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tatyana61 [14]
3 years ago
11

NEED HELP IN NUMBER 12 and 13 PLEASEEEE

Mathematics
1 answer:
pochemuha3 years ago
5 0

Answer:

12.) b = (2S/n) - a

13.) x = 1000 - 20y

Step-by-step explanation:

12.) *goal is to isolate b

S = n/2 (a + b)

S(2/n) = a + b

**multiply both sides by 2/n to get rid of n/2

(2S/n) - a= b

***subtract a from both sides to leave b alone on one side

13.) *goal is to isolate x

0.30x + 6y = 300

0.30x = 300 - 6y

** subtract 6y from both sides

x = (300 - 6y)/ 0.30

*** divide 0.30 from both sides to leave x bu itself

x = 1000 - 20y or -20y +1000

****300 ÷ 0.30 = 1000

-6 ÷ 0.30 = -20

Done!

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Which expression is equivalent to StartFraction 2 a + 1 Over 10 a minus 5 Endfraction divided by StartFraction 10 a Over 4 a squ
const2013 [10]

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\frac{(2a + 1)^2}{50a}

Step-by-step explanation:

Given

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Required

Find the equivalent

We start by changing the / to *

\frac{2a + 1}{10a - 5} / \frac{10a}{4a^2 - 1}

\frac{2a + 1}{10a - 5} * \frac{4a^2 - 1}{10a}

Factorize 10a - 5

\frac{2a + 1}{5(2a - 1)} * \frac{4a^2 - 1}{10a}

Expand 4a² - 1

\frac{2a + 1}{5(2a - 1)} * \frac{(2a)^2 - 1}{10a}

\frac{2a + 1}{5(2a - 1)} * \frac{(2a)^2 - 1^2}{10a}

Express (2a)² - 1² as a difference of two squares

Difference of two squares is such that: a^2- b^2= (a+b)(a-b)

The expression becomes

\frac{2a + 1}{5(2a - 1)} * \frac{(2a - 1)(2a + 1)}{10a}

Combine both fractions to form a single fraction

\frac{(2a + 1)(2a - 1)(2a + 1)}{5(2a - 1)10a}

Divide the numerator and denominator by 2a - 1

\frac{(2a + 1)((2a + 1)}{5*10a}

Simplify the numerator

\frac{(2a + 1)^2}{5*10a}

\frac{(2a + 1)^2}{50a}

Hence,

\frac{2a + 1}{10a - 5} / \frac{10a}{4a^2 - 1} = \frac{(2a + 1)^2}{50a}

4 0
3 years ago
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