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3 years ago

Answer must be in fraction form

Mathematics

1 answer:

Damm [24]3 years ago

8 0

Answer:

-7/18

Step-by-step explanation:

To multiply fractions, you just multiply the top number by the top number and the bottom number by the bottom number. Also, you have to watch the sign.

In this case, we have a positive fraction multiplied by a negative fraction, meaning that our answer must be negative.

So we have- 2x7 / 4x9.

This is simplified to be- 14/36, or 7/18.

However, the answer is actually -7/18, since the number must be negative.

Let me know if this helps.

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Solve | x + 6| - 7 = 8

Alex

Answer:

x = 9,-21

Step-by-step explanation:

Given:

$\displaystyle \large{|x+6|-7=8}$

Transport -7 to add 8:

$\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}$

Cancel absolute sign and add plus-minus to 15:

$\displaystyle \large{x+6=\pm 15}$

Transport 6 to subtract ±15:

$\displaystyle \large{x=\pm 15-6}$

Consider:

$\displaystyle \large{x= 15-6}$ or $\displaystyle \large{x = -15-6}$

$\displaystyle \large{x=9}$ or $\displaystyle \large{x=-21}$

Solution:

$\displaystyle \large{x = 9}$ or $\displaystyle \large{x=-21}$

__________________________________________________________

Second Method

Given:

$\displaystyle \large{|x+6|-7=8}$

Transport -7 to add 8:

$\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}$

Absolute Function Property:

$\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}$

Consider both intervals:

When x ≥ a then:

$\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}$

Transport 6 to subtract 15:

$\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}$

When x < a then:

$\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}$

Transport -6 to add 15:

$\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}$

Transport negative sign to 21:

$\displaystyle \large{x=-21}$

Solution:

$\displaystyle \large{x=9}$ or $\displaystyle \large{x=-21}$

__________________________________________________________

Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!

3 0

2 years ago

Census Bureau data shows that the mean household income in the area served by a shopping mall is $64,500 per year with the stand

Elenna [48]

Considering the situation described, the null hypothesis is given as follows:

$H_0: \mu = 64,000$ .