For f(x)=3x+4 and g(x)=x^2 find the following composite functions and state the domain of each.

For F(x)=3x+4 And G(x)=x^2 Find The Following Composite Functions And State The Domain Of Each.

Answers

Answer 1

The composite functions are:

a) f ∘ g = 3x² + 4, with domain of all real numbers.

b) g ∘ f = 9x² + 24x + 16, with domain of all real numbers.

c) f ∘ f = 9x + 16, with domain of all real numbers.

d) g ∘ g = x⁴, with domain of all real numbers.

To find the composite functions, we need to substitute the function g into the function f or vice versa, depending on the order of composition. The resulting composite function will have a domain that is restricted by the domains of the individual functions involved.

a) To find f ∘ g, we substitute g(x) = x² into f(x) = 3x + 4:

f(g(x)) = 3g(x) + 4 = 3x² + 4

The domain of f ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.

b) To find g ∘ f, we substitute f(x) = 3x + 4 into g(x) = x²:

g(f(x)) = (3x + 4)² = 9x² + 24x + 16

The domain of g ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.

c) To find f ∘ f, we substitute f(x) = 3x + 4 into f(x) = 3x + 4:

f(f(x)) = 3f(x) + 4 = 3(3x + 4) + 4 = 9x + 16

The domain of f ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.

d) To find g ∘ g, we substitute g(x) = x² into g(x) = x²:

g(g(x)) = (x²)² = x⁴

The domain of g ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.

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Related Questions

A student wants to compare the amount of money that two local movie theaters make over a two-week period for the last nightly showing of a particular movie. The following box plots show the data for the amount of money each theater makes over the period. Compare the median of each box plot.

Answers

Answer:

mt1= 995

mt2=975

Step-by-step explanation:

the line inside the box plot shows where the median is.

HELP FAST!!! EASY ALEGRA 2!

Answers

log base 16, 32 can be written as log₂⁴ 2₅.

Evaluate with logₐx, write a and x as powers of same.

a) log₁₆ 64

= log₂⁴=2⁶

b) log₈₁ 27

= log₃⁴ 3³

c) log₁₆ 32

= log₂⁴ 2₅

d) log₂₇ 243

= log₃³ 3₅

Therefore, log base 16, 32 can be written as log₂⁴ 2₅.

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How do l do this please help me asap

Answers

Answer:

[tex] {z}^{2} - 10z + 9 = [/tex]

[tex](z - 1)(z - 9)[/tex]

The Ferris Wheel can carry 4 passengers in each of its 15 cars in one ride. How many passengers can it carry on a total of 35 rides?

Answers

The Ferris Wheel can carry 2100 passengers on a total of 35 rides.

According to the question,

Number of cars in the Ferry Wheel = 15

Number of passengers in each car = 4

∴ Number of passengers in 15 cars = 15×4 = 60

So, the number of passengers on the Ferry Wheel = 60

Now,

The number of passengers the Ferry Wheel carries in one ride = 60

∴ The number of passengers in 35 rides = 60×35 = 2100.

Hence the Ferris Wheel can carry 2100 passengers on a total of 35 rides.

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Workers in a Certain Company are require to pay 5.5% of their salary into a social Security fund. Mr. Mensah has monthly salary of Gld 4500.00 How much Will he pays each month to the Social Security fund.​

Answers

He will pay about 220 (rounding to nearest tens place)

Mr. Mensah will pay 247.5 each month to the social security fund because 5.5% of 4500 is 247.5.

The total monthly salary of Mr. Mensah is 4500.

He is required to pay 5.5% of his salary into a social security fund.

Now, we have to find the amount he has to pay each month into the social security fund.

To find that, we need to find the value of 5.5 percent of 4500.

4500 ×5.5/100

45×5.5

247.5

Therefore, 5.5% of 4500 is 247.5.

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Assertion: 7V5, V2+21 are the irrational number Reason: every integer is a rational number​

Answers

Assertion: Yes, √2 is an irrational number.

Reason: The decimal expansion of √2 is 1.41421356237 which is a non-recurring and non-terminating number.

How to solve

Both (A) and (R) are true and Reason (R) is the correct explanation of Assertion (A).

Assertion: Yes, √2 is an irrational number.

Reason: The decimal expansion of √2 is 1.41421356237 which is a non-recurring and non-terminating number.

All real numbers that are not rational numbers are referred to as irrational numbers in mathematics. In other words, it is impossible to describe an irrational number as the ratio of two integers.

