Select the correct answer from each drop-down menu. Max used these steps to find the inverse of function f. Step 1 given Step 2 change to y Step 3 switch x and y Step 4 add to each side Step 5 multiply each side by Step 6 replace y with Use this information to complete the statement.

Answer:

121

Step-by-step explanation:

Given

f(x) = - (x + 8)(x - 14) ← expand factors using FOIL

     = - (x² - 6x - 112) ← distribute by - 1

     = - x² + 6x + 112

Given a quadratic in standard form. y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

f(x) = - x² + 6x + 112 ← is in standard form

with a = - 1 and b = 6, thus

\(x_{vertex}\) = - \(\frac{6}{-2}\) = 3

Substitute x = 3 into f(x) for corresponding value of y

f(3) = - (3)² + 6(3) + 112 = - 9 + 18 + 112 = 121

vertex = (3, 121 ) ← with y = 121

Answer:

D. 121

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

9x−7y=14

To find the x intercept set y = 0 and solve for x

9x = 14

Divide by 9

9x/9 = 14/9

x = 14/9

(14/9 ,0)

To find the y intercept set x = 0 and solve for y

-7y = 14

Divide by -7

-7y/-7 = 14/-7

y = -2

(0,-2)

Answer:

x = -7

Step-by-step explanation:

-30 = 5(x+1)

First, multiply out the 5

-30 = 5x + 5

Then subtract 5 from each side

-35 = 5x

Finally, divide each side by 5

-7 = x

Answer:

x = -7

Step-by-step explanation:

-30 = 5 (x + 1)

5 x -6 = -30

so x + 1 needs to equal -6

-7 + 1 = -6

so x = -7

-30 = 5(-7 + 1)

Answer:

Perimeter of rectangle 1=4x+4

Perimeter of rectangle 2=4x+4

Step-by-step explanation:

Two squares with the same dimension

Square 1: let length=x

Square 2: let length=x

Since they have same dimensions

He added two inches to the length of square 1 to make it a rectangle

Rectangle 1: width=x, length=x+2

Perimeter=2(l+w)

=2{(x+2)+x}

=2(x+2+x)

=2(2x+2)

=4x+4

He added two inches to the width of square 2 to make it a rectangle

Rectangle 2: length=x, width=x+2

Perimeter=2(l+w)

=2{(x+(x+2)}

=2(x+x+2)

=2(2x+2)

=4x+4

The two rectangles have equal perimeter

Answer: a prediction of the number of hot cocoas sold when the temperature is 0F

Step-by-step explanation: i did it on delta math

The line's y-intercept represent ''Number of hot cocoas sold''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Chloe has a part-time job at an ice skating rink selling hot cocoa.

She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Now,

Since, She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Hence, By the graph we have;

The line's x - intercept represent ''Temperature''.

And, The line's y-intercept represent ''Number of hot cocoas sold''.

Thus, The line's y-intercept represent ''Number of hot cocoas sold''.

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Answer:

Step-by-step explanation:

1+0.6

6/10 simplifed into 3/5

+1(which can be written anso as 5/5)

so 3/5 + 5/5 is 8/5 or         1 and 3/5

Answer: $0.10

Step-by-step explanation:

First we take the total ($1.10)

Then we take the total cost of the of the soap ($1.00)

Now subtract the two from each other

This will give us the cost of the towel

$1.10-$1.00

$0.10

Answer: I’m not entirely sure what you mean, but here are the following possible answers:

1.) If the soap and towel price TOGETHER is 1.10, then the price of the towel is 10 cents/ $0.10

2.) If the price of the towel is $1.10, then the price of the soap is $2.10

Step-by-step explanation: Here are the explanations coresponding to the answers:

1.) By subtracting the 1.00 from the 1.10, you find that you get .10. We do this since if the soap is 1.00 more than the towel, we need to get it away from the total price, and we do that by subtracting it.

2.) If the soap is 1.00 more than the towel, and the 1.10 is the price of the towel alone, then we add 1.00 to the towel price (1.10), getting 2.10.

Answer:

C

Step-by-step explanation:

Area of a circle = pi*r^2

Diameter is twice the radius so divide 24/2 = 12

Then use 12 as radius in the area of a circle equation.

The value of f.g(-3) is -18.

