A skating rink manager finds that revenue R based on an hourly fee F
for skating is represented by the function R = -480F² + 3120F.
What hourly fee will produce maximum revenues?

To complete the table of values for y = x² - 4x

The equivalent values to complete the table of values are 5, -1, -4 and 0

Given the function according to the table shown:

[tex]y = x^{2} -4x[/tex]

Now let us insert the values in the above given equation one by one

When we have x = -1

[tex]y = (-1)^{2} -4(-1)[/tex]

y = 1+4

y = 5

When we have x = 1

[tex]y = (1)^{2}-4(1)[/tex]

y = 1-4

y = -3

When we have x = 2

[tex]y = (2)^{2}-4(2)[/tex]

y = 4-8

y = -4

when we have x = 4

[tex]y = (4)^{2} -4(4)\\[/tex]

y = 16-16

y = 0

Hence the equivalent values to complete the table of values are 5, -1, -4 and 0

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Answer:

To the nearest tenth, the length is 6.4 meters, and the width is 3.4 meters.

Step-by-step explanation:

Let w be the width of the rectangle. Then l = w + 3, and we have:

[tex] w(w + 3) = 22[/tex]

[tex] {w}^{2} + 3w = 22[/tex]

[tex] {w}^{2} + 3w - 22 = 0[/tex]

Calculating the discriminant:

[tex] \sqrt{ {3}^{2} - 4(1)( - 22)} = \sqrt{9 + 88} = \sqrt{97} [/tex]

So by the quadratic formula, and discarding the negative solution, we then obtain:

[tex]w = \frac{ - 3 + \sqrt{97} }{2} = 3.4[/tex]

[tex]l = w + 3 = 3.4 + 3 = 6.4[/tex]

The rate of change is not the same for all the cases so,

The relationship between hours biked and the miles traveled is not proportional.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the table, we need to find the rate of change between two given hours and the miles traveled at that time.

Now,

Between 1 hour and 2 hours.

The rate of change.

= (26 - 12) / (2 -1)

= 14 / 1

= 14

Between 2 hours and 3 hours.

The rate of change.

= (30 - 26) / (3 - 2)

= 4 / 1

= 4

Between 3 hours and 4 hours.

The rate of change.

= (48 - 30) / (4 - 3)

= 18 / 1

= 18

We see that,

The rate of change is not the same for all the cases so,

The relationship between hours biked and the miles traveled is not proportional.

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The system of inequalities for the given situation is

x +y ≤ 70.

$4x +  $8x ≤ $400.

y ≤ 50.

And one possible solution is (40,30) and the graph of the inequality is attached below.

Inequality:

Inequality refers the non equal comparison of the expressions.

Given,

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 70 people. The drama club must make no less than $400 from ticket sales to cover the show's costs. Also, they can sell at most 50 adult tickets.

Here we need to find the system of inequalities graphically and also determine one possible solution for it.

Let us consider x represents the number of student tickets sold and y represents the number of adult tickets sold.

Therefore, in here we know that, they can sell at most 50 adult tickets.

Which means that the value of y can't be greater than 50.

So, in inequality it can be written as,

y ≤ 50.

And the total number of seats in the auditorium is 70.

Therefore,

x + y ≤ 70

And we also know that, they sells the ticket at the cost not less than $400.

So,

$4x +  $8x ≤ $400.

Now, we have to plot those inequality on the graph, the we get he following graph.

In the graph, the blue line represents the inequality x + y ≤ 70 and the red line represents the inequality $4x +  $8x ≤ $400.

While we looking into the graph we have identified that the solution of the graph is (40,30).

Which means there are 40 number of students and 30 number of adults.

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Answer:

8.01 is the answer

Answer:

8.01

Step-by-step explanation:

Let x be the number of books that need to be sold, then for the cost of the production and the profit to be the same we can set the following equation:

Subtracting 10x from both sides of the equation we get:

adding like terms we get:

Dividing by 11.75 we get:

Then the producer must sell 2592 books.

