristal Glam Club (Bucharest), Promise (Toronto), Club Ma22o (Amsterdam), Club 11 (Amsterdam), Studio 80 (Amsterdam), Doornroosje (NL), Solar Festival (NL), Welcome To The Future Festival (NL), Teqnology (HMH), In Qontrol (RAI), Off Corso (Rotterdam) Paradigm (Groningen), Pand48 (Groningen), Simplon (Groningen) and Dance Valley (NL)!
Her career took off from there. Her style developed quickly and in more recent years, Estroe has been known for her warm, subtle mixes of techno and tech house that fluently evolve from delicate and warm music to darker sounds with energy and groove. She likes to set the tone at the beginning of an evening, and is also in her element when performing at peaktime and not scared of throwing in some old school techno and electro.
Being a real people's person, she is able to crank up the tunes and create a brilliant vibe on the dance floor.
Many top producers started out as DJs. Estroe is one of them. Her delicate and profound productions are not about maximum compression, distorted hi-hats or full-on bass drums. Instead, they are about atmosphere and space.
Estroe started producing several EPs and singles (on labels such as Lessismore, Little-D, and Muzikism) before releasing Driven on Connaisseur Recordings in 2007. This track sparked the interest of several big names. Ellen Allien chose Driven for her Fabric.34 mix CD. John Digweed was blown away by this minimalist masterpiece and promptly asked her for a remix on his Bedrock label.
Estroe's long-awaited debut LP Elemental Assets, featuring a guest appearance from Miss Kittin, followed in 2009 via Connaisseur Recordings and received widespread critical acclaim. Just recently this year, Estroe released her second album Comfort and Closure (EevoNext Recordings).
With her sophisticated, warm and elegant productions Estroe hasn't gone unnoticed among other DJs. Dave Clarke booked her for his White Noise parties and she's a resident at his Dave Clarke Presents event (Melkweg, Amsterdam) twice a year. She is also a frequently asked remixer, as is evident from the number of times her remixes for Bedrock, Manual Music, Tulipa Recordings and Cinematique hit the charts.
Having a desire to spot and promote other artists, she acts as one of the judges in the biggest Dutch production contest Vinylized and gives workshops at the Red Bull Music Academy. Furthermore, she has her own agency www.estroe-advice.com which provides technical and managerial training for aspiring producers and dj's . Estroe also gives workshops on Ableton, and tries to provide a platform for new talents. She does this by broadcasting their mixes at her monthly Estroe Invites Proton show and by booking them at her Estroe Invites events.


text:
in: Actors, Listed on Original Cinemorgue, Scottish actors and actresses,
Death scenes by decapitation
Death scenes by monster attack
Death scenes by dismemberment
Death scenes by explosion
Death scenes by accident
Comedic death scenes
Death between changing times
Death scenes by shredding
Death scenes by head explosion
Death scenes by suicide
Death scenes by falling
Death scenes by accidental stabbing
Death scenes by murder
Characters Killed by Jack Bauer in 24
Death scenes by drowning
Death scenes by burning
Death scenes by biting
Deaths in the Marvel universe
People who died in Primeval
Actors who died in Ridley Scott movies
Actors who died in Michael Mann Movies
Actors who died in Neil Jordan Movies
Marvel Stars
Actors who died in John Moore Movies
People who died in the Underworld Films
Actors who died in David Leitch Movies
People who died in the Blade Films
Doctor Who cast members
The Mentalist Cast Members
Characters killed by The Punisher
People who died in the Punisher film or TV series
Thor Cast Members
Call of Duty Cast Members
Daredevil Cast Members
Adventure Stars
Blade Cast Members
Deaths in 24
Actors who died in a David S. Goyer movie
Ray Donovan Cast Members
People who died in a Ray Donovan series
SEAL Team Cast members
Actors who died in Len Wiseman Movies
Fangoria Chainsaw Award Nominees
Underworld Cast Members
Deaths in the New Line Cinema universe
Death scenes by sword
Death scenes by shotgun
Performers with over 20 deaths
DC Stars
The Flash Cast Members
Tony Curran's death in Cat Run
Tony Curran (1969 - )
Gladiator (2000) [Assassin #1] Stabbed in the chest with his own sword by Russell Crowe.
