Mathematics High School

If f(x)=x-7 and g(x)=x^3, what is G(f(x))?

A. x^3+x-7
B. x^3(x-7)
C. X^3-7
D. (x-7)^3

Answers

Answer 1
replace the 'x' in the formula for g(x) by f(x):-

g(f(x)) =  (x-7)^3

Its D
Answer 2

Answer:

D.  [tex](x-7)^3[/tex]

Step-by-step explanation:

Given functions are,

[tex]f(x) = x-7-----(1)[/tex]

[tex]g(x)=x^3-----(2)[/tex]

Now,

[tex]g(f(x))=g(x-7)[/tex]     ( From equation (1) ),

[tex]=(x-7)^3[/tex]            ( From equation (2) ),

[tex]\implies g(f(x)) = (x-7)^3[/tex]

Hence, Option D is correct.

Related Questions

HELP QUICK!!!
An ellipse has foci F1(9, 0) and F2(11, 6), and the point (1, 6) is on the ellipse. Identify the constant sum for the ellipse.
a 20
b 10
c 0
d 100

Answers

The first step is to find the distance from the given point to each of the two foci as follows:
Distance D1:
(D1)^2 = (9-1)^2 + (0-6)^2 = 100
D1 = 10
Distance D2:
(D2)^2 = (11-1)^2 + (6-6)^2 = 100
D2 = 10

The constant sum is the summation of the two distances as follows:
constant sum = D1 + D2 = 10 + 10 = 20

The correct choice is:
a) 20

Answer:   20

Step-by-step explanation:

The sum of two numbers is 54 . the smaller number is 12 less than the larger number. what are the numbers?

Answers

Let x=one number and x+12= the other number.  Together the numbers=54.  Set up the equation:  x+x+12=54;  Combine the variables;  2x+12=54;  Subtract 12 from both sides of the equation;  2x=42; Divide both sides of the equation by 2;  x=21 is one number and 21+12=33 is the other number.  Check:  2(21) +12=54;  42+12=54;  54=54.

Find the product.

(n + 7)(n - 2)

n² - 5n - 14
n² + 5n - 14
n² - 5n + 14

Answers

The answer is n^2 + 5n - 14.


[tex](n+7)(n-2)\\\\n*n+(-2)*n+7*n+7*(-2)\\\\n^{2}-2n+7n-14\\\\n^{2}+5n-14[/tex]
(n+7)(n-2)
=n•n+(-2)•n+7•n+7•(-2)
=n²-2n+7n-14
=n²+5n-14. In conclusion, the product of (n+7) and (n-2) or (n+7)(n-2)=n²+5n-14. Hope it help!

20 POINTS, PLEASE HELP ASAP!!!!

Answers

Question b)

17 minutes ⇒ 1 revolution = 2π
1 minute ⇒ 2π/17

Angle of rotation is 2π/17 per minute

Question c)

The period of the rotation is 2π/17 

The wheel starts rotating from the height of 5 meters from the ground and the maximum height is 125 meter from the ground.
The amplitude is 125 - 5 = 120 ÷ 2 = 60

The midline of the rotation is at 125 - 5= 120 ÷2 = 60 + 5 = 65 (this is the location of the centre of the wheel). This value is a shift of 65 from the zero midlines (which in this case would be the ground)

Question C

The movement of the wheel can be described as starting from 0° then reaching its peak at 180° and come back to its original position as it stops and it makes a complete circular turn 360°.

If we sketch this on a graph, we will obtain a curve of -cos(x)

We need to apply the period, the amplitude and the shift produced by this rotation into the equation [tex]y = -cos(x)[/tex]

The period is [tex] \frac{2 \pi }{7} [/tex] ⇒ [tex]f(t)=-cos( \frac{2 \pi }{7}t) [/tex]
The amplitude of 60 ⇒ [tex]f(t)=-60cos( \frac{2 \pi }{7}t) [/tex]
The shift of the midline by 65 units upwards ⇒ [tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]

The final equation is
[tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]

and the graph is shown in the third picture below

Twenty times the square of a non-zero number is equal to 15 times the number

Answers

i think that the answer is 5

20x^2 = 15x
20x^2 - 15x = 0
5x(4x - 3) = 0 
5x = 0, x =0
4x -3 = 0, x = 3/4

answer
non-zero number is 3/4

Write an equation for the translation of the function. y = cos x; translated 6 units up

Answers

it's just y= cos(x)+6

Answer:

[tex]y=cos(x)+6[/tex].