Answer: 2592.

Answer:

6 Seconds

Step-by-step explanation:

The car come to a complete stop after the time of 6 seconds.

For the given question;

A car's velocity is modeled by v(t) = 0.5t² – 10.5t + 45.

The time inequality is given as; 0 ≤ t ≤ 10.5.

To calculate the time for which velocity becomes zero.

Put v(t) = 0.

v(t) = 0.5t² – 10.5t + 45 = 0

0.5t² – 10.5t + 45 = 0

Divide equation by 0.5.

t² – 21t + 90 = 0

factorize the values.

(t - 15)(t - 6) = 0

t = 15 and t = 6 seconds

As, 0 ≤ t ≤ 10.5.

Thus, t = 6 seconds.

Therefore, the car come to a complete stop after the time of 6 seconds.

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Solution

Question A:

- The lounge pants already in stock are 10.

- The price of the pants was moved from $34 to $39. Thus, the markup percent is:

Answer:

Maria earns $43

Step-by-step explanation:

$165 divided by 5 = $33 + $10 = $43

(a) A point-slope form of the line is y - y₁ = m(x - x₁)

(b) The slope of the line is 2.

(c) The point (x₁, y₁) = (-1, -2).

(d) The equation of a line in point-slope form is y + 2 = 2(x + 1).

The formula for a straight line: y - y₁ = m(x - x₁), where m is the slope of the line and (x₁, y₁) is the coordinates of a specific point on the line

(a) Let the two points are (x₁, y₁) and (x₂, y₂)

Then the slope of the lines is given as

m = (y₂ - y₁)/ (x₂ - x₁)

The point-slope form of the line is given as

(y - y₁) = [(y₂ - y₁)/ (x₂ - x₁)] (x-x₁)

y - y₁ = m(x - x₁)

(b) From the graph, (x₁, y₁) = (-1, -2) and (x₂, y₂) = (1, 2)

So, slope = (2 -(-2))/ (1-(-1))

= (2+2)/ (1+1)

= 4/2

= 2

c) (x₁, y₁) = (-1, -2)

d) The equation of a line in point-slope form is given as

y - (-2) = 2(x- (-1))

y + 2 = 2(x + 1)

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The number of  bags that the merchant should prepare if he wants to make 400 is; 80 bags

The method to solve algebra word problems is as follows;

1. Carefully read through the problem thoroughly, and try to know the meaning.

2. Use variables to denote unknown numbers.

3. Translate the remaining part of the problem into a mathematical expression.

4. Solve the problem.

We are told that the merchant sells 5 for a bag. Now, he wants to make 400. This means if the number of bags is x, then;

x = 400/5

x = 80 bags

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Answer:

x=14

Step-by-step explanation:

x/7=2

7 x x/7 = 7x2

ANSWER:

2 5/6 cups

STEP-BY-STEP EXPLANATION:

To find the total cups, we must add the number of cups in each case, like this:

For ease, we'll convert each fraction so that they all have the same denominator:

That is to say that in total there are 2 5/6 cups of fruit punch

She received 1 package from SendQuick Package Service, 2 packages from Ralph's Express and 8 packages from Speedy Delivery

A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.

Let SQPS represent SendQuick Package Service

SD represent Speedy Delivery

RE represent Ralph's Express, then:

Let the number of packages from SQPS be x

The number of packages from RE will be x+1

The number of packages from SD will be 4(x+1)

Given that the total number of packages received is 11, then:

x + x+1 + 4(x+1) = 11

x + x+1 + 4x + 4 = 11

6x + 5 = 11

6x = 11-5

6x = 6

x = 1

x = 1 package from SQPS

x + 1 = 2 packages from RE

4(x+1) = 8 packages from SD

Therefore, Erica Franz received 1 package from SendQuick Package Service, 2 packages from Ralph's Express and 8 packages from Speedy Delivery

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For the negative slope equation y = -x as the value of x increases y decreases.

