Find the inverse function for:
f(x) = 2x^3 - 3

According to the question, the given rational expression can be simplified which is shown below:

Rational expression = [tex](\frac{x^{2}+8x+7}{x^{2} -x-12)} /(\frac{x^{2} +2x-8}{x^{2} +13x+24} )[/tex]

To simplify the given rational expression which is also an polynomial expression by the method of factors rule. Performing factors on numerator as well as on denominator. And later divide them with each other.

Rational expression = [tex](\frac{(x+7)(x+1)}{(x-4)(x+3)}) /(\frac{(x+4)(x-2)}{x^{2} +13x+24} )[/tex]

The factors of the denominator term is not possible. Therefore, the given expression cannot be simplified.

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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Step-by-step explanation:

the vertex form is

y = a(x - h)² + k

a is a stretch factor, (h, k) are the coordinates of the vertex of the parabola.

so, the original x-coordinate of the vertex was 4.

when we move it 6 units to the left. we subtract 6 from the x-coordinate.

that makes the new h

4 - 6 = -2

answer B is correct.

and the equation of the translated function is

g(x) = -3(x + 2)² + 5

Answer: 53

Given, expression:

Given values: a = -2, b = 5, c = -3

Substitute them inside the expression:

distribute

evaluate

simplify

Answer:

4*12=48

48*8=384

384 square inches

Answer:

5004300

Step-by-step explanation:

This number is already in standard form, but I can help if you want it in scientific notation, etc.

Answer:

[tex] <por = x \: \: \: < ros = \beta \: \: \: pos = \gamma [/tex]

The inverse function returns the original value for which the output of a function was given.

The inverse the function y = 2x + 1 is [tex]y^{-1[/tex] = x + 1/ 2.

Every logarithmic function has an exponential inverse, and vice versa.

An exponential function is a mathematical function with the formula f(x) = ax, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero.

The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.

Let the equation be y = 2x + 1

y = 2x + 1

simplifying the equation, we get

⇒ 2x = y+1

⇒ x = y+1/ 2

Therefore, the inverse is [tex]y^{-1[/tex] = x+1/ 2

Let the composition function be

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

simplifying the above equation

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

[y ₀ [tex]y^{-1[/tex]] (x) = x

The inverse of y is the image of y in the line y = x.

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It should be noted that the square root and the cube root of the number has been attached.

It should be here that the cube root of a number is the factor that we multiply by itself three times in order to get the original number.

It should be noted that thee symbol for cube root is 3✓ . Finding the cube root of a number is the opposite of cubing a number.

On the other hand, the square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.

It shouod be noted that for example, 4 and −4 are square roots of 16, because 4² = ² = 16.

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The number of bowling games played for $34 is 8

The  mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by linear equation y = 3.50x + 6.00

We are given that total money spent is $34

The number of bowling  games played is assumed to be x

Now, we have substitute the value of y in the linear equation to get number of bowling  games played

34 = 3.50x +6.00

34 - 6 = 3.50 x

28 = 3.5x

x = 28/ 3.5

x = 8

So, the number of bowling games played for $34 is 8

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Answer:

-18 + 30 s - 72 t + 12 u

Step-by-step explanation:

Expand the following:

-6 (3 - 5 s + 12 t - 2 u)

-6 (3 - 5 s + 12 t - 2 u) = -6×3 - 6 (-5 s) - 6×12 t - 6 (-2 u):

-6×3 - 6 (-5) s - 6×12 t - 6 (-2) u

-6×3 = -18:

-18 - 6 (-5) s - 6×12 t - 6 (-2) u

-6 (-5) = 30:

-18 + 30 s - 6×12 t - 6 (-2) u

-6×12 = -72:

-18 + 30 s + -72 t - 6 (-2) u

-6 (-2) = 12:

Answer:  -18 + 30 s - 72 t + 12 u

Answer:

270

Step-by-step explanation:

With a 270 rotation you move 3 boxes

Answer:

f(n + 3) = 3n + 13

Step-by-step explanation:

f(x)=3x+4 then f(n+3)=

f(n + 3) = 3(n + 3) + 4

f(n + 3) = 3n + 9 + 4

f(n + 3) = 3n + 13

I hope this helps!

The average speed of car is 14.4 m/s.

We can see that from Photo 1 to Photo 2, the car covers 9 times the 0.8 meter distance. So, calculating the total distance traveled between the time span second photo was clicked.

Total distance traveled = 0.8×9

Performing multiplication

Total distance traveled = 7.2 meters

Now, the time is given as 0.5 seconds.

Finding the average speed using formula -

Average speed = total distance traveled ÷ total time taken

Keep the given values in formula to find the average speed.

Average speed = 7.2 ÷ 0.5

Performing division

Average speed = 14.4 m/s

Hence, the average speed of the car is 14.4 m/s

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The complete question is attached in figure.

Answer:

75

Step-by-step explanation:

In math, mode is the number which appears most in the data set. When dealing with this, first put all of the numbers in numerical order, least to greatest.

19, 28, 31, 36, 44, 48, 55, 59, 68, 75, 75, 82, 93

Notice how 75 appear twice and all the other numbers appear once. Therefore the mode is 75.

