MATH: Composition of two functions...help needed with this problem

Answer:

B

Step-by-step explanation:

A hexagon has 6 sides. If you divide the perimeter(12) by the number of sides(6), you get the length of one side(2).

The polynomial function with the given properties is; y = 2(x - 3)³(x + 4)²

Polynomials are defined as algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.

We need to form a polynomial expression with the following properties;

fifth-degree, 3 is a zero of multiplicity 3, −4 is the only other zero and ,the leading coefficient is 3. Thus, the polynomial will be;

y = 2(x - 3)³(x + 4)²

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Answer:

C

Step-by-step explanation:

x = [tex]\frac{2}{3}[/tex] πr³ ( multiply both sides by 3 to clear the fraction )

3x = 2πr³ ( divide both sides by 2π )

[tex]\frac{3x}{2\pi }[/tex] = r³ ( take cube root of both sides )

[tex]\sqrt[3]{\frac{3x}{2\pi } }[/tex] = r

Answer:

[tex]r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]

Step-by-step explanation:

This question make look scary, but don't judge its book by its cover.

[tex]x=\frac{2}{3} \pi r^{3} \\\frac{2}{3} \pi r^{3}=x\\r^{3} =x / \frac{2\pi }{3} \\r^{3} =x*\frac{3}{2\pi } \\r^{3} =\frac{3x}{2\pi } \\r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]

Answer: -15625

Step-by-step explanation:

The explicit formula for the sequence is

[tex]a_{n}=-1(5)^{n-1}\\\\\implies a_{7}=-1(5)^{7-1}=\boxed{-15625}[/tex]

Answer:

No. greater than of equal to (-5) = -4,-3,-2,-1,0,1,2,3,4,5,6...........

No. less than 5 = 4,3,2,1 ,0,-1......

{ -4,-3,-2,-1,0,1,2,3,4}

A one-to-one function has an inverse. The inverse is another function that undoes the action of the first one, so if we evaluate a function [tex]f[/tex] at some point [tex]x[/tex] to get the number [tex]f(x)[/tex], evaluating the inverse at [tex]f(x)[/tex] will recover the original input [tex]x[/tex]. In other words,

[tex]f^{-1}(f(x)) = x[/tex]

The process works in the opposite direction, too:

[tex]f\left(f^{-1}(x)\right) = x[/tex]

From the given definition of [tex]g[/tex], we have [tex]g(-4) = 3[/tex], so taking inverses on both sides, we find

[tex]g(-4) = 3 \implies g^{-1}(g(-4)) = g^{-1}(3) \implies \boxed{g^{-1}(3) = -4}[/tex]

Given [tex]h(x)=2x-13[/tex], evaluating [tex]h[/tex] at its inverse will recover [tex]x[/tex], so that

[tex]h\left(h^{-1}(x)\right) = x \implies 2h^{-1}(x) - 13 = x \implies \boxed{h^{-1}(x) = \dfrac{x+13}2}[/tex]

[tex](h\circ h^{-1})(x)[/tex] is another way of writing the compound function [tex]h\left(h^{-1}(x)\right)[/tex]. As already discussed, this reduces to [tex]x[/tex], so

[tex]\boxed{\left(h\circ h^{-1}\right)(-9) = -9}[/tex]

The area of Maria’s circle is 18π square units option fourth is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The figure is missing.

Please refer to the attached picture for the figure.

We have given the radius of the circle as 3 units

r = 3 units

Area of circle = πr² = π(3)² = 9π square units

The area of Maria’s circle = 2(9π) = 18π square units

Thus, the area of Maria’s circle is 18π square units option fourth is correct.

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Answer:

x=12

Step-by-step explanation:

16x-30-(14x-6)=2x-24=0. add 24 on both sides to get 2x=24. divide by 2 on both sides to get x=12

Answer:

$809.25

Step-by-step explanation:

→ Find the sum of the sales amount

2400 + 3200 + 1900 + 800 = 8300

→ Find the amount that s commission

( 9.75 × 8300 ) ÷ 100 = $809.25

The slope of line p is -5, so substitute into point-slope form, we get

[tex]\boxed{y-37=-5(x+2)}[/tex]

Answer:

[tex]27[/tex]

Step-by-step explanation:

[tex]g(f(0))=g(2(0)+3)=g(3)=3^3=27[/tex]

The true statements are (A), (B) and (D)

Data is information that has been translated into a form that is efficient for movement or processing.

As, from the given table we can see that

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Answer: (1,4) and (1,3) because the have the same x-value

Step-by-step explanation:

A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).

Answer:

b and d

Step-by-step explanation:

there are two

but only one is an answer choice

b and d

the other which is not an answer choice is

a and c

gathmath

Answer:

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Step-by-step explanation:

i need it

Answer:

3^1 multiplied by 3^2 = 3^(1 + 2) = 3^3

162

Simplify ——————

(2•3^3)

Canceling out 2 as it appears on both sides of the fraction line

3^4 divided by 3^3 = 3^(4 - 3) = 3^1 = 3

Step-by-step explanation:

hope this helps you ♡

Answer: 49 in

Step-by-step explanation:

Answer:

20-2h

Step-by-step explanation:

20 is the original amount. The variable stands for the number of hours. You are TAKING AWAY 2 degrees every hour so you would subtract.