Step-by-step explanation:

We are asked to write an equation for the translation of the function [tex]y=cos(x)[/tex] to 6 units upwards.

Let us recall transformation rules.

[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]

[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]

[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]

[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]

Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:

[tex]y=cos(x)+6[/tex]

Therefore, our required equation would be [tex]y=cos(x)+6[/tex].

Rectangular prisms A and B are similar.
The edge of prism B is 3 times that of prism A. How many times the volume of prism A is the volume of prism B?

Answers

27 times smaller or 1/27 because 3^3 equals to 27.
[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{let's say the edge of A is \underline{k} long, then B's is \underline{3k}} \\\\\\ \cfrac{A}{B}\qquad \cfrac{k}{3k}\implies \cfrac{1}{3}\implies \cfrac{s}{s}\qquad thus \\\\\\ \cfrac{A}{B}\qquad \cfrac{1}{3}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{1}{3}=\sqrt[3]{\cfrac{s^3}{s^3}}\implies \left( \cfrac{1}{3} \right)^3=\cfrac{s^3}{s^3}\implies \cfrac{1^3}{3^3}=\cfrac{s^3}{s^3} \\\\\\ \cfrac{1}{27}=\cfrac{s^3}{s^3}[/tex]

Someone help me please !!!

Answers

Answer:

1. 10

2. 12

3. Sqrt 130

4. Sqrt 45

Step-by-step explanation:

To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the legs with a being the smallest and c is the hypotenuse.

1. a=6, b=8, c=?

[tex]6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c[/tex]

2. a=5, b=?, c=13

[tex]5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b[/tex]

3. a=7, b=9, c=?

[tex]7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c[/tex]

4. a=2, b=?, c=7

[tex]2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b[/tex]

Applying the distributive property, the expression becomes (3x)(–x) + (3x)(4) + (–5)(–x) + (–5)(4). What is the simplified product in standard form?

Answers

The answer is -3x^2 + 17x - 20.
(3x)(–x) + (3x)(4) + (–5)(–x) + (–5)(4)
= -3x^2 + 12x + 5x - 20
= -3x^2 + 17x - 20

hope it helps

The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(4)=64

Answers

check the picture below.

What is the precise definition of an angle? question 1 options:?

Answers

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

True or false the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle

Answers

The answer is TRUE!!!!!

Answer:

True

Step-by-step explanation:

Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.

Then

EB=EC;FC=FA;GA=GB.

Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then

m∠OBE=m∠OCE=90°;m∠OCF=m∠OAF=90°;m∠OBG=m∠OAG=90°.

You get three pairs of congruent triangles:

ΔOBE≅ΔOCE;ΔOCF≅ΔOAF;ΔOBG≅ΔOAG.

This gives you that

[tex]OB=OC=OA.[/tex]

Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.

Find the area of the larger regular pentagon if the smaller pentagon has an area of 43.01 inches^2. The side length of the small pentagon is 5 and the side length of the large pentagon is 8.

Answers

110.11 is the answer.

Driving on the North West Express-way, Debbie averaged 62 miles per hour for 3 & one fourth hours. How far did she drive?

Answers

1/4 = 0.25

s0 3 1/4 = 3.25

62x3.25 = 201.50 miles = 201 1/2 if you need it in fraction form

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Answers

52/2 = 26 ounces of cereal in 1 box
26 * 5 = 130 ounces of cereal in 5 boxes

Answer:

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Step-by-step explanation:

If we have 52 ounces in 2 boxes, in 1 box we have: 52/2 = 26 ounces.

If we have 5 boxes and 26 ounces in each, we have: 5 x 26 = 130 ounces in total.

