Help please this is pre calculus

For the given function f(x) = x²-16 , the inverse of the function if the domain f(x) is x> 0 is equal to f⁻¹(x) = √x+16.

As given in the question,

Given function is equal to:

f(x) = x²-16

To calculate the inverse of the function if the domain f(x) is x> 0,

Let us consider f(x) = y

y = x²-16

⇒ x² = y + 16

⇒ x = √y + 16

Now, replace x by f⁻¹(x) and y by x we get,

f⁻¹(x) = √x+16

Therefore, for the given function f(x) = x²-16 , the inverse of the function if the domain f(x) is x> 0 is equal to f⁻¹(x) = √x+16.

The complete question is:

Which function is the inverse of f(x)=x²-16 if the domain of f(x) is x> 0?

a. f⁻¹(x) = √x+16

b.  f⁻¹(x) = √x + 4

c.  f⁻¹(x) =  √x -16

d.  f⁻¹(x) =  √x - 4

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a) The value of (g/f)(-3) is  -1/2

b)  -5 and -2 are the values that are not in the domain of g(x)/f(x)

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

g(x)=x+4

f(x)=(x+5)(x+2)

a) g(x)/f(x) = (x+4)/ (x+5)(x+2)

(g/f)(-3) = (-3+4)/(-3+5)(-3+2)

            = 1/(2*-1)

           = 1/-2

           = -1/2

b)  

Set denominator to zero

(x+5)(x+2) = 0

=> (x+5)=0 or (x+2)=0

=> x = -5 and x=-2

=> -5 and -2 are the values that are not in the domain of g(x)/f(x)

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Answer: 17/25

Step-by-step explanation:

This equals 68%, which equals 68/100.

Let's divide both sides by 2.

68/2 = 34

100/2 = 50

This gives us 34/50.

We can simplify even more!

34/2 = 17

50/2 = 25.

This gives us 17/25.

We can no longer simplify, which means 17/25 is our final answer.

The four sided figure formed by opposite pairs of parallel lines is called a parallelogram.

In the attached figure we can see that the quadrilateral ABCD has the following aspects:

AB || CD

AD || BC

Which states that the opposite sides are parallel.

Now ∠A + ∠B = 180° co interior angles are supplementary.

Therefore , ∠A = 180° - ∠B

Again ∠C + ∠B = 180° co interior angles are supplementary.

And , ∠C= 180° - ∠B

Therefore from the above two statements we can say that  ∠C = ∠B.

A unique sort of quadrilateral made up of parallel lines is called a parallelogram. According to definition, a parallelogram is a shape with opposite sides that are parallel and any angle between the sides on each side.

If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. If both pairs of opposite sides of a quadrilateral remain parallel and equal, the shape is referred to as a parallelogram.

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Springfield's population in the year 2026, based on the population in 2019, and the growth rate, would be 251, 940 people

As at the year 2019, the population of Springfield was estimated to have been 202, 628 people. This number is also growing by the year, at a rate of 0. 81%.

This means that in the year 2046, the population of Springfield can be estimated using the future value formula which is:

= Current population x ( 1 + population growth rate) ^ number of years

Find the number of years as:

= 2046 - 2019

= 27 years

The population would be:

= 202, 628 x ( 1 + 0.81 % ) ²⁷

= 251, 940 people

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Answer:

BGHA

Step-by-step explanation:

Just look at the coordinates.

1 is at x=0 and y=4, so (0, 4), or B

2 is at x=-4 and y=3, so (-4, 3), or G

3 is at x=2 and y=0, so (2, 0), or H

4 is at x=0 and y=-1, so (0, -1), or A

Answer:

1. [tex]\frac{3}{7}[/tex] × [tex]\frac{4}{5}[/tex] = [tex]\frac{12}{35}[/tex]

2. [tex]2\frac{6}{8}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{11}{4}[/tex] × [tex]\frac{2}{3}[/tex]

             = [tex]\frac{11}{6}[/tex]

             = [tex]1\frac{5}{6}[/tex]

3. [tex]\frac{12}{5}[/tex] ÷ [tex]\frac{3}{7}[/tex] = [tex]\frac{12}{5}[/tex] × [tex]\frac{7}{3}[/tex]

             = [tex]\frac{28}{5}[/tex]

             = [tex]5\frac{3}{5}[/tex]

4. [tex]\frac{8}{18}[/tex] ÷ [tex]\frac{4}{6}[/tex] = [tex]\frac{8}{18}[/tex] × [tex]\frac{6}{4}[/tex]

             = [tex]\frac{2}{3}[/tex]

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be [tex]1800(1.6)=\$ 2880[/tex].

