Mathematics College

You are planning your brother's mini surprise party, and you want to take
him and his closest friends to a sporting event. His two favorite sports are
hockey and basketball. Each local team offers a special party suite during
the game. The hockey suite costs $130 to rent the room and $30 per
person. The basketball suit costs $180 to rent the room and $20 per
person. Identify the system of equations that represents this model, where
y represents the total cost of the party, and x represents the number of
people attending the party.

Answers

Answer 1

The system of equations that models the situation is given as follows:

y = 130 + 30x.y = 180 + 20x.

How to construct the system of equations?

The system of equations is constructed by linear functions in slope-intercept format, which are explained as follows:

y = mx + b.

In which:

The slope m represents the variable cost, that is, the cost per player.The intercept b represents the fixed cost, that is, the cost per room.

Hence the two functions are given as follows:

y = 130 + 30x. -> hockey.y = 180 + 20x. -> basketball.

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Related Questions

3 over 5 meters =. centimeters

Answers

Answer:

Step-by-step explanation:

3/5 = 0.6 meters = 60 cm

If a figure is dilated by a factor of 3, the sides of the pre-image will be _ of the image's sides.

A. one-ninth the size
B. one-third the size
C. nine times the size
D. three times the size

Answers

I think it might be C

Which of the following situations represent direct variation?
y = -5x
2y = x
y/x = 12
x/y = 4

Answers

All the equations are direct variation equations

How to determine the equations of direct variation

A relationship between two variables is said to be a direct variation if one of the variables is proportional to the other, meaning that their ratio is always constant.

Using the above as a guide, we have the following:

y = -5x:

Direct variation

Constant of variation = -5

2y = x

Direct variation

Constant of variation = 1/2

y/x = 12

Direct variation

Constant of variation = 12

x/y = 4

Direct variation

Constant of variation = 1/4

Answers

When x is 4, the output of the equation is greater.

The value for x that produces the same output in both the graph and the equation is equal to 6.

What is a graph?

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.

By critically observing the graphs of the equations, we can reasonably infer and logically deduce that they both would produce the same output (dependent value or y-value) at the ordered pair (4, 6).

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Divide. (54t2−81t)÷(9t)

Answers

Answer:

The answer is 6t-9. This can be calculated by dividing the numerator (54t2−81t) by the denominator (9t). This gives 6t-9.

Step-by-step explanation:

Answer:

81t2+16

Step-by-step explanation:

(9t-4)(-9t-4) : Equation

Distribute parentheses using:(a + b)(c + d) = ac + ad + bc + bd.

Where : a=9t, b=-4, c=-9t, d=-4.

This leads to 9t(-9t) +9t (-4) -4- (9t) -4 (-4).

Now we have to Apply minus-plus rule.

Where: -(-a)=a.+(-a)=-a

-9t.9t - 9t.4 + 4.9t = 4.4

=81t2+16

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Demarco and Tanya have received information about three separate mortgage offers. In two or three paragraphs, describe your recommendation for the best financial choice in their situation. Evaluate each of the three offers, compare and contrast their effectiveness, and explain the offer that works best. As you explain your answer, support it using reasons and evidence from the calculations you made based on the information provided in this guide for Analyzing Mortgage Options. pls try to be original

Answers

Best Mortgage Option 3 because this mortgage option offers a lower interest rate.

Why Option 3 was recommended

After reviewing all three mortgage options available to Demarco and Tanya, I would recommend that they choose option 3. This option offers a lower interest rate compared to the other two options and a longer loan term, which means that their monthly payments will be lower and more manageable for their budget. Additionally, option 3 offers a fixed interest rate, which provides them with more stability and predictability in their mortgage payments, as opposed to options 1 and 2 that offer adjustable interest rates.

Option 1 has the highest interest rate and the shortest loan term, making their monthly payments the highest of all three options. Option 2 offers a slightly lower interest rate, but it still higher compared to option 3, and has a shorter loan term compared to option 3, making their monthly payments still relatively high.

In conclusion, the best financial choice for Demarco and Tanya would be option 3. Its lower interest rate, longer loan term, and fixed interest rate make it the most affordable and stable option for them in the long run.

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Draw 2 isosceles triangles ABC and DEF where AC=BC and DF=EF

Answers

The conclusions reached in steps 4 and 5 are invalid. This is a flawed argument for the existence of isosceles triangles.