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The Complete Question

Assertion (A): V2 is an irrational number. Reason (R) : Decimal expansion of an irrational number is non-recurring and non terminating???? a) Both (A) and (R) are true and Reason (R) is the correct explanation of Assertion (A) b) Both (A) and ( R) are true but Reason (R) is not a correct explanation of (A) c) Assertion (A) is true and Reason (R) is false d) Assertion (A) is false and Reason (R) is true​

If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?

Answers

If you look at the six numbers (101, 203, 407, 512, 98, 642) you can see they range from 98 all the way to 642. the best interval to use for this group be 100.

What is the range?

The right interval to utilize for this set of numbers depends on the aim of the analysis.

If we want to look on the single values and small differences between them, then using interval of 10 would be more better. This would give u room to see small changes that exist between adjacent numbers.

So,  in the event that we need to look on the full range and distribution of the numbers, an interval of 100 would be more better. This would permit us to see how the numbers are shared over a larger area of values.

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See full question below

If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?

101, 203, 407, 512, 98, 642

You roll a die 2 times. What is the probability or rolling a 6 and then a 2?

Answers

Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

Camping A guy rope is attached to the top of a tent pole. The guy rope is pegged into the ground 5 feet from the tent. If the guy rope is 11 feet​ long, how long is the tent​ pole?

Answers

Pythagorean theorem: a^2+b^2=c^2
5^2+x^2=11^2
x=the length of the tent pole
answer: 9.78

Mannys pay varies directly with the number of lawns he mows. He earns $100 for mowing 4 lawns. Find k in the equation for Mannys pay. Use P=kl

Answers

Answer:

10000

otra solución es: 10⁴

Can someone help me with this pls

Answers

Answer:

Subtract the powers, 8-4.

When you simplify that equation itself, the answer is 10,000.

So when you do 10⁴, it's 10,000.

Help please

Condense to a single logarithm is possible

In(6x^9)-In(x^2)

Answers

The logarithm expression can be simplified to:

In(6x^9)-In(x^2) =7·ln(6x)

How to write this as a single logarithm?

There are some logarithm properties we can use here.

log(a) - log(b) = log(a/b)

log(a^n) = n*log(a)

(these obviously also apply to the natural logarithm)

Now let's look at our expression, it says that:

In(6x^9)-In(x^2)

Using the first rule, we can rewrite this as.

In(6x^9)-In(x^2) = ln(6x^9/x^2)

Now solving the quotient in the argument:

ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)

That is the expresison simplified.

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In circle e, Ed =4 and m/FEG = 45 find the area of shaded sector express your answer as a fraction time pi

Answers

The area of the sector is 2π/1

How to determine the area

The formula for calculating the area of a sector is expressed as;

A = θ/360 πr²

Given that the parameters are;

A is the area of the sector.θ takes the value of the angle.π takes the constant value of 3.14r is the radius of the circle

From the information given, we have that;

The angle = 45 degrees

radius, r = 4

Substitute the values, we have;

Area = 45/360 × π × 4²

Divide the values

Area = 3/ 24 × π × 16

Multiply the values, we have;

Area = 48π/24

Divide the values, we have;

Area = 2π/1

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Can you help me with this question?

Answers

Answer:

C

Step-by-step explanation:

It mentions that they charge 1.20 per kg of lettuce

(2x+1)^2 +(4x-4)^2 = (4x-1)^2

Answers

The quadratic equation is solved and the solution is x = 1 and x = 4

Given data ,

Let's expand the left-hand side of the equation:

(2x+1)² + (4x-4)²

= (2x)² + 2(2x)(1) + 1² + (4x)² - 2(4x)(4) + 4² (using the formula for the square of a binomial)

= 4x² + 4x + 1 + 16x² - 32x + 16

= 20x² - 28x + 17

Now let's expand the right-hand side of the equation:

(4x-1)²

= (4x)² - 2(4x)(1) + 1²

= 16x² - 8x + 1

Now we can set the left-hand side equal to the right-hand side and simplify:

20x² - 28x + 17 = 16x² - 8x + 1

4x² - 20x + 16 = 0

x² - 5x + 4 = 0

(x - 1)(x - 4) = 0

Hence , the solution is x = 1 and x = 4

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Help me please, this assignment is alr past due

Answers

Answer:

Step-by-step explanation:

However many decimals you move to get 1 after the first number that is not 0 is what goes in the exponent.  Negative version because to get to a decimal you move in the negative direction.