Thus, each ticket must sell for [tex]\frac{2880}{5000}=\$ 0.576[/tex]

EAnswer:her son is eight

Step-by-step explanation:

To see the graph in the below attachment. The graph of inequality is      x > -6 .

Given,

In the question:

The inequality is given as:

-4(x + 3) ≤ -2x

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Now, According to the question:

Solution set of inequality -4(x + 3) ≤ -2x

-4(x + 3) ≤ -2x

Apply the Distributive property :

-4x - 12 < -2x

Rearrange the variables:

-4x + 2x < 12

Combine like terms:

-2x  < 12

Divide both sides:

x > -12/2

Cross out the common factor:

x > -6

Hence, To see the graph in the below attachment. The graph of inequality is x > -6 .

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The measure of the second largest angle in (6x-17) (4x-12) (2x+5) is 56°.

It should be noted that the value of the angle in a triangle is equal to 180°. Therefore, we will add the angle and add them to equate 180°

This will be:

(6x-17) + (4x-12) + (2x+5) = 180

6x - 17 + 4x - 12 + 2x + 5 = 180

12x -24 = 180

Collect like terms

12x = 180 + 24

12x = 204

Divide

x = 204 / 12

x = 17

First angle = 6x - 17 = 6(17) - 17 = 85°

Second angle = 4x - 12 = 4(17) - 12 = 68 - 12 = 56°

Third angle = 2x + 5 = 2(17) + 5 = 39°

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She will have to pay 1,500

Answer:

n = 49

Step-by-step explanation:

We can find the value of n by completing the square.  The general form of the quadratic equation is ax^2 + bx + c and the formula for completing the square is (b / 2)^2.  

In the question, -14 is the b value so we can do:

[tex](-14/2)^2=(-7)^2=49[/tex]

The range of the function y= [tex]x^2-4[/tex] is (-4,∞)

What is range?

 The set of every output from a function is its range. Example: Let's have a look at the function f: AB, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range.

Here the given function is ,

=> y= [tex]x^2-4[/tex]
Now we know that x>0

Then , square on both sides

=> [tex]x^2[/tex] > 0 now add -4 thwn ,

=> [tex]x^2[/tex] -4> -4

=> y > -4

We note that value of y is greater than -4 , (not including -4)

Then range of the function is ,

=> (-4,∞)

Hence the range of the function is (-4,∞).

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Answer:

x = y + 5

Step-by-step explanation:

The difference is 5, while x is the bigger number and y the smaller number. So you have to add 5 to y to get x.

52.7gk. 1mok/39.1gk= 1.347 mol k/1133y=1 kci

The vertical line intercept the the graph more than once, the graph is of a relation but it is not a function

Hence, the vertical line intercept the the graph more than once, the graph is of a relation but it is not a function.

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Answer:

C or third option

Step-by-step explanation:

The compound interest rate is 54.23% for investment that triples in 2 years.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is calculated by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

A = P (1 + r/4)4t

Given investment triples in 2 years

3p = [tex]e^{rt}[/tex]

rt = ln(3)

r = ln(3)/2 = 0.54

Which is 54.23%

Hence the interest rate is 54.23% for investment that triples in 2 years.

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Answer:

x = -4.5

Step-by-step explanation:

[tex]20 = 2 - 4x[/tex]

[tex]18 = - 4x[/tex]

[tex] - 4.5 = x[/tex]

The solution set of the inequalities given in the task content is described as; (-infinity, -17) U [ -9, infinity).

It follows from the task content that the solution set containing values of w which render the pair of inequalities true be determined.

On this note, since the inequalities given are;

-14 > w + 3 or 3w ≥ -27

By solving the inequalities individually; we have;

-14 > w + 3

Subtract 3 from both sides of the equation so that we have;

-14 - 3 > w; Therefore, -17 > w.

Also, 3w ≥ -27

Therefore; w ≥ -9.

On this note, it follows that; w < -17 or w ≥ -9.

Consequently, the solution set of the inequalities can be represented using interval notation as;

(-infinity, -17) U [ -9, infinity)

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Answer: 100 x 1.05^(15x12) = $651739.184097

Step-by-step explanation:

Step-by-step explanation:

a line with undefined slope is a vertical line, because x does not change on this line at all, and therefore the shoe is y/0.

a vertical line is parallel to the y-axis.

and to go through the given point, it has to use the x- coordinate.

so, the equation is

x = -5

that's really it.

this is the line of all points with the x-coordinate = -5. any value for y is valid.