If F(x) = x - 7 and G(x) = x3, what is G(F(x))

Answers

Answer 1

[tex]g(f(x))=(x-7)^3=x^3 - 21 x^2 + 147 x - 343[/tex]


Related Questions

When solving (x + 35) = −7, what is the correct sequence of operations?

Answers

Answer:

x= -42

Step-by-step explanation:

put the liketerms together

x+35= -7

x=-35-7

note*the operation sign changes after crossing the equal sign

x= -42

Please answer this question now

Answers

Answer:

V = 60 m³

Step-by-step explanation:

Volume of Triangular Pyramid: V = 1/3bh

Area of Triangle: A = 1/2bh

b = area of bottom triangle (base)

h = height of triangular pyramid

Step 1: Find area of base triangle

A = 1/2(8)(5)

A = 4(5)

A = 20

Step 2: Plug in known variables into volume formula

V = 1/3(20)(9)

V = 1/3(180)

V = 60

What are the zeros of the polynomial function? f(x)=x^3+x^2−9x−9

Answers

Answer:

1: x = -1

2: x = 3

3: x = -3

Step-by-step explanation:

f(x)=x^3+x^2−9x−9

f(x)=x^2(x+1) −9x−9

f(x) = x^2(x+1) - 9(x+1)

f(x)= (x+1)(x^2-9)

f(x) =(x+1)(x-3)(x+3)

Answer:

[tex]\boxed{x=-1, \ x=-3, \ x=3}[/tex]

Step-by-step explanation:

The zeros of a function are the values of x when f(x) = 0.

[tex]x^3 +x^2-9x-9=0[/tex]

Factor left side of the equation.

[tex]x^2(x +1)-9(x+1)=0[/tex]

Take (x+1) common.

[tex](x^2-9)(x+1)=0[/tex]

Set factors equal to 0.

First possibility:

[tex]x^2 -9=0[/tex]

[tex]x^2 =9[/tex]

[tex]x=\± \sqrt{9}[/tex]

[tex]x=\± 3[/tex]

[tex]x=-3 \ \mathrm{or} \ x=3[/tex]

Second possibility:

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

The probability that it rains is about 20%.
The probability that the bus is late is about 8%.
The probability that it rains and the bus is late is about 3%.
The probability that the train is late is about 5%.
The probability that it rains and the train is late is about 1%.

6. To decide whether the rain and the train running late are dependent or independent events, first define the two events and then write their probabilities as decimals. (3 points) Let event A = ________________________. P(A) = ______. Let event B = ________________________. P(B) = ______. A and B = ________________________. P(A and B) = ______. 7. Use the probabilities from question 6 to decide whether the rain and the train running late are independent or dependent events. (2 points: 1 point for the correct math, 1 point for the conclusion)

Answers

Answer:

Step-by-step explanation:

Let A= probability it rains

P(A)=0.2

Let B be the probability that the train is late = 0.05

P(B)=0.05

A and B  is A∩B= the probability it rains and the bus is late =0.01

probability pf (A and B)=0.01

7) independent events are related by expression:

A∩B=P(A)*P(B)

       =0.2*0.05=0.01  

check :

p(A|B)=P(A∩B)÷P(B)=0.01/0.05= 0.2

the two event are independent

Answer:

The two are independent.

Step-by-step explanation:

Juan works as a tutor for $12 an hour and as a waiter for $7 an hour. This month, he worked a combined total of 110 hours at his two jobs.
Let t be the number of hours Juan worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answers

Answer:

12t+7w=D

t+w=110

Step-by-step explanation:

12t= $12 made every tutor hour

7w= $7 made every waiter hour

D= total dollars made

t+w=110 is the tutor hour and the waiter hour adding together

Answer:

12t + 7y = x

      or

5t + 770 = x

Step-by-step explanation:

12t + 7y = x

t = number of hours he worked as a tutor

y = number of hours he worked as a waiter

x = the total amount of money he earned

t + y = 110

=> y = 110 - t

=> 12t + 7(110 - t) = x

=> 12t + 770 - 7t = x

=> 5t + 770 = x

Given that T{X: 2<x ≤ 9} where x is an integer. what is n(T)

Answers

Answer:

n(T) = 7

Step-by-step explanation:

Given the set T{X: 2<x ≤ 9} where x is an integer, the element of the set T will be {3, 4, 5, 6, 7, 8, 9}.  note that from the inequality set 2<x ≤ 9, x is not equal to 2 but greater than 2. The inequality can be divided into two as shown;

If 2<x ≤ 9 then 2<x and x≤9

If 2<x, this means x>2 but not equal to 2. This is the reason why 2 is not contained in the set T.

Similarly if x≤9, this shows that x can not be greater than 9 but less than or equal to 9.

Since the set T =  {3, 4, 5, 6, 7, 8, 9}, we are to find n(T). n(T) means cardinality of the set T and cardinality of a set is defined as the total number of element in a set.

Hence n()n(T) = 7 (since there are 7 elements in the set T)

A ladder (line segment AC in the diagram) is leaning against a wall. The distance between the foot of the ladder and the wall (BC) is 7 meters less than the distance between the top of the ladder and the ground (AB). A-Create an equation that models the length of the ladder (l) in terms of x, which is the length in meters of AB. B-If the length of the ladder is 13 meters, use the equation you wrote to find the distance between the ground and the top of the ladder (AB).

Answers

Greetings from Brasil...

a)

Let's just use Pythagoras

L² = X² + (X - 7)²

L = √(2X² - 14X + 49)

b)

If L = 13, then what is the value of X ???

L² = 2X² - 14X + 49

2X² - 14X - 120 = 0

X = 12  or  X = - 5

(The distance cannot be negative, so X = 12)

what is the value of x ?

Answers

Answer:

65dg.

Step-by-step explanation:

Triangles are 180dg.

So 68dg + 47dg = 115dg.

-180dg - 115dg = 65dg.

So the missing length is 65 degrees.

Answer: 65

Step-by-step explanation:

Add both of the numbers on there. Then do 180- that number.

68+47=115

180+115=65

This is because in a triangle all the angles together equal 180.

The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?

Answers

Answer:

The original number could be 85.

Step-by-step explanation:

Let the 2 digits be x and y.

Let the number be xy then, assuming that x is the larger digit:

x - y = 3.

x = y + 3

Also

10y + x + 10x + y = 143

Substituting for x:

10y + y + 3 + 10(y + 3) + y = 143

22y + 33 = 143

22y = 110

y = 5.

So x = y + 3 = 8.

Answer:

Let the unit digit be x and tens digit be x + 3

Therefore, the original number = 10(x + 3) + x

On interchanging, the number formed = 10x + x + 3

❍ According to Question now,

➥ 10(x + 3) + x + 10x + x + 3 = 143

➥ 10x + 30 + 12x + 3 = 143

➥ 22x + 33 = 143

➥ 22x = 143 - 33

➥ 22x = 110

➥ x = 110/22

x = 5

__________________...

Therefore,

The unit digit number = x = 5

The tens digit number = x + 3 = 5 + 3 = 8

__________________...

The original number = 10(x + 3) + x

The original number = 10(5 + 3) + 5

The original number = 50 + 30 + 5

The original number = 85

Hence,the original number is 85.

expand (x-4)^4 with binomial theorem or pascal's triangle

Answers

Answer:

(x-4)^4=x⁴+4x³(-4)¹+6x²(-4)²+4x¹(-4)³+(-4)⁴

=x⁴-16x³+96x²-256x+256

A restaurant wanted to track how much of a quart of soda customers drank at a meal. The line plot displays the data collected by the restaurant. How much more soda did the customers who drank 3/4 of a quart drink than the customers who drank 1/4 of a quart?

Answers

Answer:

C

Step-by-step explanation:

13/4 simplified---->3and 1/4

A customer owes a balance of $400 on their lease. They have a $75 payment due each month. What will be their remaining balance after their next 2 monthly payments are made?

Answers

Answer:

Step-by-step explanation:

2(75)=150 that's the amount due in total for two months so

400-150= 250 they will owe $250 after two months payment

What is the probability of rolling a number greater than 6 on a number cube

Answers

Answer:

0

Step-by-step explanation:

It is not possible to roll a number greater than 6 on a number cube

Answer: 0

A probability of 0 means "impossible". This is because a standard number cube (aka a die) has sides labeled 1 through 6. There is no way to roll something larger than 6 on a single die.

Please help! Explanation please!​

Answers

Answer:

11 meters.

Step-by-step explanation:

The important thing to note here is that the backyard is a square. Since it's a square, all of its sides all equivalent in length. Thus, let's find the length of the sides. To do this, we use the area formula.

The formula for the area of a square is:

[tex]A=n^2[/tex]

Where n is a side. Since we know the area already, we can find n. Find n:

[tex]121=n^2\\n=11[/tex]

Since every side in a square are equivalent, all sides are 11 meters in length.

Therefore, each section of the fence should be 11 meters long.

To determine the relative effectiveness of different study strategies for the SAT, suppose three groups of students are randomly selected: One group took the SAT without any prior studying; the second group took the SAT after studying on their own from a common study booklet available in the bookstore; and the third group took the SAT after completing a paid summer study session from a private test-prep company. The means and standard deviations of the resulting SAT scores from this hypothetical study are summarized below:
Using the following output:
we can conclude that:
(a) the data provide strong evidence that SAT scores are related to learning strategy.
(b) the data provide strong evidence that SAT scores are related to learning strategy in the following way: The mean SAT score for students who pay for coaching is higher than the mean SAT score for students who study themselves, which in turn is higher than that of students who do not study for the test.
(c) the data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal.
(d) the data do not provide sufficient evidence that SAT scores are related to learning strategy.
(e) Both (a) and (c) are correct.

Answers

Answer:

(b) the data provide strong evidence that SAT scores are related to learning strategy in the following way: The mean SAT score for students who pay for coaching is higher than mean SAT score for students who study themselves, which in turn is higher than those students who do not study for test.

(c) The data provide strong evidence that the three mean SAT scores (representing the three learning strategies) are not all equal.

Step-by-step explanation:

Relative effectiveness is to study the extent to which an intervention of a thing does more good than harming it when two or more alternative interventions are observed. In the given question the SAT mean score for students who are paying higher for coaching than those student who believe in self study.

Let n be the number of five-digit positive integers which are divisible by 36 and have their tens digit and unit digit equal. Find n/100

Answers

Answer:

1.) 10044

2.) 100.44

Step-by-step explanation:

Since n is a number of five-digit positive integers which are divisible by 36, start multiplying 36 by number. Starting from 278.

Five digits numbers start from multiplying 36 by 278. Any multiplication below 278 by 36 will give four digits numbers.

36 × 278 = 10,008

36 × 279 = 10,044

10,044 tens digit and unit digit equal. Therefore n = 10044

To find n/100, divide 10044 by 100

10044 / 100 = 100.44

Find the difference of functions s and r shown
below.
r(x) = -x2 + 3x
s(x) = 2x + 1
(s - r)(x) =

Answers

Answer:

[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1[/tex]

And we want to find:

[tex]\displaystyle (s-r)(x)[/tex]

This is equivalent to:

[tex]\displaystyle (s-r)(x) = s(x) - r(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}[/tex]

In conclusion:

[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]

A cube whose edge is 20 cm 1 point
long, has circles on each of its
faces painted black. What is the
total area of the unpainted
surface of the cube if the
circles are of the largest
possible areas?(a) 90.72 cm2 (b)
256.72 cm² (c) 330.3 cm² (d)
514.28 cm?

Answers

Answer:

Unpainted  surface area = 514.28 cm²

Step-by-step explanation:

Given:

Side of cube = 20 Cm

Radius of circle = 20 / 2 = 10 Cm

Find:

Unpainted  surface area

Computation:

Unpainted  surface area = Surface area of cube - 6(Area of circle)

Unpainted  surface area = 6a² - 6[πr²]

Unpainted  surface area = 6[a² - πr²]

Unpainted  surface area = 6[20² - π10²]

Unpainted  surface area = 6[400 - 314.285714]

Unpainted  surface area = 514.28 cm²

Special right triangles

Answers

Answer: please find the attached files

Step-by-step explanation:

A unit circle formula and special triangle of 45, 30 and 60 degrees can be used to solve the problem.

Please find the attached files for the solution

Determine the minimum rotation (in degrees) which will carry the following figures onto itself (where all sides and verticles will match up). Assume this is a regular polygon. Round to the nearest tenth if necessary.

Answers

Answer:

60°

Step-by-step explanation:

A full rotation is 360°. The figure has six sides.

1. Divide

360 ÷ 6 = 60

Each angle of the polygon is 60°. Therefore, the polygon must be rotated at least 60° for the figure to match all sides and vertices.

hey help me with this question plzzzz

Answers

Two Answers: choice C, choice D

Look at where we don't have repeating x values. This happens with function C and function D. All the x values are unique for each choice mentioned.

In choices A, B, and E, the value x = -3 repeats itself. So we don't have a function for either of these. A function is only possible if any input (x) leads to exactly one output (y).

Find the rate of change for the situation. A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.

Answers

To find the rate of change, we need to divide the number of people by the number of pounds of chicken used. This is 36/9 = 4. Additionally, you could have done 68/17 = 4.

Can you please help me on add and subtract fractions level 1 9/8-11/8

Answers

Answer:

7/8

Step-by-step explanation:

1. Make 1 9/8 into an improper fraction

1 = 8/8

8/8 + 9/8 = 17/8

2. Subtract

17/8 - 11/8 = 7/8

7/8 is the correct answer

Christine's gross monthly salary at her job
is $5,250. She has the following
deductions from her paycheck.
What is Christine's net take-home pay per
month?

Answers

Answer:

  $2587.87 per month

Step-by-step explanation:

The listed deductions are ...

25% withheld for federal income tax9.3% withheld for California state income tax6.2% withheld for Social Security tax1.45% withheld for Medicare Tax0.9% withheld for SDI- Disability Insurance5% goes into her retirement 401K account$150 goes to health insurance/ dental for her family

The percentages have a total of ...

  25 +9.3 +6.2 +1.45 +0.9 +5 = 47.85 . . . percent

So, Christine's take-home pay is ...

  $5250(1 -0.4785) -150 = $2587.87 . . . per month

All the edges of a cube have the same length. Tony claims that the formula SA = 6s, where s is the length of
each side of the cube, can be used to calculate the surface area of a cube.
a. Draw the net of a cube to determine if Tony's formula is correct.
b. Why does this formula work for cubes?
Frances believes this formula can be applied to calculate the surface area of any rectangular prism. Is
she correct? Why or why not?
d. Using the dimensions of Length, Width and Height, create a formula that could be used to calculate the
surface area of any rectangular prism, and prove your formula by calculating the surface area of a
rectangular prism with dimensions L = 5m, W = 6m and H=8m.

Answers

Answer:

Here's what I get  

Step-by-step explanation:

a. Net of a cube

Fig. 1 is the net of a cube  

b. Does the formula work?

Tony's formula works if you ignore dimensions.

There are six squares in the net of a cube.

If each side has a unit length s, the total area of the cube is 6s.

c. Will the formula work for any rectangular prism?

No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.

d. Area of a rectangular prism

A rectangular prism has six faces.

A top (T) and a bottom (b) — A = 2×l×w

A left (L) and a right (R)    —   A = 2×l×h

A front (F) and a back (B) —   A = 2×w×h

                                  Total area = 2lw + 2lh + 2wh

If l = 5 m, w = 6 m and h = 8 m,

[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]

The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 36°.Calcule the height of the pole

Answers

Answer: Approximately 119.76 meters

===================================================

Work Shown:

x = starting length of the shadow

y = height of the pole

tan(angle) = opposite/adjacent

tan(58) = y/x

1.6003345 = y/x

1.6003345x = y

x = y/1.6003345

x = (1/1.6003345)y

x = 0.62486936y

-------------------------

When the angle changes, the adjacent side gets 90 meters longer

tan(angle) = opposite/adjacent

tan(36) = y/(x+90)

0.72654253 = y/(0.62486936y+90)

0.72654253(0.62486936y+90) = y

0.453994166y + 65.3888277 = y

65.3888277 = y-0.453994166y

65.3888277 = 0.546005834y

0.546005834y = 65.3888277

y = 65.3888277/0.546005834

y = 119.758478075162

y = 119.76

The height of the pole is about 119.76 meters.

2e - 3f = 4
2e - 5f = 8

solve this linear equation by the elimination method

please show your working ✨✨THANK YOU​

Answers

Answer:

The value of e is -1 and f is -2.

Step-by-step explanation:

The steps are :

[tex]2e - 3f = 4 - - - (1)[/tex]

[tex]2e - 5f = 8 - - - (2)[/tex]

[tex]2e - 3f - 2e - ( - 5f) = 4 - 8[/tex]

[tex]2f = - 4[/tex]

[tex]f = - 4 \div 2[/tex]

[tex]f = - 2[/tex]

[tex]substitute \: f = - 2 \: into \: (1)[/tex]

[tex]2e - 3( - 2) = 4[/tex]

[tex]2e + 6 = 4[/tex]

[tex]2e = 4 - 6[/tex]

[tex]2e = - 2[/tex]

[tex]e = - 2 \div 2[/tex]

[tex]e = - 1[/tex]

2e - 3f = 42e - 5f = 8

To solve this system of equations by addition, our first goal is to cancel

out one of the variables by adding the two equations together.

However, before we add, we need to cancel out a variable.

I would choose to cancel out the e's.

To do this, we need a 2e and a -2e and

here we have a 2e in both equations.

If we multiply the second equation by -1 however,

that will give us the -2e we are looking for.

So we have (-1)(2e - 3f) = (4)(-1).

So rewriting both equations, our first equation stays the same

but our second equation becomes -2e + 3f = -4.

Notice that every term in the second

equation has been multiplied by -1.

2e - 3f = 4

-2e + 5f = -8

Now when we add the equations together,

the e's cancel and we have 2f = -4 so f = -2.

To find e, plug -2 back in for f in the

first equation to get 2e - 3(-2) = 4.

Solving from here, e = -1.

Note that e comes before f in our final answer, (-1, -2).

To determine which variable should go first

in your answer, use alphabetical order.

My computer can download a movie in 5 hours. If I install an extra processor it can download the movie in 4 hours. How long, working alone, would it have taken the new extra processor to download the movie?

Answers

Answer:

20 hours

Step-by-step explanation:

Computer download=5 hours

Computer + Extra processor=4 hours

Computer's rate =1/5 per hour

Computer + extra processor rate=1/4 per hour

Extras processor rate=1/x

Where,

x=how long it takes extra processor to get the job done on its own.

To find x, we have to solve the equation

1/5 + 1/x = 1/4

Subtract 1/5 from both sides

1/5 + 1/x -1/5 = 1/4-1/5

1/x=1/4-1/5

1/x = 5-4/20

1/x = 1/20

Cross product

1(20)=x(1)

20=x

x=20 hours

It would have taken the new extra processor alone 20 hours to download the movie

Demerol 45mg and atropine 400mcg/ml give how much per ml to total volume to inject demerol contains 50mg/ml, atropine contains 400mcg/ml how much volume to inject

Answers

Answer:

Volume injected  = 1.65 ml

Step-by-step explanation:

mass of Demerol =45 mg.

density of pre-filled in syringe = 50 mg/ml

Volume = 45/50 = 0.9 ml

For atropine mass = 0.3 mg

density= 400 mcg/ml     [ Note : 1 mcg = 0.001 mg]

volume filled  = 0.3/400(0.001) = 0.75 ml

So, the total volume filled = 0.75+0.9 = 1.65 ml

The focus of a parabola is (3,-7) and the directrix is y = -4.
What is an equation of the parabola?

Answers

Answer:

  (a)  (x -3)^2 = -6(y +5.5)

Step-by-step explanation:

The equation of a parabola can be written as ...

  (x -h)^2 = 4p(y -k)

where (h, k) is the vertex, and p is the distance from the focus to the vertex.

The vertex is half-way between the focus and directrix, so is ...

  (h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)

The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...

  -7 -(-5.5) = -1.5

Then the equation for the parabola is ...

  (x -3)^2 = 4(-1.5)(y -(-5.5))

  (x -3)^2 = -6(y +5.5) . . . . matches the first choice

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The smartest thing a firm involved in an oligopoly market could do is to cut their prices and capture more of the market share from their competitors. a) We learned in class that the best move would be to raise prices. b) We also learned that cutting prices on an elastic demand curve will be a smart way of getting more revenues. c) Cutting prices is no gaurantee of success. Indeed if the firm does capture more market share and customers, then their costs will go up and it will be harder for them because they will have lower profit margins - if they can earn any profit at all. d) Both A and C are correct. h(x+1)=x^2-4 evaluate function by substuting x+1 How would removing invasive species from anecosystem help reduce the chances of a nativespecies becoming extinct?AThe native species would go extinctsooner.BThe native species would no longer beinfected by diseasesCThe native species would be better adaptfor survival.DThe native species would not have tocompete for necessary resources, Read this line from James Joyce's "Araby." Based on the context in which it appears, identify the correct synonym of the word amiability. I watched my master's face pass from amiability to sternness; he hoped I was not beginning to idle When HCl is added to water, the [H3O+] = 0.6 M. What is the [OH-]?What is the pH of the solution? The strategic appeal of related diversification is that it Multiple Choice allows a firm to reap the competitive advantage benefits of skills transfer, lower costs (due to economies of scope), cross-business use of a powerful brand name, and/or cross-business collaboration in creating stronger competitive capabilities. is less capital intensive than unrelated diversification because related diversification emphasizes getting into cash cow businesses (as opposed to cash hog businesses). involves diversifying into industries having the same kinds of key success factors. is less risky than unrelated diversification because it avoids the acquisition of cash hog businesses. facilitates the achievement of greater economies of scale since the company only enters those businesses that serve the same types of buyer groups and/or buyer needs. Solve for x. PLZ ANSWER FAST A list of financial statement items for Splish Brothers Inc. includes the following: accounts receivable $30,100, prepaid insurance $5,590, cash $22,360, supplies $8,170, and debt investments (short-term) $17,630.Prepare the current assets section of the balance sheet listing the items in the proper sequence. (List current assets in order of liquidity.) Is the following relation a function? (1 point) x y 1 2 2 3 3 1 6 2 No Yes Chapter 61. What is one theme you are seeing emerge in the novel A long walk to water so far? Explainyour answer. It takes a graphic designer 1.5h to make one page of a website. Using a new software, the designer could complete each page in 1.25h, but it takes 8h to learn the software. How many web pages would the designer have to make in order to save time using the new software? In the Assembly Department of Hannon Company, budgeted and actual manufacturing overhead costs for the month of April 2017 were as follows.Budget ActualIndirect materials $14,200 $13,700Indirect labor 19,100 19,900Utilities 11,400 12,100Supervision 4,600 4,600All costs are controllable by the department manager.Prepare a responsibility report for April for the cost center.