.1  =  1.0 x [tex]10^{-1}[/tex]

.01 = 1.0 x [tex]10^{-2}[/tex]

.001 = 1.0 x [tex]10^{-3}[/tex]

.000001  =,1.0 x [tex]10^{-6}[/tex]

will mark brainliest

Answers

Answer:

$74.66

Step-by-step explanation:

Plot the points on the graphing calculator (x = length of HDMI cord, y = cost). Then generate a linear regression model:

y = 3.68x + 1.06 (approximately)

x = 20, so y = 74.66

$74.66 is the correct answer.

Select the reason that best supports Statement 5 in the given proof.

Answers

Where is the given proof

The bells obtain a 30-year, $90,000 conventional mortgage at a 10.0% rate on a house selling for $120,000. Their monthly mortgage payment, including principal and interest, is $783.00. They also pay 2 points at closing.
A)What is total amount the Bells will pay for their house.
B) How much of the cost will be interest (including the 2 points)?
C) How much of the first payment on the mortgage is applied to the principal?

Answers

The total amount that the Bells will pay for their house would be $313, 680.

The cost that would be interest is $193, 680

The amount of the first payment going to mortgages is $165. 24

How to find the total amount paid ?

Find the down payment :

Down payment = House price - Mortgage amount = $120,000 - $90,000 = $30,000

Then the points paid at closing :

= $ 90,000 x 0. 02 = $1,800

Total amount paid = Total mortgage payments + Down payment + Points cost

= 281, 880 + 30, 000 + 1, 800

= $ 313, 680

The total that is interest is:

Total interest paid = Total interest paid through monthly payments + Points cost

Total interest paid = $ 191, 880 + $ 1, 800 = $193, 680

The amount of the first payment going to principal is:

Principal portion of first payment = 90, 000 - 89, 834.76 = $165. 24

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In 2015, there were roughly 1 x 10° high school football players and 2x 10° professional football players in the United States. About how many times more high school football players were there?​

Answers

The number of times more high school football players were there is 500.

Given that, in 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States.

Here, the number of times more high school football players were there

= 1×10⁶/2×10³

= 1×10³/2

= 1000/2

= 500

Therefore, the number of times more high school football players were there is 500.

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"Your question is incomplete, probably the complete question/missing part is:"

In 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States. About how many times more high school football players were there?​

I need help pleaseeee

Answers

(a) The value of the row operation of -2(row1) + row (2) is [-10     4    -12].

(b) The interchange of row 1 and row 2 is  [0     6    -3]

                                                                       [5    -2     6]

What is the row operation of the matrix?

The value of the row operation of -2(row1) + row (2) is calculated as follows;

-2 (row 1) = 2 [5   -2    6]

-2 (row 1) = [-10     4    -12]

The addition of -2(row1) to row (2) is calculated as follows;

[-10     4    -12] + [0    6    -3]

= [-10   10  - 15]

The interchange of row 1 and row 2 is calculated as follows;

R₁ ↔ R₂

= [5    -2     6]    =   [0     6    -3]

  [0     6    -3]         [5    -2     6]

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Find the slope of the line that passes through the given points.
​(−1​,−1​) and ​(3​,−4​)

Answers

Answer: [tex]\frac{-3}{4}[/tex]

Step-by-step explanation:

   To find the slope of the line, we will use change in y over change in x.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} } =\frac{-4--1}{3--1} =\frac{-4+1}{3+1} =\frac{-3}{4}[/tex]

. When completed, the Crazy Horse Monument in South Dakota will be 563 ft high. The monument is based on a 16-foot-tall scale model of the structure. What is the scale used in the construction?​

Answers

Based on the information, we identified that the scale used in the construction is approximately 1:35.2.

How to find the scale?

To find the scale used in the construction of the Crazy Horse Monument, we need to divide the height of the actual monument by the height of the model. Let's use the following formula to calculate the scale:

scale = (height of actual monument) / (height of scale model)

The height of the actual monument is 563 feet and the height of the scale model is 16 feet. Substituting these values in the formula, we get:

scale = 563 feet / 16 feet

Simplifying the fraction, we get:

scale = 35.1875

Therefore, the scale used in the construction of the Crazy Horse Monument is approximately 1:35.2.

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A major credit card company is interested in whether there is a linear relationship between its internal rating of a customer’s credit risk and that of an independent rating agency. The company collected a random sample of 200 customers and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim.