Blade II (2002) [Priest]: Tony dies two deaths. The first death occurs when he is given a mercy-killing by Matt Schulze by multiple gunshot wounds to the chest after having been bitten by a reaper. After being reanimated by the virus, Ron Perlman decapitates Tony's skull, and for good measure, Wesley Snipes incinerates Tony's body by exposing him to sunlight, leaving behind the severed head.
Flight of the Phoenix (2004) [Alex Rodney]: Shot by Anthony Wong when Anthony shoots at Tyrese Gibson and Tony shoves Tyrese out of the way. He dies shortly afterwards while talking to Dennis Quaid.
Beowulf and Grendel (2005) [Hondscioh]: Killed by Ingvar Eggert.
Underworld: Evolution (2006) [Marcus Corvinus]: Slashed to death when Kate Beckinsale knocks him into the rotor blades of a downed helicopter, after having stabbed him in the head under his chin with one of his own wing-claws.
The Lazarus Project (2008 formerly known as The Heaven Project) [William Reeds]: Commits suicide by jumping off a cliff (in a bid to escape the isolated community) as Paul Walker tries to stop him. His body is later seen being pulled up a cliff-side as Paul talks to Bob Gunton.
Ondine (2009) [Alex]: Thrown through the windshield into a store front window when Dervla Kirwan crashes intoEmil Hostina's car. (Thanks to ND)
Cat Run (2011) [Sean Moody]: Head explodes after Janet McTeer shoots him in the head with an explosive round.
X-Men: First Class (2011) [Man in Black Suit Agent]: Hurled against the ceiling by Kevin Bacon's powers. (Thanks to ND)
In the Dark Half (2012) [Filthy]: Commits suicide by drug overdose so he can join his son (Alfie Hepper) in the afterlife, he dies while talking to Jessica Barden. His body is later seen as she constructs a makeshift funeral pyre for him before setting it on fire.
Awaiting (2015) [Morris]: Shot in the throat by Rupert Hill. He dies shortly afterwards in Diana Vickers arms.
Medium: The Devil Inside, Part One (2009) [Lucas Harvey]: Shot in the back by David Cubitt while Tony is trying to drown Patricia Arquette in holy water. He returns as a ghost in the following episode (The Devil Inside, Part Two) before being dragged into purgatory by the other spirits. (Thanks to ND)
24: Day 8: 10:00pm-11:00pm (2010) [Lugo Elson]: Impaled in the neck after Kiefer Sutherland takes out a knife which Annie Wersching accidentally stabbed him with and throws it at Curran when Curran comes in after sensing that his boss Callum Keith Rennie is in danger.
Doctor Who: Vincent and the Doctor (2010) [Vincent van Gogh]: Months after the point in his life when the episode takes place, shoots himself in the chest with a 7mm Lefaucheux à broche revolver, despite the events of the episode. Though his organs weren't damaged, he died from an untreated infection during the early hours of July 29th. He is also shown in 'Doctor Who: The Pandorica Opens'.
Primeval: season 3 Episode 7 [William de Mornay]: In Chronological time he came to the present from the Medieval age and seen his grave. he became buck to his time.
The Comic Strip Presents: The Hunt for Tony Blair (2011) [Robin Cook]: Pushed off of a cliff by Stephen Mangan. (Played for comic effect.) (Thanks to ND)
Labyrinth: Episode 2 (2012) [Guy D'Evreux]: Stabbed in the stomach with a sword by Emun Elliott after Tony first stabs Emun.
Daredevil: Penny and Dime (2016)[Finn]: Face blown apart with a shotgun blast by Jon Bernthal, in addition to having been shot twice in the back by Jon.
Deadwood: The Movie (2019) [James Smith] Shot in the forehead before he can confess who hired him for the murder of Dayton Callie.
Ray Donovan: Never Going to Give You Up (2019) [Sgt. Mikey 'Rad' Radulovic]: Shot to death by Liev Schreiber.
