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2 years ago

Which expression is equivalent to

Mathematics

1 answer:

KATRIN_1 [288]2 years ago

3 0

Answer:

4) -2g - 11

Step-by-step explanation:

2(3g-4)-(8g + 3) =

6g - 8 - 8g - 3 =

- 2g - 11

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I went to a restaurant and gave the waitress a $15 tip. If the tip was 20% of the dinner how much was the dinner?

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Answer:

Dinner only: $75

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Step-by-step explanation:

If the tip was $15, and the tip was 20% of the price of dinner, then dinner was $75.

You can find this out by doing 15/20%, which should give you 75.

If the question requires you to add up the price of dinner and the tip, then the total price would be $90

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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]

Answer:

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

Step-by-step explanation:

Given

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

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,

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

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