BRIANLIEST ~
Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.

Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Answers

Answer 1

Part A

x = number of hours the scooter is rented
y = total rent (in dollars)

"Amir rented a scooter at $43 for 3 hours" means x = 3 and y = 43 giving the point (3,43)

"he rents the same scooter for 8 hours, he has to pay a total rent of $113" means x = 8 pairs up with y = 113. The second point is (8,113)

The two points (3,43) and (8,113) can be used to find the slope
m = (y2 - y1)/(x2 - x1)
m = (113 - 43)/(8 - 3)
m = (70)/(5)
m = 14

The slope of 14 tells us that it costs $14 per hour to rent the scooter

If we simply consider the hourly cost of $14 per hour (and no additional fees), then the cost break down would look like this:
1 hour costs Amir $14
2 hours costs Amir $28 (2*14 = 28)
3 hours costs Amir $42 (3*14 = 42)

If we don't have any fixed costs, then it would cost Amir $42 total to rent the scooter for 3 hours. But it says the cost is actually 43 dollars. So the fixed cost, the y intercept, must be 1 dollar. Think of the $1 as the fee that Amir pays to get into the park or maybe as some kind of insurance. This fixed fee is not dependent on the number of hours Amir rents the scooter.

In other words, if m = 14, x = 3 and y = 43, then
y = mx+b
43 = 14*3+b
43 = 42+b
b = 1

Making the equation to be y = 14x+1

Answer: y = 14x+1

---------------------------------------------------------------

Part B

All we do here is go from y = 14x+1 to f(x) = 14x+1. We simply replace y with f(x) to get it into function notation.

---------------------------------------------------------------

Part C

The y intercept is 1 as this is the value of b in y = mx+b. Compare this to y = 14x+1.

Another way to look at this is that if we plug in x = 0 into y = 14x+1, we get y = 1. So the point (0,1) is on the function. This is where the graph crosses the y axis.

Starting at (0,1) go up 14 units and then to the right 1 unit. You'll arrive at (1,15) as the next point on this graph. Draw a straight line through (0,1) and (1,15) to complete the graph of y = 14x+1

You should have "number of hours" along the x axis and "cost (in dollars)" along the y axis for your proper labels. As for intervals, I would increment x by 1 each time (0, 1, 2, 3, ...) and increment y by 2 at the smallest or 5 at the largest. It will depend on your preference really.

Related Questions

Solve for x.

x+8-3=19

Answers

x + 8 - 3 = 19

x + 5 = 19

x + 5 (-5) = 19 (-5)

x = 14

hope this helps

x is 14.

Do the problem backwards.

19 - 8 + 3 = x

11 + 4 = x

14 = x

Martin drew a pair of perpendicular lines and a pair of parallel lines.which of these statements best compares the pairs of perpendicular and parallel lines?

Answers

You need to post the statements

What is the area of the kitchen floor in this floor plan?

A-24 sq meters
B-28 sq meters
C-35 sq meters
D-42 sq meters

Answers

First you would figure out the dimensions, which are 7 ft by 5 ft. Then, multiply those together, which equals 35 sq ft. The answer to your question is C - 35 sq ft. Hope this helps!

Answer: The correct option is (C) 35 sq. meters.

Step-by-step explanation: We are given to find the area of the kitchen floor in the floor plan shown in the figure.

From the figure, we see that

the kitchen is in the form of a rectangle with length 7 meters and breadth 5 meters.

We know that

the area of a rectangle with length l units and breadth b units is given by

[tex]A=l\times b.[/tex]

For the rectangular kitchen, we have

length, l = 7 meters

and

breadth, b = 5 meters.

Therefore, the area of the kitchen floor in the floor plan is given by

[tex]A=l\times b=7\times 5=35~\textup{sq. meters}.[/tex]

Thus, option (C) is CORRECT.

What is the area of a circle with a diameter of 12.6 in.?
Use 3.14 for pi and round your final answer to the nearest hundredth

Answers

the answer would be 395.6in²

Brainly use a matrix to find the solution to the system of equations -8x-8y=-16 6x-9y=-108

Answers

We want to use a matrix to solve
-8x - 8y = -16
6x - 9y = -108

Before solving, simplify the equations as follows:
Divide the first equation by -8 to obtain
x + y = 2 (1)
Divide the second equation by 3 to obtain
2x - 3y = -36 (2)

In matrix form, the equations are
[tex] \begin{bmatrix}1&1\\2&-3\end{bmatrix} \begin{\bmatrix} x\\y\end{bmatrix}=\begin{bmatrix}2 \\ -36 \end{bmatrix}[/tex]