SEAL Team: Medicate & Isolate (2019) [Brett Swann]: Commits suicide off-screen via gunshot wound to the chest after being refused medical treatment at the Veteran's Affairs office. Tony's corpse is found by Max Thieriot at the end of the episode minutes after Tony's death. Tony's death is recorded on his personal video camera in the episode Rock Bottom.
Tony Curran's death in Underworld: Evolution
Listed on Original Cinemorgue
Scottish actors and actresses


text:
Explaining Steps for Rewriting Equations
7.1: Math Talk: Could It be Zero? (5 minutes)
HSA-REI.A
Math Talk
This Math Talk encourages students to to rely on the structure of equations, properties of operations, and what they know about solutions to equations to mentally solve problems. It also prompts students to recall that dividing a number by 0 leads to an undefined result, preparing them for the work later in the lesson. (In that activity, students will consider why dividing by a variable is not considered an acceptable move when writing equivalent equations or solving equations.)
To determine if 0 is a solution to the equations, students could substitute 0 into the expressions and evaluate them. For some equations, however, the answer can be efficiently found by making use of structure (MP7). In explaining their strategies, students need to be precise in their word choice and use of language (MP6).
Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Representation: Internalize Comprehension. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization
Is 0 a solution to each equation?
\(4(x + 2) = 10\)
\(12 - 8x = 3(x + 4)\)
\(5x = \frac12 x\)
\(\frac {6}{x} + 1 = 8\)
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
"Who can restate \(\underline{\hspace{.5in}}\)'s reasoning in a different way?"
"Did anyone have the same strategy but would explain it differently?"
"Did anyone solve the problem in a different way?"
"Does anyone want to add on to \(\underline{\hspace{.5in}}\)'s strategy?"
"Do you agree or disagree? Why?"
Speaking: MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, "First, I _____ because…." or "I noticed _____ so I…." Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
7.2: Explaining Acceptable Moves (15 minutes)
Take Turns
Previously, students saw that certain moves can be made to an equation to create an equivalent equation. In this activity, they deepen that understanding by explaining why, if a given equation is true for a certain value of the variable, performing one of those moves leads to a second equation that is also true for the same variable value. This requires more than simply stating what the moves are, and offers students opportunities to construct logical arguments (MP3).
Clarify the distinction with an example. Ask students: "Consider these equations: \(3x - 5 = 16\) and \(3x = 21\). The first equation is a true statement for a certain value of \(x\). Can you explain why the second equation must also be true for the same value of \(x\)?"
Explain that an answer such as "Adding 5 to each side of the first equation gives the second equation" is a description of the move rather than an explanation for why the second equation must be true.
An explanation may sound something like: "We know that \(3x-5\) and 16 are equal when \(x\) has a particular value. If we add the same number, like 5, to both \(3x-5\) and to 16, the results are still equal for the same variable value. This means the statement \(3x = 21\) must be true for the same value of \(x\)."
In this partner activity, students take turns giving explanations, and listening to and critiquing a partner's explanations (MP3). As students discuss their thinking, listen for explanations that are particularly clear so that they can be shared with the class later.
Tell students that they have performed a number of moves to write equivalent equations and solve equations. They will now practice explaining to a partner why those moves are legitimate. Demonstrate what it means to explain or defend the steps rather than simply describing them, as shown in the Activity Narrative.
Arrange students in groups of 2. Ask the partners in each group to choose different equations from each column. Give students a few minutes of quiet time to think about and write explanations about the equations in column A. Then, give students time to take turns sharing their explanations with their partner before moving on to column B.
Tell students that when one student explains, the partner's job is to listen and make sure that they agree and that the explanation makes sense. If they don't agree, the partners discuss until they come to an agreement.
Repeat the process with the equations in column B.
Conversing: MLR8 Discussion Supports. Display the following sentence frames for all to see: "_____ and _____ are both true because….", and "I noticed _____ and _____ are not equivalent because…." Encourage students to challenge each other when they disagree. This will help students clarify their reasoning about equivalent equations.
Here are some pairs of equations. While one partner listens, the other partner should:
Choose a pair of equations from column A. Explain why, if \(x\) is a number that makes the first equation true, then it also makes the second equation true.
Choose a pair of equations from column B. Explain why the second equation is no longer true for a value of \(x\) that makes the first equation true.