Which is heavier 9 5/8 pounds or 9 3/4 pounds

Answers

9 3/4 weighs more than 9 5/8 because 3/4 is larger than 5/8. You can draw this out if you like to see it visually, or you can divide 3 by 4 and 5 by 8 to see which is more! 5/8 = 0.625 while 3/4 = 0.75

The cells of a certain culture of bacteria double every 6 minutes. If the culture contains 100 cells in the beginning, then the total number of cells P in this culture after t minutes is given by the exponential equation P = 100(2)t/6. Identify the number of minutes it will take for the number of cells to exceed 50,000.
A) 53 min
B) 49 min
C) 48 min
D) 54 min

Answers

Since the growth is exponential, therefore I believe the correct form of the equation is:

P = 100 (2)^(t / 6)

Where t / 6 is the exponent of 2

So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:

P = 100 (2)^(t / 6)

50000 = 100 (2)^(t / 6)

500 = 2^(t / 6)

log 500 = (t / 6) log 2

t / 6 = log 500 / log 2

t = 6 * 8.96578

t = 53.8 mins = 54 mins

 

Answer:

D. 54 min

Find the area of a sector that has a central angle of 40 and a radius of 2 cm. Round your answer to the nearest 100th. Use 3.14=

Answers

I think the answer is around 1.4 as you need to multiply the area by 1/9 after finding the real area. 

Webassign find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (6, 36), and the x-axis.

Answers

first find the tangent line

dy/dx=2x
at x=6, the slope is 2(6)=12
so
use point slope form
y-y1=m(x-x1)
point is (6,36)
so
y-36=12(x-6)
y-36=12x-72
y=12x-36

alright, so we know they intersect at x=6
and y=12x-36 is below y=x^2

so we do [tex] \int\limits^6_0 {x^2} \, dx - \int\limits^6_0 {12x-36} \, dx = \int\limits^6_0 {x^2-(12x-36)} \, dx = \int\limits^6_0 {x^2-12x+36} \, dx =[/tex]
[tex][\frac{x^3}{3}-6x^2+36x]\limits^6_0=(\frac{6^3}{3}-6(6)^2+36(6))-(0)=\frac{216}{3}-216+216=[/tex] [tex]72+0=72[/tex]

the area under the curve bounded by the lines and the x axis is 72 square units

From 75 campsites to 120 campsites

Answers

subtract 75 from 120

120-75 =45 more campsites

A quiz has 4 multiple-choice questions with 4 possible answer choices each. for each question, there is only 1 correct answer.a student guesses each answer at random. what is the probability of getting exactly 3 questions correct, to the nearest percent?(3 correct and 1 incorrect)

Answers

There are 4C3 ways of getting 3 out of 4 correct. This = 4.

The probability of getting  3 correct and 1 wrong in one of these ways is 
1/4 * 1/4 * 1/4 * 3/4  =  3/256

So required probability = 4 * 3/256  = 12/256  =  4.69 %   
5% to nearest percent.

Answer:    (quartered spinner)     (4)     (1/256)

The sum of two numbers is 33. Twice the first number minus the second number equals 18. Find both numbers.

Answers

We can call the two numbers x and y. Then, x + y = 33, and 2x - y = 18. We can use substitution to solve this problem:

y = 33 - x 

SO

2x - 33 + x = 18

3x = 51

x = 17

Now, we know x. We can use this to find y:

x + y = 33

17 + y = 33

y = 16

So, the numbers are 16 and 17. 

The both numbers are = 17 and 16

Solving for the unknown numbers

The sum of two numbers = 33

Let the two numbers be X and y.

therefore X + y = 33 ----> equation 1

Twice the first number minus the second number= 18.

That is,

2x - y = 18 -----> equation 2

From equation 1 make X the subject of formula;

X = 33 – y

substitute X into equation 2,

2(33 – y) - y = 18

66 – 2y – y = 18

66 – 3y = 18

66 – 18 = 3y

48 = 3y

y = 48/3

y = 16

Substitute y = 16 into equation 1

Therefore, X +16 = 33

X = 33 –16

X = 17

Therefore, he both numbers are = 17 and 16

Learn more about summation here:

https://brainly.com/question/14322177

Please help me !!!!!!!!

