f(x) = Square root of x plus eight.; g(x) = 8x - 12 Find f(g(x))

Answers

Answer 1

Final answer:

To find f(g(x)), substitute g(x) into f(x) and simplify the expression to get the final answer. The final answer to the question would be as f(g(x)) = 8x⁴ - 32x³ + 32x² + 3

Explanation:

To find the value of f(g(x)) the following steps to be followed where the value of f(x) be substituted in g(x).

f(x) = 2x² + 3; g(x) = −2x² + 4x

Find f(g(x)) by substituting g(x) into f(x): f(g(x)) = 2(-2x² + 4x)² + 3

Simplify the expression: f(g(x)) = 2(4x⁴ - 16x³ + 16x²) + 3

Final answer after expansion: f(g(x)) = 8x⁴ - 32x³ + 32x² + 3

Related Questions

A polygon with 12 sides is called a/an

Answers

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

hope this helps!

A polygon with 12 sides is called a dodecagon.

Which of the following is an identity? A. sin2x sec2x + 1 = tan2x csc2x B. sin2x - cos2x = 1 C. (cscx + cotx)2 = 1 D. csc2x + cot2x = 1

Edit: no one answered but I figured out that the right answer is A

Answers

There are three 'Pythagorean' identities that we can look at and they are

sin²(x) + cos²(x) = 1
tan²(x) + 1 = sec²(x)
1 + cot²(x) = csc²(x)

We can start by checking each option to see which one would give us any of the 'Pythagorean' identities as its simplest form

Option A:

sin²(x) sec²(x) + 1 = tan²(x) csc²(x)

Rewriting sec²(x) as 1/cos²(x)
Rewriting tan²(x) as sin²(x)/cos²(x)
Rewriting csc²(x) as 1/sin²(x)

We have

[tex]sin^{2}(x)[ \frac{1}{ cos^{2}(x) }]+1=[ \frac{ sin^{2}( x)}{ cos^{2} (x)}][ \frac{1}{ sin^{2}(x) } ][/tex]
[tex] [\frac{ sin^{2}(x) }{ cos^{2}(x) } ]+1= \frac{1}{ cos^{2}(x) } [/tex]
[tex] tan^{2}(x)+1= sec^{2}(x) [/tex]

Option B:

sin²(x) - cos²(x) = 1

This expression is already in the simplest form, cannot be simplified further

Option C:

[ csc(x) + cot(x) ]² = 1

Rewriting csc(x) as 1/sin(x)
Rewriting cot(x) as cos(x)/sin(x)

We have

[tex][ \frac{1}{sin(x)}+ \frac{cos(x)}{sin(x)}] ^{2} =1[/tex]
[tex] \frac{1}{sin^2(x)}+2( \frac{1}{sin(x)})( \frac{cos(x)}{sin(x)})+ \frac{cos^2(x)}{sin^2(x)}=1 [/tex][tex]csc^2(x)+2csc^2(x)cos(x)+cot^2(x)=1[/tex]

Option D:

csc²(x) + cot²(x) = 1

Rewriting csc²(x) as 1/sin²(x) and cot²(x) as cos²(x)/sin²(x)

[tex] \frac{1}{sin^2(x)}+ \frac{cos^2(x)}{sin^2(x)}=1 [/tex]
[tex] \frac{1+cos^2(x)}{sin^2(x)} =1[/tex]
[tex]1+cos^2(x)=sin^2(x)[/tex]
[tex]1=sin^2(x)-cos^2(x)[/tex]

from our working out we can see that option A simplified into one of 'Pythagorean' identities, hence the correct answer

Answer: A is the correct answer.

Step-by-step explanation:

Just did the question, followed OP's advice since no one answered. Good luck.

0.43 is 10 times as mush as what

Answers

The correct answer is 0.043. Thanks for asking and have a great day!

The number that is 10 times less than 0.43 is 0.043, found by dividing 0.43 by 10.

To find the number that 0.43 is 10 times as much as, we need to divide 0.43 by 10. This is the same as multiplying by 10 raised to the power of -1, which is a division by 10.

The operation looks like this:

0.43*10^{-1} = 0.043.

Therefore, 0.43 is 10 times as much as 0.043

A chocolate bar measures 40 mm wide, 80 mm long, and 5 and 1 over 2 mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper

Answers

The amount of the wrapper that is needed in order to wrap completely the chocolate bar is equal to the surface area of the bar.