Then, switch roles until you run out of time or you run out of pairs of equations.
\(16=4(9-x)\)
\(16=36-4x\) \(9x = 5x + 4\)
\(14x = 4\)
\(5x = 24 + 2x\)
\(3x = 24\) \(\frac12x - 8 = 9\)
\(x - 8 = 18\)
\(\text-3(2x +9)=12\)
\(2x+9=\text -4\) \(6x - 6 = 3x\)
\(x - 1 = 3x\)
\(5x=3-x\)
\(5x = \text-x + 3\) \(\text-11(x -2) = 8\)
\(x-2 = 8 + 11\)
\(18 = 3x - 6 + x\)
\(18 = 4x - 6\) \(4 - 5x = 24\)
\(5x = 20\)
Students may have trouble seeing why some equations in column B are not equivalent (particularly the second item, which contains a common error). Encourage these students to choose one pair of equations, solve one equation, and then substitute the solution into the other equation to see what goes wrong.
Invite previously identified students to share their explanations on at least a couple of pairs of equations from each column. If not already clear from students' explanations, emphasize that:
If two expressions are equal, then performing the same addition (or subtraction) or multiplication (or division) to both expressions maintains the equality.
Applying the distributive, commutative, and associative properties (of multiplication or addition) to an expression doesn't change its value, so doing so to one side of a true equation doesn't change the equality.
Explain to students that next they will look at some examples where the moves made to write equivalent equations appear to be acceptable but the resulting equations turn out to be false statements.
Representation: Internalize Comprehension. Use color and annotations to illustrate student thinking. As students share their reasoning about the pairs of equations, scribe their thinking on a visible display. Invite students to compare moves described that produce equations with the same solutions, to those that create equations with different solutions.
Supports accessibility for: Visual-spatial processing; Conceptual processing
7.3: It Doesn't Work! (15 minutes)
So far, students have seen only one-variable equations that have a solution. For these equations, performing acceptable moves always led to equivalent equations that have the same solution. In this activity, students encounter an example where the given equation has no solutions and performing the familiar moves leads to an untrue statement.
Prior to this point, students have added, subtracted, multiplied, and divided a number from both sides of an equation. They have also added a variable expression to (or subtracted a variable expression from) an equation. They recognize these moves as allowable for solving equations. Here, students also come across an equation that is divided by a variable expression and make sense of why it leads to a false statement.
Arrange students into groups of 3–4. Give groups 1–2 minutes of quiet time to analyze the first set of equations and then time to brainstorm why Noah's work results in a false statement. Follow with a class discussion.
Invite students to share their explanations as to why Noah ended up with \(6=1\). Students are likely to say that the moves Noah made were allowable and can be explained, but they may struggle to say why they end up with a false statement.
Draw students' attention to the third line of Noah's work. Ask them to interpret the expression on each side of the equal sign: \(x + 6\) can be interpreted as 6 more than a number and \(x + 1\) as 1 more than that same number. Then, ask them to try to find a value of \(x\) that could make that equation true. (There is none!)
Highlight that it's not possible for 6 more than some number, no matter what that number is, to be equal to 1 more than that number. If no value of \(x\) could make the third equation true, the same could be said about the original equation—it had no solution. So even though Noah performed acceptable moves, the final equation is a false equation. Because all of these equations are equivalent, this means the original equation is also a false equation. It has no solutions because no value of \(x\) could make the equation true.
Repeat the process to analyze the second set of equations. See Activity Synthesis for discussion questions.
Noah is having trouble solving two equations. In each case, he took steps that he thought were acceptable but ended up with statements that are clearly not true.
Analyze Noah's work on each equation and the moves he made. Were they acceptable moves? Why do you think he ended up with a false equation?
Discuss your observations with your group and be prepared to share your conclusions. If you get stuck, consider solving each equation.