Answer:

3x^2 + 3xz

Step-by-step explanation:

Under the assumption that I need to distribute,

(x + z)(x + 2x)

(x + 2x) is (3x)

3x(x + z) becomes 3x*x and 3x*z

3x*x = 3x^2

3x*z = 3xz

combine, 3x^2 + 3xz

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Step-by-step explanation:

To get the angle of QPR, we subtract 90-60=30. This proves that the triangle is a 30,60,90, as angle QRP must be 60°. To get the area, we must know the length and width. These can be derived from a known relationship within 30,60,90 triangles.

[tex]qp = \frac{\sqrt{3}}{2} n[/tex]

[tex]qr = \frac{1}{2} n[/tex]

[tex]pr = n[/tex]

because half of pr is 10, we can conclude that n is 20. So we plug 20 into N for QP and QR, and get values of

[tex]qp = 5 \sqrt{3} [/tex]

[tex]qr = 5[/tex]

Now we multiply (l*w)/2 and get:

[tex] \frac{(5 \sqrt{3} \times 5)}{2} = 21.65 \: units[/tex]

Answer:

x = 9 or B

Step-by-step explanation:

Formula

(x + 2)^2 = 121                        

Comment

The easiest way to do this is to take the square root immediately, which is usually possible.

Solution

√(x + 2)^2 = √121                     Take the square root

x + 2 = 11                                   Subtract 2 from both sides

x + 2 -  2 = 11 - 2

x = 9

Answer: B) 9 inches by 9 inches

Step-by-step explanation:

Edg 2022

The coordinate of C( a+c , b) ,  AC are ((a+c)/2 , b/2) , BD are ((a+c)/2 , b/2)

Coordinates is the value assigned to a point in a x-y graph to determine its location.

The coordinates of parallelogram is

A ( 0,0) B (a,0) , C ( __ , ___) , D ( c , b)

The y coordinate is same as D as b

and the x coordinate will be a+c

C( a+c , b)

The coordinate of the mid point of AC are ((a+c)/2 , b/2)

The coordinate of the mid point of BD are ((a+c)/2 , b/2)

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Answer:

p = 4

Step-by-step explanation:

[tex]m =\frac{p}{2} +3r[/tex]

[tex]\Longrightarrow m-3r=\frac{p}{2}[/tex]

[tex]\Longrightarrow 2m-6r=p[/tex]

[tex]\Longrightarrow p = 2m-6r[/tex]

If m = 5 and r = 1

Then

p = 2(5) - 6(1)

  = 10 - 6

  = 4

"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is

D= 510 km. Option B. This is further explained below.

Generally, In the study of astrodynamics, an ellipse of the satellite is often referred to as a Kepler Orbit

The function of the elliptical orbit is

[tex]\frac{(x-h)^2}{a^2}+\frac{(x-k)^2}{b^2}=1[/tex]

compared to

[tex]\frac{(x^2)^2}{47334400}+\frac{(y^2)^2}{43956900}=1[/tex]

Hence

a = √(47,334,400 km²)

a= 6,880 km.

In conclusion, The distance of the satellite above the Earth's surface.

D = a - r

D= 6,880 km - 6,370 km

D= 510 km

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"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is D= 510 km. Option B.

An elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0.

The function of the elliptical orbit is

[tex]\frac{{(x-h)}^2}{a^2}+ \frac{{(y-k)}^2}{b^2} = 1[/tex]

compared to

  √([tex]\frac{({x^2)}^2}{47,334,400} + \frac{({y^2)}^2}{43956900} = 1[/tex]

a = √(47,334,400 km²)

a= 6,880 km.

Now,

D = a - r

D= 6,880 km - 6,370 km

D= 510 km

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Answer: A. She substituted incorrectly into the distance formula

She should be subtracting x from x and y from y but she is subtracting y from x.

Answer: C

Explanation:i got it right on my test

The equation for the red graph is f(x) = -x².

From the information given, g(x) = 4 - x².

The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:

(x, y) = (x, y -4).

The equation of the function will be:

f(x) = g(x) - 4

f(x) = (4 - x²) - 4

f(x) = -x²

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Step-by-step explanation:

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Answer:

x = 3

Step-by-step explanation:

8/2 = 4

6/2 = 3

x = 3

The function that represents the Scooter Company's total profit is given by:

P(x) = -2x² + 250x - 2,000.

The profit function is calculated by the revenue function subtracted by the cost function, hence:

P(x) = R(x) - C(x).

In this problem, we have that:

Hence the profit function is:

P(x) = R(x) - C(x).

P(x) = 400x - 2x² - (150x + 2000).

P(x) = -2x² + 250x - 2,000.

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