The surface area of the rectangular prism is calculated through the equation,
SA = 2LW + 2WH + 2LH

Substituting the known values,

SA = (2)(80 mm)(40 mm) + 2(40 mm)(5.5 mm) + 2(80 mm)(5.5 mm)
SA = 6400 mm² + 440 mm² + 880 mm²
SA = 7720 mm²

Thus, the least area needed to completely cover or wrap the chocolate bar is 7720 mm².

Answer:

Will’s Wrapping Company needs 7,720 mm of paper to wrap the chocolate bar.

To make lemonade, you used one gallon of water, four quarts of lemon juice, and 32 ounces of honey. How much lemonade did you make?

Answers

We know that 1 gallon = 4 quarts and 1 quart = 32 ounces.
We have 4 quarts of lemon and it is 1 gallon ( and we also have 1 gallon of water ). Also we have 32 ounces of honey, which is 1 quart more.
4 quart + 4 quart + 1 quart = 9 quarts = 2 gallons 1 quart
Answer:
There is 9 quarts or 2 gallons and 1 quart of lemonade.

Practice writing linear equations in different forms. Line AB goes through the points A (0, –4) and B (6, 2). Which equation represents line AB? y – 4 = 3x y – 2 = 3(x – 6) y + 4 = x y + 6 = x - 2

Answers

(0,-4)(6,2)
slope = (2 - (-4) / (6 - 0) = 6/6 = 1

y = mx + b
slope(m) = 1
(0,-4)..x = 0 and y = 4
sub and find b
4 = 1(0) + b
4 = b

equation is : y = x + 4...or x - y = -4
or y + 4 = 6(x - 0) ...or y - 2 = 6(x - 6)

the answer is c . y + 4 = x

Emily is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 14 km/h. After nine hours, the velocity of the cyclist is 4 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 10 hours? (5 points)

Answers

Assume that Emily starts from rest so that the velocity is zero at 0 hours.

Define the function v(t) for velocity in km/h, and t in hours.

Part A
From t=0 to t=4, v changes from 0 to 14.
Let v(t) = mt + b
The slope is
m = 14/4 = 3.5, and the y-intercept is
b = 0.
Therefore
v(t) = 3.5t, for 0 ≤ t ≤ 4

Fromt=4 to t=9, changes from 14 to 4.
Let v(t) = mt + b
The slope is
m = (4 - 14)/(9 - 4) = -2
Therefore
v = -2t + b
When t=4, v=14, therefore
14 = -2*4 + b = -8 + b
22 = b
v(t) = -2t + 22, for 4 < t ≤ 9.

Answer:
The equation for the velocity is
v(t) = 3.5t, 0 ≤ t ≤ 4
= -2t + 22, 4 < t ≤ 9

Part B
The equation for velocity is a piecewise function that is graphed as shown below. If we assume that the second part of the equation is valid at t=10, then
v(10) = -2*10 + 22 = 2 km/h

An ostrich that is 108 inches tall is 20 inches taller than 4 times the height of a kiwi. What is the height of a kiwi in inches?

Answers

Let the height of the Kiwi be 'x'

'4 times the height of a kiwi' = 4x
'20 inches taller than 4 times the height of a kiwi' = 4x + 20

An ostrich is 108 inches tall and this is EQUAL to 4x + 20

108 = 4x + 20
108 - 20 = 4x
88 = 4x
88 ÷ 4 = x
x = 22

The height of the kiwi is 22 inches

In a 45-45-90 triangle, the length if the hypotenuse is 11. Find the length of one of the legs

Answers

the answer is B, picture shows how to solve it although the answer is written slightly different

Answer:

[tex] \frac{11\sqrt{2}}{2}[/tex]

Step-by-step explanation:

In a 45-45-90 triangle, the length if the hypotenuse is 11

WE use the common ratio of 45-45-90 degree triangle

common ration is x: x: x sqrt(2)

x sqrt(2) is the length of the hypotenuse

[tex]x\sqrt{2} = 11[/tex]

Divide by sqrt(2) on both sides

[tex]x= \frac{11}{\sqrt{2}}[/tex]

To rationalize the denominator, multiply by sqrt(2) at the top and bottom

sqrt(2) * sqrt(2) = 2

[tex]x= \frac{11\sqrt{2}}{2}[/tex]

Use the information in the figure. If m∠F = 76°, find m∠E

Answers

52 because the whole triangle is 180 if you subtract that by 76 you get 102 since both sides equal each other the angles equal each other so you devide that by 2 you get 52

Answer:

m∠E=52°.

Step-by-step explanation:

The given triangle has two sides equal. In isosceles triangle two sides are equal and base angles are equal.m∠E=m∠D.