\(\begin {align} x + 6 &= 4x + 1 - 3x &\quad& \text{original equation}\\ x + 6 &= 4x - 3x + 1 &\quad& \text{apply the commutative property}\\ x + 6 &= x + 1 &\quad& \text{combine like terms}\\ 6 &= 1 &\quad& \text{subtract }x \text{ from each side} \end {align}\)
\(\begin {align} 2(5 + x) -1 &= 3x + 9 &\quad& \text {original equation}\\ 10 + 2x -1 &= 3x + 9 &\quad& \text{apply the distributive property}\\ 2x -1 &= 3x - 1 &\quad& \text{subtract 10 from each side}\\ 2x &= 3x &\quad& \text{add 1 to each side}\\ 2 &= 3 &\quad& \text{divide each side by } x \end {align} \)
We can't divide the number 100 by zero because dividing by zero is undefined.
Instead, try dividing 100 by 10, then 1, then 0.1, then 0.01. What happens as you divide by smaller numbers?
Now try dividing the number -100 by 10, by 1, by 0.1, 0.01. What is the same and what is different?
In middle school, you used tape diagrams to represent division. This tape diagram shows that \(6 \div 2 = 3\)
Draw a tape diagram that shows why \(6 \div \frac12 = 12\).
Try to draw a tape diagram that represents \(6 \div 0\). Explain why this is so difficult.
Some students may point to a step that is valid and mistakenly identify it as an error. For instance, in the first set of steps, they may object to replacing \(+1 - 3x\) with \(-3x+1\), thinking that it should be rearranged to \(+3x-1\). Push their reasoning with a simpler example. Ask, for instance, if \(+7 - 4\) is equivalent to \(+4 - 7\). Remind students that we can think of \(+7 -4\) as \(+7 + (\text-4)\) and then apply the commutative property of addition to get \(\text-4 + 7\).
If students hypothesize about two equations being equivalent but are not sure how to check if it's actually the case, suggest that a good way to check is by finding the solution to one equation, then checking whether that value is also a solution to the second equation.
Invite students to share what they thought was the problem with Noah's work. They are likely to say that Noah seems to have performed allowable moves and did them correctly. Then, draw students' attention to the second to last step: \(2x = 3x\). Ask students:
"Earlier, when looking at \(x + 6 = x + 1\), we reasoned that there's no value of \(x\) that could make this equation true. Is there a value of \(x\) that could make \(2x = 3x\) true?" (Yes, 0.)
"If there is a value that can make \(2x=3x\) true, what do we know about the original equation? Is it also true?" (Yes, they are all equivalent equations.) "What is its solution?" (0)
"So the equations are true up through the third step. The last step is where we have a false statement, after Noah shows division by \(x\). If \(x\) is 0, what might be problem with dividing by \(x\)?" (If \(x\) is 0, then we are dividing both sides by 0, which gives an undefined result.)
Explain that dividing by the variable in the equation is not done because if the solution happens to be 0, it could lead us to thinking that there is no solution while in fact there is (the solution is the number 0).
Revisit the lists of acceptable and unacceptable moves compiled in earlier activities. Add "dividing by the variable" and "dividing by 0" to the list of unacceptable moves.
Speaking, Representing: MLR8 Discussion Supports. Give students additional time to make sure everyone in their group can explain their analysis of Noah's moves. Invite groups to rehearse what they will say when they share with the whole class. Rehearsing provides students with additional opportunities to speak and clarify their thinking, and will improve the quality of explanations shared during the whole-class discussion.
Design Principle(s): Support sense-making; Cultivate conversation
Display the following sets of equations and questions for all to see. Tell students that each set represents an original equation and the first step taken to solve it.
\(\begin{align} 5(x-3)&=5\\x-3&=1 \end{align}\)
\(\begin{align} 5x-3&=5\\5x&=2 \end{align}\)
\(\begin{align} 5(x-3)&=5x\\x-3&=x \end{align}\)
\(\begin{align} (5-3)x&=5x\\ 5-3&=5 \end{align}\)
For each set of equations, ask students:
"What move was made to the original equation to obtain the second equation?"
"Is the solution to the second equation the same as the solution to the original equation? Why does it stay the same or why does it change?"
Make sure students see that:
A: The move made is dividing each side by 5. The solution is the same (\(x=4\)) because dividing both sides by the same number keeps the two sides equal.
B: The move made is adding 3 to the left side and -3 to the right. The solution of the first equation (\(x=\frac85\)) no longer makes the second equation true because the two sides of the equation are no longer equal.