What is a slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Given that the graph of a linear function has a negative slope. Suppose the equation with a negative slope is y = -x.

It would look like y = -m(x) + b.

As an illustration, m is 1 and b is 0. (You can try any random number; however, I looked for the most straightforward one so that we could easily observe it.) It will be written as y = -x. (You can also omit this and use random numbers)

If x = 3, y = -3 ; x = 5, y = -5  (x increases, y decreases)

If x = -1, y = 1 ; x = -5, y = 5 (x decreases, y increases)

Hence the answer is for the negative slope equation y = -x as the value of x increases y decreases.

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By using the formula of perimeter of square and triangle, the following results are obtained.

Length of the side of square = 9

length of the side of triangle = 12

Area of square = 81

What is perimeter of square and triangle?

Perimeter of square and triangle is the total space taken by the square and triangle.

If the side of the square is a, then perimeter of square is 4a

If the side of the equilateral triangle is a, then perimeter of square is 3a

Length of the side of square = 4x - 3

Length of the side of triangle = 5x - 3

Perimeter of square = 4(4x - 3) = 16x - 12

Perimeter of triangle = 3(5x - 3) = 15x - 9

By the problem,

[tex]16x - 12 = 15x - 9\\16x - 15x = 12 - 9\\x = 3[/tex]

Length of the side of square = [tex]4 \times 3 - 3 = 9[/tex]

Length of the side of triangle =  [tex]5 \times 3 - 3=12[/tex]

Area of square = [tex]9 \times 9 = 81[/tex]

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a. The scale that is being used for the image is: 1 inches to 6 inches or 1 inches = 6 inches.

b. The actual book is 18 inches tall.

An image is the new figure formed when an original figure is dilated, either by enlargement or by reduction. The image is a similar figure to the preimage (original figure).

Given the following:

a. The scale being used = width of image : width of preimage (actual book)

Scale = 1.5 : 9

Scale = 1 : 6

This is, 1 inches to 6 inches or 1 inches = 6 inches.

b. Height of image = 3 inches

Height of actual book (preimage) = 3 × 6 = 18 inches.

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The measure of each angle is A = 113°, B = 25° and C = 42°, the length is each side is a = 8 mm, b = 5 mm, c = 5.4 mm.

Triangles:

Triangles are geometric figures of three sides with three internal angles. We can apply different laws and rules to solve different types of triangles. For example, the law of cosines allows us to solve oblique triangles. We can find sides and angles by applying this law. We can use the law of cosines if we have the length of two sides of a triangle and the angle formed by them.

Given that

a = 8

b = 5

c = 42°

To solve the triangle, we are first going to make a diagram with the given information:

We start by applying the law of cosines to find the length of

[tex]c^{2} = a^{2}+ b^{2}-2abcosc[/tex]

Substituting a =8, b = 5 and c = 42°, we have

[tex]c^{2} = 8^{2}+5^{2} -2(8)(5)cos42^{0}[/tex]

[tex]c^{2} = 64+25 - 59.45[/tex]

[tex]\sqrt{c^2} =\sqrt{64-34.45}[/tex]

c = 5.435 = 5.4

Now, we apply the law of cosines to find the measure of angle B

[tex]b^2 = a^2+c^2-2accosB[/tex]

Substituting the lengths a = 8, b = 5, c = 5.4

[tex]5^2 = 8^2+5.4^2- 2(8)(5.4)cosB\\[/tex]

Note: we can substitute the lengths of the sides without the unit. Simplifying, we have:

25 = 64+29.16 - 86.4 cos B

25 = 96.16 - 86.4 cos B

cosB = 0.603

Now, we must apply inverse cosine on both sides of the equation:

[tex]cos^-1(cos B) = cos^-1(0.603)\\\\[/tex]

B = 25.256°

B = 25°

Lastly, we apply summation of internal angles of a triangle to find the angle A:

A + B + C = 180°

we need to isolate angle A:

A + 25°+ 42° = 180°

A + 67° = 180°

A = 113°

Hence the answer is, the measure of each angle is A = 113°, B = 25° and C = 42°, the length is each side is a = 8 mm, b = 5 mm, c = 5.4 mm.