Answers

It's C the missing side is 9 units long so since cosine is adjacent divided by hypotenuse it would be 9/41
41^2 - 40^2 = 1681 - 1600 = 81

side xy = square root 81 = 9

cosine(X) = Adj / Hypo
cosine(X) = 9/41
answer
C. 9/41

Evaluate 9 - b when b = 8

Answers

9 - b = ?
9 - 8 = 1
So, your answer is 1. Hope this helps, please mark brainliest and have an amazing day!

Equations are expressions separated by an equal sign. The value of the expression 9-b is b is 8 is given as 1

Equations and expressions

Equations are expressions separated by an equal sign

Given the expression  9 - b

If b = 8, we will have to substitute the value of 8 into the expression to have:

f(b) = 9 - b

f(8) = 9 - 8

f(8) = 1

Hence the value of the expression 9-b is b is 8 is given as 1

Learn more on function and values here: https://brainly.com/question/2284360

At a sandwich shop they offer 3 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. Each type of sandwich has a combination of exactly 3 ingredients: 1 bread, 1 meat, and 1 cheese. How many types of sandwiches are possible?

Answers

Final answer:

The sandwich shop could yield a total of 45 types of sandwiches based on the three categories provided; namely, bread, meat, and cheese. According to the counting principle in mathematics, you multiply the amount of options available from each category to get the total combinations possible.

Explanation:

In the scenario described, to determine the possible number of sandwiches, we need to analyze the provided combinations. We have 3 types of bread, 5 kinds of meat, and 3 kinds of cheese. Each sandwich exactly contains one item from each category.

To find out all possible sandwich combinations, we multiply the number of choices in each category. This is known as the counting principle.

So, the formula would be:
Number of sandwich combinations = Types of Bread * Types of Meat * Types of Cheese

Plugging the given numbers into this formula, we get:
Number of sandwich combinations = 3 * 5 * 3 = 45

So, there are 45 possible sandwich combinations available in this sandwich shop.

Learn more about Counting Principle here:

https://brainly.com/question/29594564

#SPJ12

What is -11-8-13(-10)? And how did you get you're answer

Answers

-11-8-13(-10)

First, multiply since multiplication goes before subtraction according to the order of operations.

-11-8+130

Then add and subtract from left to right.

-11-8= -19
-19+130=111

Final answer: 111

A tea bag is shaped like a regular square pyramid. Each leg of the base is 4 cm, and the slant height is 5 cm. Find the VOLUME of the tea bag.

Answers

(16[tex] \sqrt{21} [/tex])/3
The volume of a pyramid is V=1/3Bh (One-third the area of the base times height). Since your pyramid has a square base, you have to find the area of the base, multiply it by the height, and then divide it by 3.

So, the area of the base is 4x4, which is 16, then you multiply it by the height, 5, and 16x5 is 80, and 80/3 is approximately 26.6

The answer would be 26.6 cm^3

Solve 2x + 5y = −13
3x − 4y = −8

Answers

2x+5y=-13
3x-4y=-8

Rearrange the first equation to solve for x in terms of y. This will be needed to apply the substition method.

2x+5y=-13
2x=-5y-13
x=-5/2y-13/2

Now plug this in for x in the second equation.

3(-5/2y-13/2)-4y=-8
-15/2y-39/2-4y=-8
-23/2y-39/2=-8
-23/2y=11.5
y=-1

Now plug this y value in to one of the original equations.
2x+5(-1)=-13
2x-5=-13
2x=-8
x=-4

Final answer: (-4,-1). <=============

To check:

2(-4)+5(-1)=-13
-8+5(-1)=-13
-8-5=-13
-13=-13
True

3(-4)-4(-1)=-8
-12-4(-1)=-8
-12+4=-8
-8=-8
True


Julio checked the temperature of a bag of frozen peas and found it was at −13°C. After he left the bag out of the freezer for an hour, its temperature rose to 8°C. What was the change in temperature in an hour?
a)−21°C
b)21°C
c)5°C
d)−5°C

Answers

The change is the difference final temperature less initial temperature.

ΔT = final temperature - initial temperature = 8°C - ( -13°C) = 8°C + 13°C = 21 °C.

So, the temperature raised 21 °C, and that is the change in temperature.

Answer: change = option b) 21°C.
The correct answer is option A



solve the equation by completing the square. round to the nearest hundredth if necessary. x^2-6x=20

Answers

x^2 - 6x = 20
x^2 - 6x + 9 = 20 + 9
(x - 3)^2 = 29
x - 3 = (+-) sqrt 29
x = 3 (+-) sqrt 29
x = 3 (+-) 5.39

x = 3 + 5.39 = 8.39 <=
x = 3 - 5.39 = - 2.39 <=
x^2-6x+(b/2)^2=20+(b/2)^2
x^2-6x+(6/2)^2=20+(6/2)^2
x^2-6x+(3)^2=20+(3)^2
x^2-6x+9=20+9
(x-3)^2=29
x-3=5.38 or -5.38
x=5.38+3 or -5.38+3
x=8.38 or -2.38




























Other Questions
How to solve and why the answer is (A) During the discovery phase of pre-trial procedures, a lawyer learns that evidence against his client was obtained without a warrant. During the pretrial motion, the lawyer may argue to ___________, a motion which, if granted, would disallow the evidence from trial. A.change venueB.continueC.exclude evidenceD.discover the evidence Match the correct form of the ver tre with the subject pronoun. nous read answer items for question 1 tu read answer items for question 1 vous read answer items for question 1 ils read answer items for question 1 on read answer items for question 1 je read answer items for question 1 answer a. sont b. tes c. es d. suis e. est f. sommes The Tunnel of Fear ride climbs straight up to its peak 50 meters above the ground. Then, it drops 65 meters into an underground tunnel. What is the elevation of the tunnel relative to the ground? Which indicates that a chemical reaction has occurred? A. a broken egg sinks after its has been sitting out for several days. B. you smell gasoline when you remove the cap on a gas tank. C. an unripe orange on a tree doesn't smell at all Given a mean of 8 and a standard deviation of 0.7, what is the z-score of the value 9 rounded to the nearest tenth? A biology teacher wants students to remember the various components of a cell (nucleus, cytoplasm, cell membrane). considering what research tells us about long-term memory storage, the teacher would be well advised to help students encode information about the cell Which sentence is the most subjective statement? A. Bryan thanked the owners for the raise and vowed to continue his hard work. B. Bryan worked hard for the company and earned the pay raise he was given. C. Bryan was given a pay raise because the owners appreciated his hard work. D. Bryan has been with the company for five months and plans to stay in the job. A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $14. For 5 pounds of jelly beans and 6 bounds of trail mix, the total cost is $28. Find the cost for each pound of jelly beans and each pound for trail mix. The first stage of labor is divided into 4 parts, prodromal, latent active and transition. true or false? What is meant by the term aquaculture? planting water building dams and canals for agriculture cultivation of water animals, such as eels and fish new name for a whale A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. What is the height of the pole? Round to the nearest hundredth.12.00 feet19.60 feet24.17 feet38.40 feet A researcher is interested in estimating the average salary of police officers in a large city. She wants to be 99% confident that her estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200? how did the long era of imperial warfare beginning in 1689 affect the colonies, native americans and relations between them Almost 40 percent of all federal criminal statutes passed after the civil war were enacted between ________. which statement best summarizes the ottoman Empire's role in the Middle East during World War 1 From the point of view of anyone considered to be an "inmate," what type of formal organization is the person in? A local hamburger shop sold a combined total of 436 hamburger and cheeseburgers on Friday. There were 64 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Friday? Which transition word best introduces a contrast? Evidently Furthermore However Similarly if y varies inversely as x, and y=20 as x=3, find y for the x value 4 Steam Workshop Downloader