C: The move made is dividing each side by 5. It is a valid move, but because the original equation does not have a solution (5 times a number, \(5x\), cannot be equal to 5 times a smaller number, \(5(x-3)\)), the second equation also does not have a solution (3 less than a number, \(x-3\), cannot be equal to that number, \(x\)).
D: The move made is dividing each side by \(x\). The second equation doesn't have a solution even though the original solution does. The move is problematic because it would eliminate the variable and make us miss the solution, namely \(x=0\).
7.4: Cool-down - If This, Then That (5 minutes)
When solving an equation, sometimes we end up with a false equation instead of a solution. Let's look at two examples.
Example 1: \(\qquad \qquad 4(x+1) = 4x\)
Here are two attempts to solve it.
\(\begin {align} 4(x+1) &= 4x &\hspace{0.1 cm} &\text{original equation}\\ x + 1 &= x &\hspace{0.1 cm} &\text{divide each side by 4} \\ 1 &=0 &\hspace{0.1 cm} &\text{subtract }x \text{ from each side} \end{align}\)
\(\begin {align} 4(x+1) &= 4x &\hspace{0.1 cm} &\text{original equation}\\ 4x + 4 &= 4x &\hspace{0.1 cm} &\text{apply the distributive prop}\\ 4 &= 0 &\hspace{0.1 cm} &\text{subtract }4x \text{ from each side}\end {align}\)
Each attempt shows acceptable moves, but the final equation is a false statement. Why is that?
When solving an equation, we usually start by assuming that there is at least one value that makes the equation true. The equation \(4(x +1) = 4x\) can be interpreted as: 4 groups of \((x+1)\) are equal to 4 groups of \(x\). There are no values of \(x\) that can make this true.
For instance, if \(x=10\), then \(x+1=11\). It's not possible that 4 times 11 is equal to 4 times 10. Likewise, 1.5 is 1 more than 0.5, but 4 groups of 1.5 cannot be equal to 4 groups of 0.5.
Because of this, the moves made to solve the equation would not lead to a solution. The equation \(4(x+1) = 4\) has no solutions.
Example 2: \(\qquad \qquad \qquad 2x - 5 = \dfrac {x-20}{4}\)
\(\begin{align} 2x - 5 &= \dfrac{x-20}{4} &\quad &\text{original equation}\\ 8x - 20 &= x - 20 &\quad &\text{multiply each side by 4}\\ 8x &= x &\quad &\text{add 20 to each side}\\ 8 &= 1 &\quad &\text{divide each side by }x \end {align}\)
Each step in the process seems acceptable, but the last equation is a false statement.
It is not easy to tell from the original equation whether it has a solution, but if we look at the equivalent equation \(8x = x\), we can see that 0 could be a solution. When \(x\) is 0, the equation is \(0 = 0\), which is a true statement. What is going on here?
The last move in the solving process was division by \(x\). Because 0 could be the value of \(x\) and dividing by 0 gives an undefined number, we don't usually divide by the variable we're solving for. Doing this might make us miss a solution, namely \(x=0\).
Here are two ways to solve the equation once we get to \(8x = x\):
\(\begin{align} 8x &= x &\hspace{0.15cm} &\text{}\\ 7x &= 0 &\hspace{0.15cm} &\text{subtract }x \text{ from each side}\\ x&=0 &\hspace{0.15cm} &\text{divide each side by 7} \end {align}\)
\(\begin{align} 8x &= x &\hspace{0.15cm} &\text{}\\ 0 &= \text-7x &\hspace{0.15cm} &\text{subtract }8x \text{ from each side}\\ 0 &=x &\hspace{0.15cm} &\text{divide each side by -7} \end {align}\)


Asturias on the Spanish northern coast is not only the green lung of the peninsula but also a paradise for art lovers and gourmands.
"The heroic city rested at noon. The warm, light southerly wind drove the whitish clouds in front of itself as they came undone from their journey northwards." One has to think of those first lines of Clarín's "The President", the classic novel with its wonderful heroine, who moved through the streets and squares of Oviedo (which in the novel is called Vetusta). Places from the novel like the mighty cathedral can still be found but you cannot feel of the social narrowness any more that Leopold Alas portrays under pseudonym in his key novel published in 1885.
