All categories

2 years ago

Evaluate the composition of functions.

Mathematics

1 answer:

valina [46]2 years ago

7 0

Answer:

Step-by-step explanation:

Fill in each function's argument and do the arithmetic.

$h(g(f(\sqrt{10})))=h(g(2(\sqrt{10})^2-7))=h(g(2\cdot 10-7))=h(g(13))\\\\=h(\dfrac{4-13}{9})=h(\dfrac{-9}{9})=h(-1)\\\\=\sqrt{-(-1)+3}=\sqrt{4}=\boxed{2}$

You might be interested in

Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) and select the correct answer below:

Marizza181 [45]

<h3>Answer:</h3>

-84

<h3>Explanation:</h3>

(f·g)(2) = f(2)·g(2)

... = (3·2²+2)·(2-8) = 14·(-6) = -84 . . . . . put the numbers in the function and do the arithmetic

7 0

3 years ago

Read 2 more answers

Explain the different types of motion of a sewing machine

Lana71 [14]

Answer:

linear.

rotary.

reciprocating.

oscillating.

hope it wil help you

4 0

3 years ago

1.) A 20° sector in a circle has an area of 21.5π yd².

a_sh-v [17]

<u>Part 1)</u> A 20° sector in a circle has an area of 21.5π yd².

What is the area of the circle?

we know that

the area of a circle represent a sector of $360$ degrees

so by proportion

$\frac{21.5\pi }{20} =\frac{x}{360} \\ \\ x*20=360*21.5\pi \\ \\x=(360*21.5*3.14)/20\\ \\x= 1,215.18\ yd^{2}$

therefore

<u>the answer part 1) is</u>

The area of the circle is $1,215.18\ yd^{2}$

<u>Part 2)</u> What is the area of a sector with a central angle of 3π/5 radians and a diameter of 21.2 cm?

we know that

the area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

in this problem we have

$Diameter=21.2\ cm\\ r=Diameter/2\\r=21.2/2\\r= 10.6\ cm$

<u>Find the area of the circle</u>

$A=\pi r^{2}$

$A=\pi*10.6^{2}$

$A=352.8104\ cm^{2}$

<u>Find the area of the sector</u>

we know that the area of the circle represent a sector of $2\pi$ radians

by proportion

$\frac{352.8104}{2\pi }=\frac{x}{(3\pi/5)} \\\\x*2\pi=(3\pi*352.8104)/5\\ \\x= 105.84\ cm^{2}$

therefore

<u>the answer part 2) is</u>

the area of the sector is

$105.84\ cm^{2}$

7 0

3 years ago

If A= (6,11), B= (1,5), and C= (7,0), show by means of slopes that ABC is a right triangle. Name the hypotenuse.

nexus9112 [7]

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

<h3>Right angled triangle</h3>

A right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.

For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.

Find the slopes of AB, BC and AC

Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5

Slope of BC = 0-5/7-1
Slope of BC = -5/6

Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11

Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

Learn more on right angle triangle here: brainly.com/question/22790996

#SPJ1

6 0

1 year ago

Your family is planning a vacation for spring break and want to get the best deal. Option

marshall27 [118]

Answer:

Step-by-step explanation:

5 nights

5 0

3 years ago