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3 years ago

9

Adia plans to wallpaper her bedroom. The measurements are 10’ by 12’ with 8’ ceilings. Part 1: What is the total area of the wal

ls? Answer: _ square feet (type the number only)

1 answer:

Leokris [45]3 years ago

7 0

10' x 12' are the dimensions for the floor and roof, both of which will not be covered with wallpaper.

The room will have two identical walls with the following dimensions:
10 x 8
12 x 8

The total area to be covered is:
2 x 10 x 8 + 2 x 12 x 8

Total area = 352 square feet

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Answer:

1. $P(x)$ ÷ $Q(x)$ ---> $\frac{-3x + 2}{3(3x - 1)}$

2. $P(x) + Q(x)$ ---> $\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}$

3. $P(x) - Q(x)$ ---> $\frac{-2(12x - 5)}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x)$ --> $\frac{12}{(3x - 1)(-3x + 2)}$

Step-by-step explanation:

Given that:

1. $P(x) = \frac{2}{3x - 1}$

$Q(x) = \frac{6}{-3x + 2}$

Thus,

$P(x)$ ÷ $Q(x)$ = $\frac{2}{3x - 1}$ ÷ $\frac{6}{-3x + 2}$

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

$\frac{2}{3x - 1}*\frac{-3x + 2}{6}$

$\frac{2(-3x + 2)}{6(3x - 1)}$

$= \frac{-3x + 2}{3(3x - 1)}$

2. $P(x) + Q(x)$ = $\frac{2}{3x - 1} + \frac{6}{-3x + 2}$

Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

$\frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)}$

$\frac{12x - 2}{(3x - 1)(-3x + 2)}$

$= \frac{2(6x - 1}{(3x - 1)(-3x + 2)}$

3. $P(x) - Q(x)$ = $\frac{2}{3x - 1} - \frac{6}{-3x + 2}$

$\frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)}$

$\frac{-24x + 10}{(3x - 1)(-3x + 2)}$

$= \frac{-2(12x - 5}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2}$

$P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)}$

$P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)}$

4 0

3 years ago