Let m∠D=m∠E= x

The sum of angles in any triangle is 180°.

Or,

x+x+76= 180

Addling like terms :

2x+76=180

Subtracting 76 both sides,

2x=104.

Dividing by 2:

x=52.

m∠E= 52°.

200 gallon tank fills at 3 gallons/minute and loses 2 gallons/minute how long does it take to fill up

Answers

it fills at 3 gallons per minute, but loses 2 gallons per minute

3-2 =1, so it fills at 1 gallon per minute

200 gallons at 1 gallon per minute = 200 minutes,

200/60 = 3 hours and 20 minutes

Please HELP
1-) Solve the equation using the Properties of Equality.

11 − c = −17
2-)Solve the equation using the Properties of Equality.
1/2y + 1/5=1/2

Answers

Problem 1:
11-c = -17
First, we need to isolate the term with the variable. We can simply do that by subtracting 11 from both sides as follows:
11-11-c = -17-11
-c = -28
Then, we will multiply both sides by -1 to get the positive value of c as follows:
-c x -1 = -28 x -1
c = 28

Problem 2:
1/2 y + 1/5 = 1/2
First, we need to isolate the term with the variable by subtracting 1/5 from both sides as follows:
1/2 y = 1/2 - 1/5 = 3/10
Then, we will get rid of the coefficient in the term with variable by dividong both sides with 1/2, this will give the following output:
y = 3/5

lady runs 20 miles in 4 hours. write an equation representing the direct relationship between distance and time

Answers

d=rt
20=40t
divide by 20
t=2
d=10

HELP
If f(x)=-6x+12, then f^-1(x)=?

Answers

The inverse is (x-12)/-6

Find the midpoint of the segment below

Answers

1.
If we are given 2 points A(a, b) and B(c, d),

the midpoint M, of segment AB has coordinates:

[tex]M_A_B=( \frac{a+c}{2} , \frac{b+d}{2} )[/tex]

2.
We are given the points A(2, 3) and B(10, 3)

the midpoint of AB, is given by the above formula:

[tex]M_A_B=( \frac{2+10}{2} , \frac{3+3}{3} )=(6, 3)[/tex]

3.
Remark, since the segment is horizontal, that is the y-coordinate of both points is 3, the y coordinate of the midpoint will also be 3.

While the x coordinate is still found by [tex]\frac{2+10}{2}[/tex]

Answer: (6, 3)

PLEASE HELP!!!
How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?

3y − x = −6
4y − x = 44

3y + x = −6
4y + x = 44

3y − 3x = −6
4y − 4x = 44

3y + 3x = −6
4y + 4x = 44

Answers

y=1/3x-2
3y=x-6
3y-x=-6
y=1/4x+11
4y=x+44
4y-x=44

Answer: Hello!

we have that:

one third x − 2 = one fourth x + 11

this means:

(1/3)x - 2 = (1/4)x + 11

if this are equal numbers, we can write it as:

(1/3)x - 2 = y = (1/4)x + 11

now we have the system of equations:

(1/3)x - 2 = y

(1/4)x + 11 = y

if we "simplify" the rational therm in each equation, we get:

3*(1/3)x - 3*2 = 3y

x - 6 = 3y

and

4*(1/4)x + 4*11 = 4y

x + 44 = 4y

Then our system of equations is:

x - 6 = 3y

x + 44 = 4y

Now we can subtract x in each side of both equations:

-6 = 3y - x

44 = 4y - x

Then the right option is the first one.

3y - x = -6

4y - x = 44

Find the number of permutations of the first 8 letters of the alphabet taking 4 letters at a time.

Answers

The permutations of the first letters of alphabet taking 4 letters at once will be given by:
8P4
using the calculator this will give us:
8P4=1,680
This tells us that there are more than 1,680 different ways that the leteers will be selected.

What is the solution set of the following equation? 3x2 - 6x = 0

Answers

The solutions are x=0 and x=2 because you have to find the gcf first and factor it. The gcf is 3x so, the factor is 3x(x-2)=0. When you solve that you get x=0 and x=2 for the solutions. 3x=0 divide both sides by 3 and you get x=0 and x-2=0 add 2 on both sides and you get x=2. Thanks for letting me help you.

Find the measure of an angle whose supplement is 9 times the measure of its complement

Answers

if the angle is x , then

180 - x = 9(90-x)
180-x = 810 - 9x
8x = 630
x = 78.75 degrees

The equation is 180 - x = 9 (90 - x).Then the measure of the angle will be 78.75 degrees.