The determinant of the matrix is
D = (1)(-3) - (1)(2) = -5

Use Cramer's Rule.
[tex]x = \frac{1}{D} det(\begin{bmatrix}2&1\\-36&-3 \end{bmatrix} ) = \frac{1}{-5} (-6+36) = -6[/tex]
Similalrly,
[tex]y= \frac{1}{-5} det(\begin{bmatrix} 1&2\\2&-36\end{bmatrix} ) = \frac{1}{-5}(-36-4) =8[/tex]

Answer: (-6, 8) or x = -6, y = 8

TWO EASY QUESTIONS 8TH GRADE MATH
9. Complete the missing steps in the paragraph proof of Theorem 3-8.
11. Solve for the value of x in the triangle shown below. Show your work! (1 point for equation, 1 point for answer)

Answers

9.
<2 and <6 are right angles by the definition of perpendicular lines.
Since corresponding angles are congruent, m || n.

11.
In a triangle, the measures of the three angles add to 180 degrees.
If one angle is a right angle, then that angle measures 90 degrees. The other two angle measures plus 90 degrees add to 180 degrees, so the other two angle measures add to 90 degrees. In a right triangle there is a right angle and two other angles that are complementary.

Now look at your problem.
One angle is a right angle.
The other two angles are complementary, so their measures add to 90 deg.

8x + 2 + 9x + 3 = 90

17x + 5 = 90

17x = 85

x = 5

A scale model of a merry-go-round and the actual merry-go-round are similar.
a. How many times greater is the base area of the actual merry-go-round than the base area of the scale model? Explain. The ratio of the corresponding lengths is : 1. So, the ratio of the areas is : 1 and the base area of the actual merry-go-round is times greater than the base area of the scale model.
b. What is the base area of the actual merry-go-round in square feet? The base area of the actual merry-go-round is square feet.

Answers

Final answer:

The base area of the actual merry-go-round is the same as the model due to the 1:1 scale. Without further information, the actual base area of the merry-go round cannot be calculated.

Explanation:

To understand this, we need to know a key principle of scale models. In a scale model, when the ratio of the lengths is 1:n, the ratio of the areas is square of that, or 1:n2. Hence, if the scale of models is 1:1 as given, the base area of the actual merry-go-round is equal to the base area of the scale model, meaning the ratio is also 1:1.

For part b, without the specific measurements of the base area of the scale model or the scale used, it is impossible to calculate the base area of the actual merry-go-round in square feet. We need one or the other to make this calculation.

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Final answer:

The base area of the actual merry-go-round is 16 times greater than the base area of the scale model. The base area of the actual merry-go-round in square feet can be calculated using the base area of the scale model.

Explanation:

The base area of the actual merry-go-round is 16 times greater than the base area of the scale model. This is because the ratio of the corresponding lengths is 1:4, so the ratio of the areas is 1:16.

To find the base area of the actual merry-go-round in square feet, you will need to know the base area of the scale model in square feet. If you provide the base area of the scale model, I can help you calculate the base area of the actual merry-go-round.

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Is (2,5) a solution of y=3x-10?

Answers

To see if (2,5) is a solution of the line y = 3x - 10, you need to plug in the coordinate values for x and y. This gets you 5 = 3(2) - 10. Evaluating the right side gives 5 ≠ -4, which is not a true statement. This means that the answer to your problem is no, (2,5) is not a solution of y = 3x - 10. Hope this helps and have a nice day!

No, (2,5) is not a solution of y = 3x-10

What is equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, an equation y = 3x-10, we need to check whether (2,5) is solution of the give equation or not,

For that put x = 2 in 3x-10 and check whether it equals to 5 or not, if not then (2,5) is not a solution of the equation,

= 3×2-10

= 6-10

= -4

∵ -4 ≠ 5

Hence, No, (2,5) is not a solution of y = 3x-10

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Solve each system by substitution {4p+2q=8 and q=2p+1} {x+6y=2 and 5x+4y=36}

Answers

4p +2q = 8
Q=2p+1

4p +2(2p + 1)=8
4p + 4p + 2=8
8p = 6
P=3/4

Substituting p=3/4 into the first equation
4(3/4) +2q =8
3+2q =8
2q=5
Q=5/2

You have 120 pieces of fabric to make a blanket. Each piece of fabric is a square with a side length of 6 inches. you can use as many pieces of fabric as possible to create a square blanket. What is the area of the blanket? How many pieces of fabric or left over. How many more pieces of fabric what you need to increase the size of the blanket