H0:β1=0Ha:β1≠0


The test yielded a t
t
-value of 3.34 with a corresponding p
p
-value of 0.001. Which of the following is the correct interpretation of the p
p
-value?

Answers

The correct interpretation of the p-value is 3.34.

We are given that;

t-value=3.34

Number of customers= 200

Now,

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming that the null hypothesis is true. In this case, the p-value of 0.001 means that there is a 0.1% chance of getting a t-value of 3.34 or higher (or -3.34 or lower) if the true slope of the linear relationship between the two ratings is zero. The p-value is very small, which indicates that the data provide strong evidence against the null hypothesis and in favor of the alternative hypothesis.

The p-value of 0.001 means that there is a 0.1% chance of getting a t-value of 3.34 or higher (or -3.34 or lower) if there is no linear relationship between the two ratings.

Therefore, by probability the answer will be 3.34

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Samantha is designing a new three-dimensional puzzle in the form of a square pyramid. She knows that the design and the general formula for finding the volume are as follows, where h is the height and a is the side length of the base. All of her measurements are in centimeters.

An illustration of a pyramid, with the height of h and width a.

Samantha's puzzle must have a certain volume and height, but she needs to determine the side length of the base to complete the design. Which equation can Samantha use to find the side length of the base in terms of the volume and height of her puzzle?

Answers

An equation which Samantha can use to find the side length of the base in terms of the volume and height of her puzzle is: A. a = √(3V/h)

How to calculate the volume of a square pyramid?

In Mathematics and Geometry, the volume of a square pyramid can be calculated by using the following formula:

Volume of a square pyramid, V = 1/3 × a² × h

Where:

h represent the height of a square pyramid.a represent the side length of the base of a square pyramid.

By making "a" the subject of formula, the side length of the base of a square pyramid can be determined as follows;

V = 1/3 × a² × h

3V = a²h

a² = 3V/h

By taking the square root of both sides of the equation, we have:

a = √(3V/h)

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X 2 3 4 5 6 p(x=x) find the value of p(x>3)

Answers

From the given data, we have:

| x   | 2   | 3   | 4   | 5   | 6   |

| --- | --- | --- | --- | --- | --- |

| p(x) |    |    |    |    |    |

We need to find the value of p(x > 3).

We know that the sum of all the probabilities is equal to 1. So, we can find the missing probability by subtracting the sum of the probabilities we know from 1.

p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = 1

We don't know the value of p(x = 2), so we can't directly calculate p(x > 3). But we can find p(x ≤ 3) and subtract it from 1 to get p(x > 3).

p(x ≤ 3) = p(x = 2) + p(x = 3)

To find p(x = 2), we can use the fact that the sum of all the probabilities is 1:

p(x = 2) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6))

Now we can substitute this into the equation for p(x ≤ 3) and solve:

p(x ≤ 3) = p(x = 2) + p(x = 3)

p(x ≤ 3) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6)) + p(x = 3)

p(x ≤ 3) = 1 - (p(x = 4) + p(x = 5) + p(x = 6))

Finally, we can subtract p(x ≤ 3) from 1 to get p(x > 3):

p(x > 3) = 1 - p(x ≤ 3)

p(x > 3) = 1 - (1 - (p(x = 4) + p(x = 5) + p(x = 6)))

p(x > 3) = p(x = 4) + p(x = 5) + p(x = 6)

Therefore, the value of p(x > 3) is the sum of the probabilities for x = 4, 5, and 6.

A principal of $3900 is invested at 4.25% interest, compounded annually. How much will the investment be worth after 5 years?

Answers

If principal of $3900 is invested at 4.25% interest, compounded annually, the investment will be worth approximately $4,756.89 after 5 years.

To calculate the future value of the investment, we use the formula for compound interest:

A = [tex]P(1 + r/n)^{(n*t)[/tex]

where A is the future value, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $3900, r = 4.25%, n = 1 (compounded annually), and t = 5. Plugging these values into the formula, we get:

A = 3900(1 + 0.0425/1)⁵

A = 3900(1.0425)⁵

A ≈ $4,756.89

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Please help! Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5
z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2

Answers

Daniel incorrectly applied the square root to both terms on the left side of the equation and he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.

Let's first look at the first equation that Daniel solved incorrectly:

25x²-16=9

Daniel's solution:

√(25x² )-√16=√9

5x-4=±3

5x=±7

x=±7/5

What Daniel did wrong here is that he incorrectly applied the square root to both terms on the left side of the equation.