According to the question,

We have the following information:

f(a) = a-1 and g(a)= a² + a

Now, we have to find the value of f.g(-3).

So, we will first find the product of f ad g. We know that when two terms are in multiplication and their base is the same then their powers are added.

f.g = (a-1) (a² + a)

f.g = \(a^{3} +a^{2} -a^{2} -a\)

f.g = \(a^{3} -a\)

Now, we will put the value of a in this expression as -3 and then we will solve the expression:

f.g(-3) = \((-3)^{3} -(-3)\)

f.g(-3) = -27+9

f.g(-3) = -18

Hence, the value of f.g(-3) is -18.

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32. Solving integral equation using the convolution theoremThe convolution theorem states that the convolution of two signals in the time domain is equivalent to multiplication in the frequency domain.

Therefore, to solve the given integral equation using the convolution theorem, we need to take the Fourier transform of both sides of the equation.

y(t) = ∫_{-∞}^{∞} sinh(−)g() + ∫_{-∞}^{∞} sinh(−−)g()Taking the Fourier transform of both sides, we haveY() = 2π[G()sinh() + G()sinh(−)]where Y() and G() are the Fourier transforms of y(t) and g(t), respectively.Rearranging for y(t), we gety(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]e^(j) d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)](cos()+j sin())d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d+ j(1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()dTherefore, the solution to the integral equation is given by:y(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d + (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()d

It is always important to understand the principles that govern an integral equation before attempting to solve them. In this case, we used the convolution theorem to solve the equation by taking the Fourier transform of both sides of the equation and rearranging for the unknown signal. The steps outlined above provide a comprehensive solution to the equation.  33. Fourier series representation of f(x)

The Fourier series representation of a periodic signal is an expansion of the signal into an infinite sum of sines and cosines. To find the Fourier series representation of the given signal, we need to first compute the Fourier coefficients, which are given by:an = (1/T) ∫_{-T/2}^{T/2} f(x)cos(nx/T) dxbn = (1/T) ∫_{-T/2}^{T/2} f(x)sin(nx/T) dxFurthermore, the Fourier series representation is given by:f(x) = a_0/2 + Σ_{n=1}^{∞} a_n cos(nx/T) + b_n sin(nx/T)where a_0, a_n, and b_n are the DC and Fourier coefficients, respectively. In this case, the signal is given as:f(x) = -1, -π

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Answer: 13

Step-by-step explanation:

The square root and exponent cancel out and you are left with 13.

The ordered pair of the solution of the equation, x - 2y - 6 = 0 is d. (4,-1).

The solution of a linear equation is the points or the set of all possible values for the variables that satisfy the specified linear equation is the solution set of the system of linear equations.

Here we have  

Equation x - 2y - 6 = 0 ----- (1)

Now we need to find the solution to the equation from the given points  

Substitute each given point in equation (1) and check which point will satisfy equation (1)

Checking For a. (2,4)

=> 2 - 2(4) - 6 = 0

=> 2 - 8 - 6 = 0

=> -12 ≠ 0

Checking For b. (0,3)

=> 0 - 2(3) - 6 = 0

=> - 6 - 6 = 0

=> -12 ≠ 0

Cheking For c. (-4,1)

=> - 4  - 2(1) - 6 = 0

=> - 12  = 0

=> -12 ≠ 0

Cheking For d. (4,-1)

=> 4 - 2(-1) - 6 = 0

=> 4 + 2 - 6 = 0

=> 0 = 0  

By the above calculation,

The Equation x - 2y - 6 = 0 is satisfied only at d. (4,-1)

Therefore,

The ordered pair of the solution of the equation, x - 2y - 6 = 0 is d. (4,-1).

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Complete Question:

Which of the following ordered pairs is the solution of the equation

x - 2y - 6 = 0

a. (2,4)   b. (0,3)   c. (-4,1)     d. (4,-1)

Answer:

\(y = \frac{ - 3x + 6}{2} = \\ x = 4 \\ y = \frac{ - 3 \times 4 + 6}{2} = \frac{ - 12 + 6}{2} = \frac{ - 6}{2} = - 3\)

Answer:

(6, 13) is not

(9, 16) is

Step-by-step explanation:

The Expression that represents how much Margo will have to pay for the storage unit if Carissa contributes is 14m + 2 while Margo will pay $86 if she uses the storage unit for 6 months.​

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

Let m represent amount of monthly payments

Margo's payment = 17m + 3

Carissa's payment = 3m + 1

The payment will be = 17m + 3 - (3m + 1)

Total payment = 14m + 2

For 6 months, m = 6

Substituting in the equation 14m + 2

Payment for 6 months = 14(6) + 2

Payment = $86

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If a person of interest has been identified by the police. the appropriate location of the person of interest is: D. The person is at about (5, -4)).