Answers

Area of blanket = 25 sq ft Pieces left over = 20 Need 1 more piece to make the blanket 5.5 ft on edge. Since you want a square blanket, the first step is to calculate the square root of 120, which is 10.95. Since you cannot use a fractional piece of cloth, that means the final blanket will have 10 squares of cloth per edge. What is the area of the blanket? Since there's 10 pieces of cloth per edge and each piece of cloth is a 6 inch square, each edge is 5 feet long. So the total area is 5 * 5 = 25 square feet. How many pieces of fabric is left over? Since there's 10 pieces of cloth per edge, the total number of pieces used will be 10 * 10 = 100. So the number of pieces left over will be 120 - 100 = 20 How many pieces of fabric do you need to increase the size of the blanket? Since the current size is 10x10, the next larger size is 11x11 which means a total of 121 pieces of fabric is needed. Of those 121 pieces, 100 is already being used for the blanket, so you need to add 121 - 100 = 21 pieces of fabric to the blanket. You already have 20 pieces available, so you only need to get 21 - 20 = 1 more piece to make the blanket larger.

suppose you planted 3 trees around the north and west sides of one of the houses worth $100,000 on the map. You have increased he property value of the house by $10,000. In addition, the owner will save an average of$50 per year in heating costs. Assuming that the homeowner lives in the house for another 20 years, what is the total dollar value of the trees to the homeowner and the community?

Answers

that would be 10,000 + 20(50) = 10,000 + 100 = $11,000

The total dollar value of the trees to the homeowner and the community will be $11,000.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Suppose you planted 3 trees around the north and west sides of one of the houses worth $100,000 on the map. You have increased the property value of the house by $10,000. In addition, the owner will save an average of$50 per year in heating costs.

Assuming that the homeowner lives in the house for another 20 years.

Then the total dollar value of the trees to the homeowner and the community will be

⇒ 10,000 + 50 x 20

⇒ 10,000 + 1,000

⇒ $11,000

The total dollar value of the trees to the homeowner and the community will be $11,000.

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original cost: 1.25; Markup %:80

Answers

To figure this out, you need to find out what 80% of the cost would be, and add it to the original price.

To find out 80% of 1.25, you need to convert 80(%) to a decimal. You can do this by dividing 80 by 100.

80/100 = 0.8

Add this to the original cost.

1.25 + 0.8 = 2.05

Your total cost in the end would be $2.05

The first thing that you would do would be to make the 80% into a decimal; then you would multiply 0.8 to 1.25 and then add the answer to 1.25.

80/100=0.8
1.25x0.8=1
1.25+1=2.25

The new price would be $2.25

Hope this helps!

How to write 0.924 in two other forms

Answers

Hi there!

Your question:

How to write 0.934 in two other forms?

My answer:

Since 0.924 is a decimal, the two other ways are going to be a fraction and a percent. To make it a fraction you are going to find out what it's out of. in this case, it's 1,000.

The answer is: 924/100 and 92.4%

Please help!!

4) Use the figure below to answer parts A and B. Show your work. (4 Points)

A.)Explain, in words, a series of rigid motions that would map ∆MJS onto ∆DWP.

B.)Write the ordered-pair rule for each transformation in the sequence

Answers

Part A:

The series of rigid motions that would map ∆MJS onto ∆DWP are:

a.) A rotation of 90 degrees about the point J in the clockwise direction.
b.) A translation of 1 units to the right and 5 units up.

Part B:

The ordered-pair rule for each transformation in the sequence are:

a.) R (J, 90 degrees)
b.) (x, y) → (x + 1, y + 5)

Suppose A and B are points. How many lines contain both A and B?

Answers

One and only one line contains both A and B (assuming, that A and B do not overlap)

Point A and point B should both contain one line

What is the value for x?
Enter your answer in the box.

Answers

A is equal to C
73=8y-7
+7
80=8y
y=10
73+73=146
180-146=34
6x+4=34
-4
6x=30
x=5

x=5
y=10

5=x. angles a and c are equivalent, so you just add them together and subtract from 180, then solve for x plugging in difference of the two.

1. Mrs.vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 3.2 ft, the width is 1.5 ft and the height is 27 ft?

2. What is the volume of a cylinder that has a radius of 6 inches and height of 8 inches?

Answers

1. 4.5 square feet of surface area, 129.6 cubic feet of swimming volume. 2. 288 pi cubic inches or approximately 904.8 cubic inches. For the turtles, since they're in a rectangular prism, the volume will be the product of the length, width, and height. So 3.2 ft * 1.5 ft * 27 ft = 4.5 ft^2 * 27 ft = 129.6 ft^3 Therefore the turtles have 4.5 square feet of surface area to get to in order to breath and 129.6 cubic feet in which to swim. The volume of the cylinder will be the area of it's cross section which is pi r^2 multiplied by the height. So pi * 6^2 * 8 = pi * 36 * 8 = pi * 288 = approximately 904.8 cubic inches.

5. 7x + 2 + 4y Identify the terms

I'm sorry... I'm a dumb person and these confuse me the most

Answers

The terms are 7x, 2, and 4y. Hope this helps and have an extraordinary day!

