In the figure below, L || m. Find x.

Andrews [41]

when it comes to checking if a function is even or odd, it boils down to changing the argument, namely x = -x, and if the resulting function is the same as the original, then is even, if the resulting function is the same as the original but negative, is odd, if neither, well then neither :).

anyway, that said, let's first expand it and then plug in -x,

$\bf f(x)=(x^2-8)^2\implies f(x)=(x^2-8)(x^2-8)\implies f(x)=\stackrel{FOIL}{x^4-16x^2+64}\\\\[-0.35em]~\dotfill\\\\f(-x)=(-x)^4-16(-x)^2+64\qquad \begin{cases}(-x)(-x)(-x)(-x)=x^4\\(-x)(-x)=x^2\end{cases}\\\\\\f(-x)=x^4-16x^2+64\impliedby \stackrel{\textit{same as the original}}{Even}$

3 0

4 years ago

The Walters bought a house and calculated they would pay 28% of their combined income of $5436.68 toward their monthly mortgage

Aleonysh [2.5K]

We have been given that the Walters bought a house and calculated they would pay 28% of their combined income of $5436.68 toward their monthly mortgage payment on the house.

To find the amount of monthly mortgage payment, we will find 28% of combined income.

$\text{Amount of monthly mortgage payment}=\$5436.68\times \frac{28}{100}$

$\text{Amount of monthly mortgage payment}=\$5436.68\times 0.28$

$\text{Amount of monthly mortgage payment}=\$1522.2704$

$\text{Amount of monthly mortgage payment}\approx \$1522.27$

Therefore, the Walters will pay approximately $\$1522.27$ for their monthly mortgage payment.

4 0

3 years ago

1. If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter o

scZoUnD [109]

Answer:

Part 1) The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor (see the explanation)

Part 2) The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) The new figure and the original figure are not similar figures (see the explanation)

Step-by-step explanation:

Part 1) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its perimeters is equal to the scale factor

so

The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor

Part 2) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the area of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its areas is equal to the scale factor squared

so

The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) What would happen to the perimeter and area of a figure if the dimensions were changed NON-proportionally? For example, if the length of a rectangle was tripled, but the width did not change? Or if the length was tripled and the width was decreased by a factor of 1/4?

we know that

If the dimensions were changed NON-proportionally, then the ratio of the corresponding sides of the new figure and the original figure are not proportional

That means

The new figure and the original figure are not similar figures

therefore

Corresponding sides are not proportional and corresponding angles are not congruent

so

A) If the length of a rectangle was tripled, but the width did not change?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2W ----> P=6L+2W

The perimeter of the new figure is greater than the perimeter of the original figure but are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W) ----> A=3LW

The area of the new figure is three times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

B) If the length was tripled and the width was decreased by a factor of 1/4?

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2(W/4) ----> P=6L+W/2

The perimeter of the new figure and the perimeter of the original figure are not proportionals

Area

The original area is A=LW

The new area would be A=(3L)(W/4) ----> A=(3/4)LW

The area of the new figure is three-fourth times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

4 0

3 years ago

What’s 5/9 times 6?????????????????

Ksenya-84 [330]

Answer:

3.33333333333

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

BRAINLIEST!!

Alona [7]