What is an angle?

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

Let 'x' be the angle. Then the equation is given as,

180 - x = 9 (90 - x)

180 - x = 810 - 9x

8x = 630

x = 78.75 degrees

The measure of the angle will be 78.75 degrees.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ5

10-2v=-5-50
+5 +5
10-3v=-50
+3 +3
10=47

Answers

hello :
10-2v=-5-50
add : 5
10 - 2v + 5 = 5 - 5 - 50
15 -2v = -50
add : -15
-15 +15 -2v = -15 -50
-2v =-65
v = 65/2

Zeus Industries bought a computer for $2011. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 5 years?

Answers

The value of the computer after five years will be as follows;
Value after 1 year:
24/100*2011
=$482.64
2011-482.64
=$1528.36
or
76/100*2011
=$1528.26

Value after 2nd year:
76/100*1528.36
=$1,161.55

Value after 3rd year:
76/100*1,161.55
=$882.78

Value after 4th year:
76/100*882.78
=$670.91

Value after 5th year:
76/100*670.91
=$509.89
hence the value after five years will be: $509.90

what would be the measure of angle DGF, if segment DG is a bisector of angle G

30 degrees.60 degrees.90 degrees.None of the choices are correct.

Answers

check the picture below.

a bisector, means, it "cuts in two equal halves".

Find the value of x in the equation √ x + 5 = √ x + 45.

Answers

there is no solution since 5 doesn't equal 45

The sum of three interior angles of a convex Pentagon is 420°.if the remaining angles are equal how much does each angle measure?

Answers

The sum of interior angles of any polygone is:

Sum of angles = (n-1)x180°, where n is the number of sides. For the pentagone n = 5, then Sum of angles of a PENTAGONE = (5-1)x180° = 720°.
Already the sum of 3 angles is 420°, the measure of the 2 remaining one is
720° - 420° = 300°. Since the remaining angles are equal, hence each one will have a measure of 300°/2 = 150°

Each one of the remaining angles measures 60°.

How much does each angle measure?

We know that the sum of the interior angles of a closed figure of n sides is given by:

(n - 2)*180°.

A pentagon has 5 sides, so we use n = 5 and we get:

(5 - 2)*180° = 540°

Now we know that 3 angles add up to 420°.

Then the other two angles must add up to:

540° - 420° = 120°

And those two angles are equal, then each one measures:

120°/2 = 60°.

If you want to learn more about angles, you can read:

https://brainly.com/question/17972372

which of the following fractions will convert to repeating decimals?

a. 1/3
b. 1/6
c. 1/4
d. 3/8
e. 1/5

Answers

Well, that's odd. both a and b are repeating decimals.

a. 1/3 = 0.33333333
b. 1/6 = 0.16666666
c. 1/4 = 0.25
d. 3/8 = 0.375
e. 1/5 = 0.2

Carissa is budgeting for her next semester at college. She spent $50 on gas this month. Economists are predicting gas prices to rise 8% per month for the next 6 months. How much should she budget for gas if classes start next month and are 4 months long?

The answer is D.243.33
(I looked up the question and couldnt find it so i thought i'd post it for anyone who needed it)

Answers

Spent on gas this month = $50.

Predicted spent of gas next month = $50 * 1.08

Predicted spent of gases for the four months:

$50 * 1.08
$50 * 1.08^2
$50 * 1.08^3
$50 * 1.08^4

Total spent for the four months: $50 (1.08 + 1.08^2 + 1.08^3 + 1.08^4) = $50 * (4.8666) = $243.33, which is the option D. 243.33

A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volume the same?

Answers

No. the square prism has volume of 5x5xheight
The square pyramid has a volume of
5x5xheight/3

The perimeter of a rectangle is 42 m. the length of the rectangle is 3 m more than twice the width. find the dimensions of the rectangle.

Answers

42/2 = 21

21 = w +2w+3

21 = 3w +3

18 =3w

w = 18/3 = 6

width is 6

length = 6x2=12+3 = 15

6+6+15+15 = 42

width = 6 m

length = 15 m

A card is chosen at random from a standard deck of 52 playing cards. What is the probability that the chosen card is a jack or a queen?

Answers

since there are 4 jacks and 4 queens in a deck, there are a total of 8 jacks and queens in 52 cards. this translates to 8/52, ( simplified 2/13 ) or 15%.

The perimeter of a triangle is 510 ft and the sides are in the ratio of 11:16:24. Find the area of the triangle. Need help, is there a specific formula for this?