The linear equation of the graph is y = x - 5

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (1, -4) and (5, 0)

Calculate the slope (m) using

m = (y2 - y1)/(x2 - x1)

So, we have

m = (0 + 4)/(5 - 1)

Evaluate

m = 1

The equation is then calculated as

y = m(x - x1) + y1

So, we have

y = 1 * (x - 5) + 0

Evaluate

y = x - 5

Hence, the linear equation of the graph is y = x - 5

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The solution for the x for the inequality ||3x −1|+5| <1 is x<7/3

In the given problem basically, ||3x −1|+5| <1, we are dealing with the absolute value, which for real numbers is referred to as the non-negative value of that number without regard for consideration to its sign. Denoted by the symbol "| |', it is also known as the modulus of the number, and also with the inequality, which is a non-equal comparison between two numbers, additional mathematical expressions.

the inequality equation we got is ||3x-1|+5|<1

now we are taking the absolute value of it, we get

=>3x + 1 + 5 < 1

subtracting 1, and 5 from both sides, we get

=>3x < 1 + 5 + 1

=>3x < 7

=>x < 7/ 3

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The 50% probability that a student chosen randomly from the class does not play a sport.

According to the statement

We have to find that the probability.

So, For this purpose, we know that the

Probability is that the branch of mathematics that studies the possible outcomes of given events along with the outcomes' relative likelihoods and distributions.

From the given information:

In a class of scholars, the subsequent data table summarizes what percentage students play an instrument or a sport.

Then

In total, there are 8 + 7 + 3 + 12 = 30 students.

And Of this total, 3 + 12 = 15 don't play a sport.

Then

Probability = 15/30

Probability = 0.5

Then

50% probability that a student chosen randomly from the class does not play a sport.

So, The 50% probability that a student chosen randomly from the class does not play a sport.

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The complete representation of the expression is 7/ 10^-1 = 7 x 10^1

Index forms are simply defined as the exponent or power of a number raised to a variable or number.

It is known as the standard form of a number.

It is also known as the exponential representation of an expression or number .

Example;

The index form of 200 is 2 × 10^2

The index form of 40 is 4 × 10 ^1

Given the expression;

7/10-  = 7x10^

We have;

7/ 10^-1 = 7 x 10^1

Thus, the complete representation of the expression is 7/ 10^-1 = 7 x 10^1

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Answer: $86.67

Step-by-step explanation:

34 x 7% OR 34 x .07 = 2.38

Skirt = $36.38

47 x 7% = 3.29 47+3.29 = 50.29

50.29+36.38=86.67

Answer:

2.61625

Step-by-step explanation:

The function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the y axis is (x, y) ⇒ (x + 4, -y)

Transformation is the movement of a plane figure from one point to another. Transformation may also be an increase / decrease in the size of the figure. Examples of transformation are reflection, rotation, translation and dilation.

Dilation is the increase or decrease in size of a figure by a scale factor.

The function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the y axis is (x, y) ⇒ (x + 4, -y)

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Answer:

Step-by-step explanation:

The exponential function for to represent the balance of the account will be y = 14 ( 1.16) ˣ

We have that:

The saving account has initially = $ 14

After 1 year, the balance became = $ 16.24

After 2 years, the balance became = $ 18.84
Difference in the initial amount and amount after 1 year = $ 16.24 - $ 14 = $ 2.24

Difference in the amount after 1 year and amount after 2 years = $ 18.84 - $ 16.24 = $ 2.60.

An exponential function is defined as y = a ˣ where x is a variable, and a is a constant called the base of the function.

Here, the exponential function will be:

y = 14 ( 1.16) ˣ where x is the time period

Money after 20 years = 14 ( 1.16)²⁰ = $ 272.45

Therefore, we get that, the exponential function for to represent the balance of the account will be y = 14 ( 1.16) ˣ

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Answer:

no

Step-by-step explanation:

half of 250k would be 125k and if you add that to 250k that would be 375k

Answer:

y=2880x+26500

Step-by-step explanation:

Basically, this question wants you to write an equation where you can figure out how much money Tony has at any year.

1. They already told us how much the raise was: $2880

2. He started off with $26,500, so we know we have to add that at the beginning. That is our y-intercept.

3. A function is written as y=mx+b. Y is what you are solving for. M is the constant change (x doesn't mean anything, it just tells us which number is m). B is the y-intercept, which is 26,500 in this case. Its what you are starting with. If he had no money, there would be nothing to start with. There would be no y-intercept.

4. Because he gets the same raise every year of 2880, that is constant. It does not change, but it increases constantly.

5. So, y=2880x+26500 is your answer.

x = 9 is not an extraneous solution of the equation.

√x=√(x-8) + 2

Squaring both the sides of the equation, we get

(√x)² = (√(x-8)+2)²

x = (✓(x - 8))² + 2² + 2(✓(x - 8))(2)

x = x - 8 + 4 + 2(✓(x - 8))(2)

Subtracting x on both the sides of the equation, we get

- 4 + 2(✓(x - 8))(2) = 0

Adding 4 on both the sides of the equation, we get

4(✓(x - 8)) = 4

Dividing both sides of the equation by 4, we get

(✓(x - 8)) = 1

Squaring again on both the sides of the equation

x - 8 = 1

x = 9

Check for extraneous solution by putting the value of x = 9 in the original equation, we get

✓9 = ✓(9 - 8) + 2

✓9 = ✓1 + 2

3 = 1 + 2

3 = 3

⇒ LHS = RHS

∴ x = 9 is not an extraneous solution of the equation.

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When the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set.

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

From the number line in the question, we can see that:

As a general rule, open circles implies that the number at that endpoint is not included part of the solution set.

Hence, the complete statement is "when the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set."

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