h(x)=(x+1)^2 find functions f(x) and g(x) so that h(x)=f(g)(x))

Answers

Answer 1

9514 1404 393

Answer:

f(x) = x²g(x) = x+1

Step-by-step explanation:

There are numerous possible solutions. Perhaps the simplest is to look at what happens to x in the expression for h(x).

x has 1 addedthe sum is squared

This suggests that f(x) will square the result of g(x), and that g(x) will add 1 to x:

  g(x) = x +1

  f(x) = x²

__

Check

  h(x) = f(g(x)) = f(x+1) = (x+1)² . . . . as required

_____

Additional comment

For some (almost) arbitrary function g(x), the function f(x) can include its inverse (to get the value of x+1), then perform the square. If g(x) involves powers of x, then f(x) only needs to do enough of an inverse to find (x+1)². Here's a relatively simple example.

  g(x) = 2x+3

  f(x) = (x -1)²/4

Then h(x) = f(g(x)) = f(2x +3) = ((2x +3) -1)²/4 = (2(x+1))²/4 = (x+1)²


Related Questions

Sumo wrestler decided to go on a special diet to gain weight rapidly at a constant rate. After 8 months he weighed 138 kilos. He started at 90 kilos.
Complete equation for the relationship between the weight and number of months.

Answers

Answer:

138-90=48

48/8=6

6 kil I s per month

or 13.2 pounds per m o nth appoximztly

Use the following diagram to answer questions

Answers

9514 1404 393

Answer:

ΔDEH ~ ΔGEF∠G = 89°∠F = 22°

Step-by-step explanation:

17c. We cannot see the entire diagram, but based on what we can see, if we assume that segments FG and DH are parallel, then angles D and G correspond. The similarity statement is then ...

  ΔDEH ~ ΔGEF

__

Corresponding angles are congruent, and are listed in the same order in the similarity statement. This means we have ...

  ∠D ≅ ∠G = 89° . . . . answer to 17b

  ∠E ≅ ∠E = 69°

  ∠H ≅ ∠F = 22° . . . . answer to 17a

_____

Additional comment

The second choice listed for part 17c can be rejected simply on the basis that ΔEGH does not exist in the figure. Points G and H are not in the same triangle.

Consider the following polynomial inequality.

x^2(x+5)(x−6)>0

Set one side equal to zero and list the interval endpoints (the only points at which the non-zero expression can change sign).


Separate multiple answers with a comma.

Answers

Answer:

Well, x^2(x+5)(x−6)>0= x<-5 or x>4

Step-by-step explanation:

Just have to simplify it as I can't type the equations right now.

The polynomial expression of inequality is x² ( x + 5 ) ( x - 6 ) > 0 is given by the values ( x < -5 ) and ( x > 6 )

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x² ( x + 5 ) ( x - 6 ) > 0

So , the values of x that are greater than 0 is given by

x² > 0

So , the value of x > 0

when ( x + 5 ) > 0

Subtracting 5 on both sides , we get

x < -5

when ( x - 6 ) > 0

Adding 6 on both sides , we get

x > 6

So , the inequalities are ( x < -5 ) and ( x > 6 )

Hence , the polynomial inequality is solved

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what is 25% of 32
explain please​

Answers

Answer:

25% of 32

[tex] \frac{25}{100} \times 32 \\ = 8[/tex]

A movie theater sells out 7 times per month. Chloe counted 168 sellouts at the theater. How long was Chloe recording sales? a year

Answers

Answer: 2 years

Step-by-step explanation:

The rate is 7 sellouts/month.

(168 sellouts)/(7 sellouts/month) = 24 months, or 2 years at 12 months/year.

What is the first step in simplifying the expression (2-3•4+5)^2 ?
(1) square 5
(2) add 4 and 5
(3) subtract 3 from 2
(4) multiply 3 by 4

Answers

The answer is (4)- multiply 3 by 4.

The following is the correct order of steps to simplify an expression.

1.) Parenthesis
2.) Exponents
3.) Multiply and Divide left to right
4.) Add and Subtract left to right.

Since there are parenthesis in the expression, you must do whatever is inside before anything else.

