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3 years ago

Consider the following pair of equations.

Mathematics

1 answer:

RUDIKE [14]3 years ago

4 0

Answer:

(- 2, 2 )

Step-by-step explanation:

Given the 2 equations

y = x + 4 → (1)

y = - 2x - 2 → (2)

Substitute y = x + 4 into (2)

x + 4 = - 2x - 2 ( add 2x to both sides )

3x + 4 = - 2 ( subtract 4 from both sides )

3x = - 6 ( divide both sides by 3 )

x = - 2

Substitute x = - 2 into either of the 2 equations abd evaluate for y

Substituting into (1)

y = - 2 + 4 = 2

solution is (- 2, 2 )

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Answer:

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3 years ago

True or false: the population proportion and sample proportion always have the same value.

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What is 3.4 in fraction

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3 years ago

The circumference of Circle K is pi. The circumference of Circle L is 4xpi.

dmitriy555 [2]

Answer:

Ratio of circumferences: $\displaystyle\frac{1}{4}$

Ratio of radii: $\displaystyle\frac{1}{4}$

Ratio of areas: $\displaystyle\frac{1}{16}$

Step-by-step explanation:

Hi there!

We are given:

- The circumference of Circle K is $\pi$

- The circumference of Circle L is $4\pi$

Therefore, the ratio of their circumferences would be:

$\displaystyle\frac{\pi}{4\pi}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for circumference is $C=2\pi r$ , where r is the radius. To find the ratio of the circles' radii, we must identify their radii through their given circumferences.

If the circumference of Circle K is $\pi$ , or $1\pi$ , then its radius is $\displaystyle\frac{1}{2}$ .

If the circumference of Circle L is $4\pi$ , then its radius is $\displaystyle\frac{4}{2}$ , which is 2.

Therefore the ratio their radii would be:

$\displaystyle\frac{\frac{1}{2}}{{2}}$ ⇒ $\displaystyle\frac{1}{2}*\frac{1}{2}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for area is:

$A=\pi r^2$

First, let's find the area of Circle K:

$A=\pi (\displaystyle\frac{1}{2})^2\\\\A=\displaystyle\frac{1}{4}\pi$

Now, let's find the area of Circle L:

$A=\pi (2)^2\\A = 4\pi$

Therefore, the ratio of their areas would be:

$\displaystyle\frac{\frac{1}{4}\pi}{4\pi}$ ⇒ $\displaystyle\frac{\frac{1}{4}}{4}$ ⇒ $\displaystyle\frac{1}{4} * \frac{1}{4}$ ⇒ $\displaystyle\frac{1}{16}$ when simplified

I hope this helps!

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