Answers

1.
The side lengths are in the ratio 11:16:24, so let them be

11k, 16k, and 24k for some number k.

11k+16k+24k=510
k(11+16+24)=510
51k=510
k=10

so the actual sides are 110, 160 and 240 feet.

2.
There is a famous formula, called Heron's formula, which calculates the area of a triangle, given its sides a, b and c.

we first calculate the half perimeter, which we usually denote by u:

[tex]u= \frac{a+b+c}{2} [/tex]

then the theorem states that the area A is as follows:

[tex]A= \sqrt{u(u-a)(u-b)(u-c)} [/tex]

3.

In our case:

[tex]u= \frac{a+b+c}{2} =\frac{110+160+240}{2} = \frac{510}{2} [/tex]

[tex]u-a= \frac{510}{2} -110= \frac{510-220}{2} = \frac{290}{2} [/tex]

[tex]u-b= \frac{510}{2} -160= \frac{510-320}{2} = \frac{190}{2} [/tex]

[tex]u-a= \frac{510}{2} -240= \frac{510-480}{2} = \frac{30}{2} [/tex]

[tex]A= \sqrt{\frac{510}{2}*\frac{290}{2}* \frac{190}{2} * \frac{30}{2}} =7,258.745[/tex] feet squared

Answer:D 7,258.745 ft squared

Final answer:

To find the area of a triangle with sides in a given ratio, first find the value of x by setting up and solving an equation using the perimeter. Then, multiply each side by x to find the base and height of the triangle. Finally, substitute the base and height into the formula for the area of a triangle.

Explanation:

To find the area of a triangle, we can use the formula: Area = 1/2 × base × height. In this case, we don't know the base and height directly, but we do know that the sides of the triangle are in the ratio of 11:16:24. Let's assume the sides are 11x, 16x, and 24x. The perimeter of the triangle is 510 ft, which means 11x + 16x + 24x = 510. Simplifying this equation, we get 51x = 510. Therefore, x = 10. Now we can find the base and height of the triangle by multiplying the corresponding sides by 10. The base is 11x * 10 = 110 ft and the height is 16x * 10 = 160 ft.

Now we can substitute these values into the formula to calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 110 ft × 160 ft = 8800 square feet.

Other Questions

Mccollum v. board of education (1948) was an important case on religion and education. in its ruling, why wouldn't the supreme court allow the public school released time program? What is the range of the function given in the graph in interval notation.[-4,8](-4,3)U(3,8](-4,8][-4,3)U(3,8) In the book Anything but typical What was Jason diagnosed with in the third grade? Leonardo da vinci's mona lisa is 21 inches wide and 30.25 inches tall. what is the area of the painting in square centimeters? The GCD(a, b) = 18, LCM(a, b) = 108. If a=36, find b. "I do not like to walk up there and hand up my membership in the American Railway Union because when a man asks me to give up my principles, my rights as an American citizen, he might just as well ask for my life." What result of the Pullman Strike is the worker describing? A circuit contains a 6.0-v battery, a 4.0-w resistor, a 0.60-f capacitor, an ammeter, and a switch all in series. what will be the current reading immediately after the switch is closed? An arterial condition in which there is thickening, hardening, and loss of elasticity of the walls of arteriesresulting in decreased blood supplyespecially to the lower extremities and cerebrum is known as hardening of the arteries If your BAL is .10 you can expect a _______ drop in complex performance compared to the sober level how are people chosen to serve in the government??! please I'm desperate! What was the outcome of the Supreme court case Wocester v. Ga? The ultimate source of energy that powers the sun is Subsidizing medical services through medicare a. makes medical services available to a large percentage of the? population, who otherwise could not afford them. b. drives a wedge between the price received by providers and the price perceived by consumers. c. is a relatively low percentage of u.s. gdp compared to other nations. d. all of the above are true. e. only a and b are true. What is the solution to the equation 0.8m 4 = 0.8m? Which of the following did Martin Luther believe was required for people to gain salvation? Faith Charity Bible study Good works Which are the solutions of the quadratic equation? x2= 5x 3 5, 0 5, 0 In order to use the commit command in oracle, you need to clear the check mark from the ____ check box. Which word or phrase correctly completes this conversation? Pamela: __________ cuesta la computadora? Leonardo: La computadora cuesta 400. The Iran-Contra affair during the Reagan administration began with the U.S. selling arms to Iran in exchange for what? If a Rubiks Cube has a volume of 384 cubic centimeters, how long is one side of the cube? Steam Workshop Downloader