Inside the parenthesis, there is a subtraction, multiplication, and addition. Since multiplication comes before addition and subtraction in the order of operations, you must do that first. Therefore, the correct answer is multiply 3 by 4.

Answer:

(4) multiply 3 by 4

Step-by-step explanation:

(2-3•4+5)²

Firstly multiply 3 by 4

(2-12+5)²

Then add 2 and 5

(-12+7)²

Now subtract -12 from 7

-5²

= (-5)(-5)

= 25

Thus, the first step in simplifying the expression (2-3•4+5)^2 is (4) multiply 3 by 4.

The base of a triangle is 4 inches more than 3 times the height. If the area of the triangle is 66 square inches, find the base and height.

Answers

Answer:

base = b = 11

height = h = 2

Step-by-step explanation:

.5 * b * h = 11

.5 * (4h + 3) * h = 11

(4h + 3) * h = 22

4h2 + 3h = 22

4h2 + 3h - 22 = 0

(4h + 11) (h - 2) = 0

h = -11/4 OR h = 2

solve pls brainliest

Answers

Answer:

[tex]2.06[/tex]

Step-by-step explanation:

Divide 33 by 16.

[tex]2.0625[/tex]

6 is in the hundredth place. If you look at the thousandth place, a 2 is placed there, rounding [tex]2.0625[/tex] to [tex]2.06[/tex] in the hundredth place.

Hence, the answer is [tex]2.06[/tex].

Answer above is correcttttttt

I have 50 questions to complete in 45 minutes. How much time per question can I have in order to complete all 50 questions in 45 minutes?

Answers

Answer:

54 Seconds per question

Step-by-step explanation:

45/50*60

In how many ways can 5 people sit in 5 chairs if Frankie and Johnny want to sit next to each other?

Answers

Answer:

48

Step-by-step explanation:

HELP ME PLZ PEOPLE!!

Answers

Answer:

I may be wrong but i think it's -27

Step-by-step explanation:

-3 ( p - q) exponet of 2

Pemdas : Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Parentheses

-3 (p - q) exponet of 2

-3 ( 5 - 2 )  exponet of 2

-3 ( 3 )  exponet of 2

Exponents

-3 ( 3 )  exponet of 2

-3 ( 3 )  exponet of 2 = -3 (3 x 3 = 9)

-3 (9)

Multiplication

-3 (9)

Answer: -27

pls awnser (immediate)

Answers

Answer:

A. a route more than 27 miles per day.

Step-by-step explanation:

he got his answer by dividing 2,900 by 80

Edna has a box of chocolates. There are 36 chocolates in the box, and one-ninth of them
contain nuts. How many chocolates in Edna's box contain nuts?

Answers

Answer: 4

Step-by-step explanation:

[tex](36)(\frac{1}{9} )[/tex]

= 4

please give me a brainliest answer

Jaimee is moving in with her dad next year, and she wants to know how much farther her trip to school will be from his house than it was from her mom’s house. Jaimee’s dad lives 12.65 miles from school, and her mom lives 4 1/6 miles from school. About how much farther will Jaimee have to travel to school?

Answers

Answer: Hello! your answer is going to be 8.5! AKA letter B!

Step-by-step explanation: J a i m e e Ran 8.5 miles

Work out the percentage change when a price of £10 is increased to £12.

Answers

Answer:

20%

Step-by-step explanation:

Use the percent change formula: difference = % * original cost

12 - 10 = 2

The difference is 2 and the original cost is 10. Now, we have the equation

2 = % * 10. We don’t know the percentage right? So now we have to find the percentage. To do this, you will have to do 2 divided by 10, which is 0.20. Lastly, we have to turn 0.20 into a percentage by multiplying it by 100, leaving you with 20%. So therefore, 20% is the percent increase. Hope this helps!

Does -a squared = (-a) squared Explain why or why not.

Answers

Answer:

Yes

Step-by-step explanation:

This is because based on this equation PEMDAS/Order of operation says that you will get the same answer no matter whether there are parenthesis or not.