Instead of attending church services, people prefer to sit in one of the street cafés these days and enjoy the midday sun, while children play football outside the church gate. It is not that traditions are not treasured here. On the contrary. But the Asturians, whose regional capital is Oviedo, know very well what is worth preserving. And this has a lot to do with pleasure, especially the culinary one. Apart from the Basque coastal city of San Sebastián to the east, hardly any other part of the world has a higher density of excellent restaurants, including nearby France. And a lot of them at affordable prices.
As Asturias is quite atypical for Spain it is rather an insider tip for international travellers. Anyone who knows other parts of Spain will rub his eyes when he arrives in Asturias for the first time. The lush and wild vegetation, the rugged rock faces and the sometimes stiff sea breeze resemble regions much futher north. But Asturias does not only differ from the rest of Spain in terms of landscape. Instead of vines and olive trees, apple trees and dairy cattle populate the lush pastures. Unique cheeses, typical for the region ripen in countless rock caves in the mountains. They can easily compete with French produce.
Asturias is the cradle of present-day Spain in a way, if you look at history. The Reconquista started here in 718, the recapture of the Iberian Peninsula after the Muslim settlement. You have to keep that in mind to understand how Asturias' independence is managed in these days. The Autonomous Region is rightly proud of its history, culture and gastronomy. The regional anthem is sung in all of Spain when people meet for a party. The patriotism of the Asturians is not one that excludes, as in Catalonia or the Basque Country. To explore the region it is advisable to rent a car. The three larger cities of the region, Oviedo, Gijón and Avilés, are all less than 20 kilometres apart, but the surrounding areas can best be accessed by car.
There are beautiful beaches on the Cantabian coast which are mainly frequented by Spaniards but still are an insider tip for other Europeans. They are much more relaxed and less crowded than the seaside resorts on the Mediterranean coast or the Iberian Islands. Small fishing villages such as Lastres and Ribadesella or the rocky coast are spectacular destinations for excursions. The pre-Romanesque churches of the region are architectuarlly outstanding They date from the 9th and 10th centuries, when Asturias was still an independent kingdom.
The region is not short of contrasts and has long since arrived in present days. The Niemeyer Cultural Centre in Avilés, which opened in 2011, looks like a monolith in its radiant white, avant-garde austerity as it stands in the harbour of the old industrial city. With its imposing architecture, the star-rated restaurant and the outstanding programme, it takes away a bit the focus on the rest of the city, which from here offers mainly smoking factory chimneys as an eye catcher. But those who keep exploring Avilés further will be rewarded with numerous discoveries and an enchanting old town.
After all the cultural and culinary delights, we are keen on eventually getting to know the local gay scene. Starting the night in Gijón can't be done any better than at Tabú, an intimate and lovingly furnished fifties bar where owner Jorge prepares the presumably best hamburgesas in town. Feeling refreshed and restored we move on, first to the ES Collection, a basement club serving half-litre-sized G&Ts, then to Oh La La, where barkeeper Rodrigo is mixing excellent drinks. He also entertains everyone who hasn't already chatted up someone. The best way to greet the next morning is on San Lorenzo beach at sunrise and make a vow to come back soon. Until then we will have managed to digest the 926 pages about the amorous adventures of the "President".
Comprehensive website of the Spanish Tourism Board about the entire country, i.a. information for gays and lesbians.
Tips about Asturias including a guide of the those restaurants carrying the label ,Mesas de Astruias'. The website is available in Spanish, English and German.
The airport of Asturias is located in the triangle between the three largest cities in the region, Avilés being the closest at 14km distance. There are no direct flights from Germany. Air Berlin offers flights via Palma de Mallorca, Iberia via Madrid or Barcelona, Vueling via Barcelona or Paris. Best rent a car at the airport so that you can be flexible exploring the region.
For services within Spain, also high-speed trains consult the national train operator Renfe (www.renfe.com).
All information on the gay scene can be found in SPARTACUS INTERNATIONAL GAY GUIDE or Spartacus App!