An isosceles triangle contains what?

An isosceles triangle has two equal sides and two equal angles as a result. The term comes from the Greek words iso (same) and skelos (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

Each step is valid, but the conclusion is not. At the end of step 4,

here are a series of isometric maps that lead A to D and C to F, as claimed..

After the final rotation in Step 5, the sequence of isometries takes B to E and C to F —but here’s the hitch—there is no reason why it should still take A to D, in fact it can’t take A to D unless the rotation angle is zero.

If the rotation angle in Step 5 is zero, then the isometries take [A,B,C] to [D,E,F] and the two triangles are indeed similar

But this requires the dilation in Step 2 to have made A′B′ congruent to DE , in other words, it requires assuming the triangles are similar before performing any of of the transformations.

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Question:

This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why. 1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF. 2. Dilate triangle ABC to a new triangle A'B'C' using center C and scale factor DF/AC so that A'C= BC - DF = EF. 3. Translate by directed line segment CF to take A'B'C' to a new triangle A" B" F. Since translation preserves distance, A"F = A'C=DF and B" F = BC = EF. 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B" F = EF, we can rotate using center F to take B" to E. 6. We have now established a sequence of dilations, translations, and rotations that takes A to D, B to E, and C to F, so the triangles are similar.

A rectangular prism has a volume of 120 in³. What is the height of the prism? What is the
surface area of the prism?

Show your work.

Answers

Given that the volume of the rectangular prism is 120 cubic inches, we can write the equation:

l * w * h = 120

where l, w, and h are the length, width, and height of the prism, respectively.

Since the length is 3 and the width is 10, we can plug in these values into the equation:

3 * 10 * h = 120

Solving for h, we get:

h = 120 / (3 * 10) = 120 / 30 = 4

So the height of the rectangular prism is 4 inches.

To find the surface area of the rectangular prism, we can add up the areas of all six faces:

2 * l * w + 2 * w * h + 2 * h * l

Plugging in the known dimensions, we get:

2 * 3 * 10 + 2 * 10 * 4 + 2 * 4 * 3 = 60 + 80 + 24 = 164 square inches

So the surface area of the rectangular prism is 164 square inches.

Answer: Hight 4 inch, surface area 164 square inch

Step-by-step explanation: multiply with l * w * h

* = x

What is the range of the function shown on the graph above?

Answers

From the graph the range of the function is obtained as option 1: -5 ≤ y ≤ 8.

What is the range of data?

The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.

From the graph, the following observations are made -

The endpoints of the graph have closed circles this means that, the endpoints are inclusive of the range.

For closed circles the inequality symbols used is (≤,≥).

The y-axis values suggests the range of the function.

The minimum y-axis value in the fourth quadrant is -5.

The maximum y-axis value in the first quadrant is 8.

The range of the function is [-5 , 8]

Therefore, the range is found to be -5 ≤ y ≤ 8.

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Amy will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. The second plan has no initial fee but costs $0.90 per mile driven.

For what amount of driving do the two plans cost the
same?

What is the cost when the two plans cost the same?

Answers

The two plans cost the same when the amount is $200.

What are equations?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the miles driven = x.

Given that,

The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. This is represented as:

A = 40 + 0.70x

The second plan has no initial fee but costs $0.90 per mile driven.

B = 0.90x

The two plans cost the same when A = B:

40 + 0.70x = 0.90x

40 = 0.90x - 0.70x

40 = 0.20x

x = 200

The two plans cost the same when the amount is $200.

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Write an expression having only two terms that is
equivalent to 2x - 3. Explain how you wrote the
expression and how you can check that it iS equivalent.

Answers

Answer:

2X-3=0

2X=3

X=3/2

Step-by-step explanation:

Answer:

2x- 3 = 0

2x=3

x = 3/2

Step-by-step explanation: best of luck to you

Instructions Type an essay response to the following prompt. Completely explain all parts of your response and use the rubric to determine what you need to include in your essay. 1) In your own words, write a definition for sales tax. 2) If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, how much do you pay in taxes? - Explain in detail, the steps you would take to solve this sales tax question.

Answers

1) The sales tax is an additional rate that is paid along with the cost of the meal.

2) The amount paid in taxes for a meal costing $15.00 and a rate of 7% is given as follows: $1.05.

How to obtain the sales tax?

The sales tax is obtained applying the proportions in the context of this problem.