2/8+3/8=______ whole

Answers

Answer:

5/8

Step-by-step explanation:

The path of a skateboarder can be modeled by the equation (x – 4)2 = –4(y – 9), where distance is in feet and air resistance is insignificant. If the skateboarder makes a jump from a ramp at x = 0, what is her maximum height and how far is she horizontally from the end of the ramp when she lands?
Maximum height 4 feet; horizontal distance 12 feet
Maximum height 5 feet; horizontal distance 10 feet
Maximum height 9 feet; horizontal distance 12 feet
Maximum height 9 feet; horizontal distance 10 feet

Answers

Answer:

Maximum height 9 feet; horizontal distance 10 feet

Step-by-step explanation:

First, let's get the distance out of they way

When the skateboard lands, her height will be at 0 feet, so y has to equal 0

(x - 4)² = -4(0 - 9)

(x - 4)² = -4(-9)

(x - 4)² = 36

Square root both sides

√(x - 4)² = √36

x - 4 = 6

Note that x - 4 = -6 is also possible

Add 4 to both sides

x - 4 = 6

 + 4  + 4

x = 10

Note that x = -2 is also an answer. but not valid

To find the max height

Remember our zeros? x = -2, x = 10

The number in the middle would be 4

Plug 4 in place of the x in the original equation

(4 - 4)² = -4(y - 9)

(0)² = -4(y - 9)

0 = -4(y - 9)

You can divide both sides by 4

0/4 = (-4(y - 9))/4

0 = y - 9

+ 9    + 9

y = 9

Vertex is (4,9); or in other words, 9 feet is the max height

PLEASE HELP ME ASAPP if can of not then just leave it

Answers

Answer:

b

Step-by-step explanation:

fraction in simplest form: 2/3 + 1/12

Answers

Answer:

3/4

Step-by-step explanation:

3/4 and in decimal form 0.75


Given b = 40 and c=-16, b + c is equal to the product
of -4 and what number?
F.-14
G.-6
H.6
J.14
K. 160

Answers

Answer:

-6

Step-by-step explanation:

40-16=24

24/-4=-6

(b + c) is equal to the product of -4 and -6.

What is the Product of two numbers?

The product of two numbers is the result you get when you multiply them together.

Given that b = 40 and c = -16

(b + c) = 40 -16 = 24

24 = -4*-6

Hence, (b + c) is equal to the product of -4 and -6.

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Can someone explain how you do this and not only give me the answer so I could know the formula?

Answers

Answer: 9/7 or 1 2/7

Step-by-step explanation:

Multiply 4 by the denominator and add 1:

29/7

Multiply 2 by seven (denominator) and add 6:

20/7

29/7 - 20/7 = 9/7

9/7 = 1 2/7

7 fits one time into nine and 2 is left.

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I provide detailed explanations for math questions for as little as $1!

PLEASE HELP I DONT GET THIS

Answers

Step-by-step explanation:

(a) yes it is answer.

i cheak it is true.

Solving systems of equations by substitution 2x - 3y = 19
x - 2y = 11​

Answers

Answer:

[tex]\boxed {\boxed {\sf (5, -3)}}[/tex]

Step-by-step explanation:

We are asked to solve the system of equations by substitution. We must isolate a variable and plug it into the other equation.

We are given these 2 equations;

[tex]2x-3y=19[/tex]

[tex]x-2y=11[/tex]

1. Isolate a Variable

We can easily isolate x in the 2nd equation. 2y is being subtracted from x. The inverse operation of subtraction is addition. Add 2y to both sides of the equation.

[tex]x-2y+2y=11 +2y \\x= 11+2y[/tex]

2. Substitute and Solve for y

x is equal to 11 + 2y, so we can substitute this expression in for x in the 1st equation.

[tex]2x-3y=19[/tex]

[tex]2(11+2y)-3y=19[/tex]

Now we can solve for y by isolating the variable First, distribute the 2. Multiply each term in parentheses by 2.

[tex](2*11) + (2*2y) -3y = 19[/tex]

[tex]22 + 4y-3y = 19[/tex]

Combine the like terms.

[tex]22+y=19[/tex]

22 is being added to y. The inverse operation of addition is subtraction. Subtract 22 from both sides of the equation.