Instead, he should have simplified the left side first, using the fact that √(a²) = |a|, before applying the square root. So the correct solution is:

25x²-16=9

25x²=25

x²=1

x=±1

Now let's look at the second equation that Daniel solved incorrectly:

z³-2=6

Daniel's solution:

z³=8

∛(z^3 )=∛8

z=±2

What Daniel did wrong here is that he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.

In fact, z³ = 8 has three roots: z = 2, z = -1 + i√3, and z = -1 - i√3. So the correct solution is:

z³-2=6

z³=8

z=2

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22 randomly picked people were asked if they rented or owned their own home, 9 said they rented. Obtain a point estimate of the proportion of home owners. Use a 95% level of confidence.
point

Answers

Answer:

True proportion of homeowners in the population lies between 0.333 and 0.847

Step-by-step explanation:

If 9 out of 22 randomly picked people said they rented their homes, then the remaining 13 must own their homes. Therefore, the point estimate of the proportion of homeowners is:

Point estimate = Number of homeowners / Total number of people surveyed

Point estimate = 13 / 22

Point estimate = 0.59 (rounded to two decimal places)

To calculate the 95% confidence interval for the true proportion of homeowners, we can use the following formula:

Confidence interval = Point estimate ± (Z-value x Standard error)

where the Z-value corresponds to the desired level of confidence and the standard error is given by:

Standard error = sqrt [ (Point estimate x (1 - Point estimate)) / Sample size]

For a 95% confidence interval, the Z-value is 1.96 (from the standard normal distribution). Using the point estimate obtained earlier, the sample size is 22, and we can calculate the standard error as:

Standard error = sqrt [ (0.59 x 0.41) / 22 ]

Standard error = 0.131 (rounded to three decimal places)

Substituting these values into the formula, we get:

Confidence interval = 0.59 ± (1.96 x 0.131)

Confidence interval = 0.59 ± 0.257

Confidence interval = (0.333, 0.847)

Therefore, with 95% confidence, we can say that the true proportion of homeowners in the population lies between 0.333 and 0.847.

NO LINKS!! URGENT HELP PLEASE!!

This prism has a right angle for a base.
What is the volume of the prism?

Explain your thinking

Answers

Answer:

48 unit cube

Step-by-step explanation:

Solution Given:

For Triangle ABC

hypotenuse AB= 5

base AC=4

By using hypotenuse law

height BC=[tex]\sqrt{5^2-4^2} =3[/tex]

Now Area of the right-angled triangle is 1/2 * base*height

=1/2*AC*BC=1/2*4*3=6 units square

As we know that

The volume of triangular prism: Area of base * height

over here Area of the base= Area of the Triangle and the height is the length of the prism

=6 units square*CF

=6 units square*8

=48 unit cube

Answer:

The volume of the given prism is 48 cubic units.

Step-by-step explanation:

The volume of a prism can be calculated by multiplying the area of its base by its height.

The bases of the given prism are the congruent right triangles ABC and DEF.

We have been given the measures of sides AB and AC of triangle ABC.

To determine the area of ΔABC, we first need to calculate the measure of side BC using Pythagoras Theorem:

[tex]\implies AC^2+BC^2=AB^2[/tex]

[tex]\implies 4^2+BC^2=5^2[/tex]

[tex]\implies 16+BC^2=25[/tex]

[tex]\implies BC^2=9[/tex]

[tex]\implies BC=3[/tex]

The area of a triangle is half the product of its base and height.

The base and height of a right triangle are its legs.

[tex]\begin{aligned}\textsf{Area of base}&=\textsf{Area of $\triangle ABC$}\\\\&=\dfrac{1}{2} \cdot BC \cdot AC\\\\&=\dfrac{1}{2} \cdot 3 \cdot 4\\\\&=6\; \sf square\;units\end{aligned}[/tex]

Therefore, the area of the base of the prism is 6 square units.

Finally, to find the volume of the prism, multiply the area of the base by the height of the prism:

[tex]\begin{aligned}\textsf{Volume of prism}&=\textsf{Area of base} \cdot \sf height\\\\&=\textsf{Area of $\triangle ABC$} \cdot \overline{CF}\\\\&=6 \cdot 8\\\\&=48\; \sf cubic\;units\end{aligned}[/tex]

Therefore, the volume of the given prism is 48 cubic units.

Other Questions
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