Write an equation for g(x), a translation of f(x) 4 units to the right and 3 units down.

If xh=10 feet and mxy =100 degrees then determine the arc length of xy

schepotkina [342]

Answer:

The arc length XY is equal to $\frac{50}{9}\pi\ ft$ or $17.4\ ft$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the circumference of the circle H

The circumference is given by the formula

$C=2 \pi r$

we have

$r=xh=10\ ft$

substitute

$C=2 \pi (10)\\C=20\pi\ ft$

step 2

we know that

The circumference of a circle subtends a central angle of 360 degrees

so

using proportion

Find out the length of the arc xy if the central angle is equal to 100 degrees

Remember that

$m\angle XHY=arc\ XY=100^o$ ---> by central angle

$\frac{20\pi}{360^o}=\frac{x}{100^o}\\\\x=20\pi(100)/360\\\\x=\frac{2,000}{360}\pi\ ft$

Simplify

$x=\frac{50}{9}\pi\ ft$ ----> exact value

To find out the approximate value

assume

$\pi=3.14$

substitute

$x=\frac{50}{9}(3.14)=17.4\ ft$ ----> approximate value

therefore

The arc length XY is equal to $\frac{50}{9}\pi\ ft$ or $17.4\ ft$

7 0

4 years ago

What is the area of each semicircle of the following composite figure?

Alina [70]

It will equal 22.5 since you need to multiple

3 0

3 years ago

7 times the difference between m and 8

aniked [119]

Answer:

7(m-8)

Step-by-step explanation:

We are given: 7 times the difference between m and 8

We want to write an expression. Let’s begin with “the difference between m and 8”.

Difference means subtraction. Therefore, we must subtract m and 8.

(m-8)

Now, let’s add on “7 times”

Times means multiply. Therefore, we must multiply 7 and the expression we just wrote.

7(m-8)

Therefore, 7 times the difference between m and 8 can be written as: 7(m-8)

6 0

4 years ago

Read 2 more answers

Subtract -3x-4 from 7x^2-7x

professor190 [17]

Answer:

−49x8−3x−4

Step-by-step explanation:

−3x−4−49x7x

=−3x+−4+−49x8

hope this helps

4 0

4 years ago

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each s

JulsSmile [24]

The required equations are use to solve this problem;

$x + y =126$

$2.25x + 1.50y = 223.75$

There are x = 49 hot dogs, and y = 77 sodas were sold.

Given that,

Each hot dog costs $2.25 and each soda costs $1.50.

At the end of the night, you made a total of $225.75.

You sold a total of 126 hot dogs and sodas combined.

We have to determine,

What equations did you use to solve this.

And How many hot dogs were sold and how many sodas were sold.

According to the question,

Let, The x represent the number of hot dogs,

And y represent the number of sodas.

Then,

You sold a total of 126 hot dogs and sodas combined.

Number of sell hot dogs + number of sell sodas = Total of hot dogs and sodas combined.

$x + y =126$

And Each hot dog costs $2.25 and each soda costs $1.50.

At the end of the night, you made a total of $225.75.

Then,

Cost of each hot dogs + cost of each soda = total earning end of the night

$2.25x + 1.50y = 223.75$

On solving both the equation,

$x + y = 126\\\\x = 126-y$

Substitute the value of x in the equation 2,

$=2.25(126-y) + 1.50y = 225.75\\\\= 283.5 -2.25y + 1.50y = 225.75\\\\= - 0.75 y = 225.75 - 283.5\\\\= - 0.75y = -57.75\\\\= y = \dfrac{-57.75}{-0.75}\\\\= y = 77$

Then,

Substitute the value of y in the equation 1,

$x + y = 126\\\\x + 77 = 126\\\\x = 126-77\\\\x = 49$

Hence, There are x = 49 hot dogs, and y = 77 sodas were sold.

To know more about the Equation click the link given below.

brainly.com/question/24070713

5 0

3 years ago

Read 2 more answers