To find the location of the person of interest, we can use a method called trilateration. Trilateration involves using the distances between the person and three known locations to determine the person's location.

Let (x, y) be the coordinates of the person of interest. Then, we can set up three equations based on the distances between the person and the three known locations:

sqrt((x - (-2))^2 + (y - 9.9)^2) = 6

sqrt((x - (-8))^2 + (y - (-4.7))^2) = 10

sqrt((x - (-12))^2 + (y - 4)^2) = 9

Squaring both sides of each equation and simplifying, we get:

(x + 2)^2 + (y - 9.9)^2 = 36

(x + 8)^2 + (y + 4.7)^2 = 100

(x + 12)^2 + (y - 4)^2 = 81

Expanding the squared terms and simplifying, we get a system of three linear equations in two variables:

x^2 + 4x + y^2 - 19.8y = 4

x^2 + 16x + y^2 + 9.4y = 52.59

x^2 + 24x + y^2 - 8y = 21

We can solve this system of equations to find the values of x and y that satisfy all three equations. One way to do this is to use elimination to solve for one variable in terms of the other, and then substitute into one of the equations to solve for the other variable. After some algebraic manipulation, we find:

y = (-11.94 + 6x) / 19.8

Substituting this expression for y into the first equation, we get a quadratic equation in x:

x^2 + 4x + ((-11.94 + 6x) / 19.8)^2 - 19.8((-11.94 + 6x) / 19.8) - 4 = 0

Simplifying and solving for x, we get:

x = -0.217 or x = 5.184

Substituting these values of x into the expression for y, we get:

y = 1.283 or y = -3.772

Therefore, the person of interest is located at approximately (5.184, -3.772). This is closest to option D: (5, -4).

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Answer:

Step-by-step explanation:

When u look at the graph u get -11,0 as point of B

Answer:

(-3, 8) or (8, -3)

The value of x/w is 1/3.

...........

Answer:

its easy figure it out lol good luck

Step-by-step explanation:

Answer: 1,176 miles

Step-by-step explanation:

490 / 5 = 98 miles

98 mph X 12 hours is 1,176

Answer:

D. 1.3

Step-by-step explanation:

5(1.3) = 6.5

Since the value of r is .2 less than b, b would be 1.5

2(1.5) = 3

6.5+3=9.5

The component form of the resultant vector is ⟨3, 4⟩.

To find the component form of the resultant vector, we need to perform scalar multiplication and vector subtraction.

Let's start by performing the scalar multiplication:

1/3 = 1/3 × ⟨-9, 6⟩

= ⟨-9/3, 6/3⟩

= ⟨-3, 2⟩

Next, we perform vector subtraction:

-2 = -2 × (3, 1)

= ⟨-23, -21⟩

= ⟨-6, -2⟩

Now, we can find the resultant vector by subtracting the two vectors we obtained:

Resultant vector = 1/3- 2

= ⟨-3, 2⟩ - ⟨-6, -2⟩

= ⟨-3 - (-6), 2 - (-2)⟩

= ⟨-3 + 6, 2 + 2⟩

= ⟨3, 4⟩

Therefore, the component form of the resultant vector is ⟨3, 4⟩.

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Answer:

If the "-" after "3y" is a typo, then y = 8/7, x = 24/7

Step-by-step explanation:

Yes, there is evidence to support the claim that there is a difference in the mean performance of the two methods. To test this, we can perform a two-sample t-test. The p-value for the test is 0.034. This means that there is a 3.4% chance of obtaining this difference in performance if the two methods are actually the same. Since this is lower than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant difference in the mean performance of the two methods.

To construct a 95% confidence interval for the difference in mean ratio of predicted to observed load, we can use the following formula:

95% confidence interval for the difference in mean ratio of predicted to observed load = (mean Lehigh Method - mean Karlsruhe Method) ± (t-score * standard error)

Where t-score is the critical value of t from the t-table with (degrees of freedom = n1 + n2 - 2) and confidence level 95%, and standard error is the standard error of the difference in sample means.

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Answer:

8 student tickets and 2 adult

Step-by-step explanation:

$12 for popcorn

$12 for drink

12+12=24

9x8=72

24+72=96

12x2=24

96+24=120

I gotchu homie

Step-by-step explanation:

4×3 =12 (the drinks)

6+6=12 (popcorn)

even if they purchased 12 student tickets for the cheapest price of 9$ it will be a total of 108...and just with the food and drinks which would add another 24 to it?

how is this possible?

If the drinks and snacks arent added on it would work such as

4 adults ($12 each) = $48

8 student tickets ($9 each) = $72

total price = $120

Given the price the stickers can be sold for, and the cost in total of the stickers, you can make profit.

The total revenue that can be made on the sale of the 600 stickers that you got, would be:

= ( Number of stickers in total / Number of stockers per pack ) x Price per sticker pack

= 600 / 10 x 2

= 60 x 2

= $ 120

Your profit would be:

= Total revenue from stickers - total cost

= 120 - 26. 97

= $ 93. 03

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The solution is not feasible since it is impossible to make a profit of $2,500. Therefore, option (b) is the correct option.

The company produces expensive bedspreads and pillows. The production process for each is similar in that both require a certain number of Prep work (P) and a certain number of labor hours in Finishing and Packaging (FP).

Each bedspread requires 0.5 hours of P and 0.75 hours of FP departments.

Each pillow requires 0.3 hours of P and 0.2 hour in FP.

During the current production period, 200 hours of P and 100 hours of FP are available. Each pillow sold yields a profit of $10; each bedspread sold yield a $25 of profit.

The company wants to find calculate whether this combinations of pillows and bedspreads will result in the profit of $2,500.

A linear equation for the bedspreads can be written as; P (prep work) = 0.5 bedspreads

FP (Finishing and Packaging) = 0.75 bedspreads

A linear equation for the pillows can be written as; P (prep work) = 0.3 pillows

FP (Finishing and Packaging) = 0.2 pillows

The company wants to calculate whether this combination of pillows and bedspreads will result in a profit of $2,500. Let's define our variables; x = the number of bedspreads produced

y = the number of pillows produced

T

From the graph above, we can see that the feasible region is the region enclosed by the dotted lines. Therefore, we can calculate the corner points of the feasible region.

They are;(0, 1000)(133.33, 800)(200, 466.67)(0, 0)If we substitute these points into the profit function, we have the following;

P(0, 1000) = 10,000

P(133.33, 800) = 22,833.3

P(200, 466.67) = 17,166.75

P(0, 0) = 0

From the above calculations, we can see that the maximum profit possible is $22,833.3. Therefore, the solution is not feasible since it is impossible to make a profit of $2,500. Therefore, option (b) is the correct option.

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Answer:

Step-by-step explanation:

Dont do it. Just take the detention

The insurance company expects the interest rate to be around 4.16%.

To find the expected interest rate, we can use the formula for present value of an annuity:

PV = PMT x (1 - (1 + r)^(-n)) / r

Where:

PV = present value of the annuity, which is the amount the insurance company needs to deposit

PMT = payment per period, which is $45,000

r = interest rate per period, which is what we need to find

n = total number of periods, which is unknown

We know that the insurance company needs to deposit $2,500,000 to make the payments, so we can set:

PV = $2,500,000:

$2,500,000 = $45,000 x (1 - (1 + r)^(-n)) / r

To solve for r, we can use trial and error or an iterative method. Here, we'll use trial and error.

Let's assume n = 20, which is a reasonable number of years for an insurance policy. Then we can solve for r:

$2,500,000 = $45,000 x (1 - (1 + r)^(-20)) / r

$2,500,000r = $45,000 x (1 - (1 + r)^(-20))

(1 + r)^(-20) = 1 - ($45,000 / $2,500,000) x r

1 + r = (1 - ($45,000 / $2,500,000) x r)^(-1/20)

r ≈ 0.0416 or 4.16%

Therefore, the insurance company expects the interest rate to be around 4.16%.

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