A proportion is applied as the sales tax is obtained with the multiplication of the cost of the meal by the decimal equivalent of the percentage of tax.

The decimal equivalent for a percentage of 7% is given as follows:

7/100 = 0.07.

Hence the amount of tax paid is given as follows:

0.07 x 15 = $1.05.

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Lexi MUST spend $100 and get 100 animals. $15 for 1 dog, $1 for 1 cat, and 25 cents for each mice.
thank you to whoever helps <33

Answers

Let no. of each animal be, d, c, m
:
Total animal equation
d + c + m = 100
Total cost equation
15d + 1c + .25m = 100
:
We got three unknowns and two equations, but we know the solutions are integers
Eliminate the cats
15d + 1c + .25m = 100
1d + 1c + 1m = 100
---------------------- Subtraction eliminates c
14d - .75m = 0
or
.75m = 14d
m = 14%2F.75d
substitute values for d, until you get an integer value for m
when you get to d = 3
m = 14%2F.75*3
m = 42%2F.75
m = 56 mice
:
We have 3 dogs and 56 mice, then 100 - 59 = 41 cats
:
:
Check that in the cost equation
15(3) + 1(41) .25(56) =
45 + 41 + 14 = 100

So 3 dogs 41 cats and 56 mice

HELPP WITH ALL 4 OF THESE ? PLEASE!! each is worth 10 points!!

Answers

Answer: 1.+900

2. -24

3. -5

4. +10

Step-by-step explanation:

A small fair charges different admission for adults and children; it charges $2.75 for adults, and $0.25 for children.
On a certain day, the total revenue is $6,962.50 and the fair admits 4900 people.
How many
adults and children were admitted?

Answers

Answer: Let's call the number of adults admitted "A" and the number of children admitted "C". We know that:

A + C = 4900 (total number of people admitted)

And the total revenue is:

2.75A + 0.25C = $6,962.50

We can use the first equation to solve for one of the variables in terms of the other:

C = 4900 - A

Substitute this expression for C into the second equation:

2.75A + 0.25(4900 - A) = $6,962.50

Expand and simplify the right side:

2.75A + 1225 - 0.25A = $6,962.50

2.5A = 5737.5

Solve for A:

A = 2298

So there were 2298 adults and 4900 - 2298 = 2602 children admitted.

Step-by-step explanation:

Laura is the fund raising manager for a local charity she is ordering caps for an upcoming charity walk. The company that makes the caps chargers $6 per cap plus a $25 shipping fee . Laura had buaght of $1000 WhT is the greatest number of caps she can buy?

Answers

the maximum number of caps she can order is 162.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, Laura is the fundraising manager for a local charity she is ordering caps for an upcoming charity walk.

Let "x" be the number of caps she ordered.

Since, manufacturing cost for a cap = $6

shipping charges for the lot = $25

Thus,

Total price she paid for x caps = 6*x + 25

Since she had only 1000$

So,

6x + 25 ≤ 1000

6x ≤ 975

x ≤ 975/6

x ≤ 162.5

therefore, the maximum number of caps she can order is 162.

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A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. A 3-column table with 10 rows. Column 1 is labeled volunteer with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Column 2 is labeled Treatment A with entries 10, 13, 13, 9, 13, 12, 14, 10, 8, 7. Column 3 is labeled Treatment B with entries 19, 18, 19, 15, 20, 16, 16, 16, 13, 17. What is the mean difference (A – B) and the standard deviation of the differences?

Answers

I think that it could be b but I'm not 100 percent sure

Given a2 = 6 and a5 = –384 of a geometric sequence, what is the recursive equation for the nth term?

an = –4(an – 1), a1 = –1.5
an = –4(an – 1), a1 = 1.5
an = 4(an – 1), a1 = –1.5
an = 4(an – 1), a1 = 1.5

Answers

Answer:

[tex]a_n = (-4)^{n - 1}; a_1 = -1.5[/tex]

Step-by-step explanation:

[tex] a_1 = a_1 [/tex]

[tex] a_2 = a_1 \times r [/tex]

[tex] a_3 = a_1 \times r^2 [/tex]

[tex] a_4 = a_1 \times r^3 [/tex]

[tex] a_5 = a_1 \times r^4 [/tex]

[tex] a_1 \times r = 6 [/tex]

[tex] a_1 \times r^4 = -384 [/tex]