[tex]22-22+y=19-22\\y= 19-22 \\y= -3[/tex]

3. Solve for x

We know that y is equal to -3, so we can plug it back into either original equation and solve for x. Let's use the 2nd equation.

[tex]x-2y=11[/tex]

[tex]x-2(-3)=11[/tex]

Multiply -2 and -3.

[tex]x+6=11[/tex]

6 is being added to x. The inverse operation of addition is subtraction. Subtract 6 from both sides of the equation.

[tex]x+6-6=11-6\\x=11-6 \\x=5[/tex]

We found that y=-3 and x=5. Coordinate points are written as (x,y), so the solution for this system of equations is (5, -3).

PLEASE HELP WILL MARK BRAINLIEST!! (THANK YOU)

Answers

The answers for the angles are
1=58
2=122
3=58

Answer:

1 - 58°

2 - 122°

3 - 58°

Step-by-step explanation:

Important notes:

• Vertical Angles Theorem - The angles that are opposite to each other on an intersection of 2 lines are always congruent.

• Linear Pair - The two angles that are formed when a straight line is split. Linear pairs are supplementary angles.

• Supplementary Angles - An angle pair whose total measure = 180°.

Angle 1 is supplementary to the angle with measure 122°.

So, ∡1 = 180 - 122.

∡1 = 58°

Based on the Vertical Angles Theorem, ∡1 ≅ ∡3, so ∡3 is also 58°.

Based on the Vertical Angles Theorem, ∡2 ≅ 122°, so ∡2 = 122°.

∡1 = 58°

∡2 = 122°

∡3 = 58°

What is the answer to this question?

Answers

Answer:

27 23/25

Step-by-step explanation:

Answer: 27 13/14
To make this more simple, we can separate the fractions into two parts.

We can start off with subtracting the mixed numbers; 43 - 15 = 28

We are now left with 1/2 - 4/7
The lowest common denominator is 14

So we do 1/2 x 7 and 4/7 x 2
7/14 - 8/14 = 1/14

28 - 1/14 is changed to 28/1 - 1/14
Again we have to find a common denominator so we times 28/1 by 14

392/14 - 1/14 = 391/14
Simplified, this is 27 13/14

find the area of a square with a side length of 1/5 in.

Answers

Answer:

.04 inches squared

Step-by-step explanation:

1/5 of an inch is .2

A = Length times Width

Since squares have 4 equal sides, its length is equal to its width.

0.2 times 0.2 = .04 in^[tex]^{2}[/tex]

Stella needs to make at least 8 cakes for a bake sale. A chocolate cake requires 5 cups of flour, and a fruit cake requires 3 cups of flour. She has at most 120 cups of flour.

Which system of inequalities represent the number of chocolate cakes (c) and the number of fruit cakes (f) Stella can make?
A.


B.


C.


D.

Answers

Answer:

A. c + f > 8

5c + 3f < 120

Step-by-step explanation:

Let c = chocolate cakes

Let f = fruit cakes

She must make at least 8 cakes

c+f ≥8

A chocolate cake requires 5 cups of flour, and a fruit cake requires 3 cups of flour and she has only 120 cups of flour

5c+3f ≤120

The two equations are

c+f ≥8

5c+3f ≤120

20) In the town of Eagle Pass, 5 out of 13 vehicles are trucks. What
percent of the vehicles are trucks? Round to the nearest tenth. *
48.5%
38.5%
24.5%
12.5%

Answers

Answer:

38.5%

Step-by-step explanation:

5/13=38.5.........

Answer:

38.5%

Step-by-step explanation:

1. 5 - 13 = 0.38461538461

2. 0.3846 [1538461] - take away most of the extra numbers

3. 0.3846

4. Round it to the nearest tenth - 0.385

5. Take your answer and times my 100 - 0.385 * 100 = 38.5

and make that into a percentage - 38.5%

What type of angle is shown below?



acute
straight
obtuse
right

Answers

acute, it is less than an 90 degree angle

Answer:

Acute

Step-by-step explanation:

So, straight would be a line, right would be like a corner of a square, acute would be less than a right, and obtuse would be more than a right but less than a straight.

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