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The image of the dilation is P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5) and the graph is attached

The coordinates of the polygon are given as

P(-1, -1), Q(0, -1), R(2, 1) and S(1, 1)

The transformation is given as

A dilation with a scale factor of 5 about the origin

The dilation has the algebraic rule of

(x, y) ⇒ (5x, 5y)

So, we have

P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5)

Hence, the coordinates of the image using the dilation rule is P'(-5, -5), Q'(0, -5), R'(10, 5) and S'(5, 5)

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the polynomial expression that represents the area of the soccer field is

5x^2 -16xy +3y^2

given length of a rectangular soccer is 5x -y

and width of a rectangular soccer is x- 3y

find the polynomial expression that represents the area of the soccer field.

we know that the formula for the area of a rectangle is

area= length * width

       =( 5x-y)*( x-3y)

       = 5x^2 -15xy-xy +3y^2

        = 5x^2 -16xy +3y^2

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The △ABC is congruent to triangle △ADE (△ABC ≅ △ADE) under (B) SAS condition.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

You can move, flip, twist, and turn these triangles to produce the same effect.

So, first label the two triangles as △ABC and △ADE.

Now, to prove that △ABC ≅ △ADE:

BA = DA  (Given)

AC = ED  (Given)

∠BAC = ∠ADE (Since, both lines are similar, so the angle between them will also be soililar and congruent.

So, we can say that △ABC ≅ △ADE is under SAS conditions.

Therefore, the △ABC is congruent to triangle △ADE (△ABC ≅ △ADE) under (B) SAS condition.

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Complete question:
Determine if the triangles are congruent. If so, a state which reason proves the triangles are congruent.

Group of answer choices

a. Not congruent

b. SAS

c. HL

d. SSA

Answer:

y = 8*(9/4)^x

Point (1.5, 27)

Step-by-step explanation:

We can solve each unknown in separate steps.  The first step is to take advantage of given point (0,8) to find the value of a.  Since x is zero, b^x will just be 1, regardless of b.  That makes it easy to solve for a, which is found to be 8.      

Once a is known, we can use the next point (1,18) to solve for b.  b is (9/4).  

Once we have a and b, we have the full equation:  y = 8*(9/4)^x

k is found by entering the x value and solving for y (which is k).  k = 27

See attached worksheet

The point slope form is:

where m is the slope and (x0,y0) is a point of the line.

In this case, we know the point (0,-5) and the slope is m=2.

Then, we can write the equation in slope point form as:

Answer: y+5=2x (option b)

Answer: The expected value of X is 672.75

Expected value can be calculated using the below formula

Therefore, the expected value of X is 672.75

The formula for finding slope is expressed as

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

where

y2 and y1 are final and initial values of the y coordinates respectively

x2 and x1 are final and initial values of the x coordinates respectively

Considering line PQ,

x1 = - 6, y1 = 16

x2 = 2, y2 = - 4

Slope = (- 4 - 16)/(2 - - 6) = - 20/8

Slope = - 2.5

Considering line RS,

x1 = - 6, y1 = 14

x2 = - 2, y2 = 4

Slope = (4 - 14)/(- 2 - - 6) = - 10/4

Slope = - 2.5

If the slope of two lines are equal, it means that they are parallel. We can see that the slopes of PQ and RS are equal. Thus,

Line PQ is parallel to line RS

2

Answer:

a = 9

Step-by-step explanation:

[tex]a^{2}[/tex] = a*a

a = -3

-3 * -3 = 9

NOTE: 2 negative numbers multiplied by each other always equals a positive

So.... a = 9

Answer:

B

Step-by-step explanation: