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3 years ago

Finding the inverse of linear functions

Mathematics

1 answer:

mezya [45]3 years ago

7 0

Answer:

y = -1/2x - 4

Step-by-step explanation:

To find the inverse of a linear function, simply switch the x and y positions. Solve for y.

y = -2x - 8

x = -2y - 8

x + 8 = (-2y - 8) + 8

x + 8 = -2y

(x + 8)/-2 = (-2y)/-2

-1/2x - 4 = y

y = -1/2x - 4

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Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Vaselesa [24]

Answer:

$\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}$

Step-by-step explanation:

The circumference of a circle with radius $r$ is given by $C=2\pi r$ . The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle $\theta^{\circ}$ is equal to $2\pi r\cdot \frac{\theta}{360}$ .

Formulas at a glance:

Circumference of a circle with radius $r$ : $C=2\pi r$
Length of an arc with central angle $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

$C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}$

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

$\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}$

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting $r=2$ into our circumference formula, we get:

$C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}$

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

$\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}$

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2 years ago

Renee has 1/4 yard of floral fabric. She cuts it into 5 equal pieces. How long is each new piece of fabric?

Zinaida [17]

Answer:

$\dfrac{1}{20}\ \text{yards}$

Step-by-step explanation:

Given that,

Renee has 1/4 yard of floral fabric.

She cuts it into 5 equal pieces.

We need to find the length of each new piece of fabric. It is equal to the total length divided by the total number of pieces. So,

$l=\dfrac{\dfrac{1}{4}}{5}\\\\=\dfrac{1}{4}\times \dfrac{1}{5}\\\\=\dfrac{1}{20}\ \text{yards}$

So, each new piece pf fabric is $\dfrac{1}{20}\ \text{yards}$ .

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zysi [14]

1 student will attend the assembly in the morning

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