7x, 2, and 4y

I hope that's what you were looking for

Multiply or divide as indicated 10x^5/2x^2

Answers

To perform the following operation, make sure to do the division parts separately and place them back together in the final answer.

10/2 and x^5/x^2

5 and using the exponential laws of division X ^m/X^n = X ^ m-n

The second part evaluates to X^3.

Putting the terms together we get the final answer, which is 5x^3.

Final answer:

The expression [tex]10x^5/2x^2[/tex] simplifies to [tex]5x^3[/tex] by dividing the coefficients (10/2) to get 5 and subtracting the exponents (5 - 2) in [tex]x^5[/tex] and[tex]x^2[/tex]to get 3.

Explanation:

To solve the given expression, [tex]10x^5/2x^2[/tex], you would first divide the coefficients and then deal with the bases (x) separately.

The coefficients (numbers without variables), 10 and 2, divide to give you: 10/2 = 5.

For the part that includes x, [tex]x^5/x^2[/tex], you subtract the lower exponent from the higher exponent because when you divide powers with the same base you subtract the exponents. So 5 - 2 = 3.

Thus, the final answer is: [tex]5x^3[/tex].

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What is 997,000 rounded to the nearest 10 thousand?

Answers

1,000,000 i dont really know how to explain it. sorry

The transitive property of equality states that:

if a = b, then b = a
if a = b, then ac = bc
if a = b and b = c, then a = c
if a = b and c = c, then a + b = b + c

Answers

the transitive property of equality states that if a = b, then b = c, then a = c.

hope that helps, God bless!

Answer: The correct option is

(C) if a = b and b = c, then a = c.

Step-by-step explanation: We are given to select the correct statement for the transitive property of equality.

We know that

if x, y and z are three real numbers, then the transitive property of equality states that

if x = y and y = z, then x = z.

So, for reals a, b and c, the property states that

if a = b and b = c, then a = c.

Option (C) is CORRECT.

sam is paid $50 per room that he paints and he can paint a room in exactly 2 hours. on sunday sam hopes to make at least $150 painting rooms and can work for exactly 12 hours. which of the following sets represents the range of rooms(r) that sam can paint without violating either his monetary or time restriction?
A. r={3,6}
B. r={6,10}
C. r={3,5}
D. r={3,10}

Answers

the answer is A because 3 rooms takes 6 hours

the answer would be A because 3 rooms would equal 150 and that would only take 6 hours to complete.

1/4 (4r - 8) = r - 2

Answers

Solve for r.

Use distributive property.

4/4r - 8/4 = r - 2

4/4 can be written as 1 and -8/4 can be written as -2.

r - 2 = r - 2

You have an infinite amount of solutions.

Hope this helps!

My number has nine digits it is evenly divisible by 100 the value of one of the digits is 700,000 the digit in the millions place is both even and prime the digit in the hundreds place is the temperature at which water freezes the digit in the ten millions place is triple the number in the millions place the digit in the thousands place is the number of fluid ounces in a cup the digit in the hundred millions place is a special number because it is a factor of every number.

Answers

Let's go for it:
Nine digits: nnn,nnn,nnn

Divisible by 100 = last two digits are 00
hundred thousands place = 7
one millions place is even and prime = 2 [the only prime even number]
hundreds place = 0 [water freezes at 0 °C]
Ten millions place is triple one millions place = 6 [2x3]
one thousands place = 8 [8 ounces in one cup]
Hundred millions place = 1 [only number that's a factor of every number]

162,708,000

Convert into mixed number 81/3 and -29/2

Answers

hmmmm to convert from improper to mixed, simply do the division of both, the quotient gets upfront, the remainder as the numerator, for example,

how many times 3 goes into 81? well, 27 times, with a remainder of 0, thus [tex]\bf 27\frac{0}{3}[/tex]

how many times does 2 go into 29? well 14 times, with a remainder of 1, thus [tex]\bf -14\frac{1}{2}[/tex]

81/3 is 27

-29/2 is -14.5

Which mathematical symbol would best fill in the blank to compare the two real numbers?

square root of 7 blank 14 over 5
<
>
=
≈

Answers

square root of 7 is rounded to 2.645

14 over 5 is rounded to 2.8

square root of 7 < 14 over 5

Answer: The correct option is (A) < .

Step-by-step explanation: We are given to select the correct mathematical symbol that would best fill in the blank to compare the following two real numbers :

[tex]\sqrt7~~~?~~~\dfrac{14}{5}.[/tex]

First , we need to find the values of both the real numbers in decimal form.

We have

[tex]\sqrt7=2.64575...,\\\\\dfrac{14}{5}=2.8.[/tex]

Since, [tex]2.64575<2.8,[/tex] so we get

[tex]\sqrt7<\dfrac{14}{5}.[/tex]

Thus, the correct mathematical symbol is <.

Option (A) is CORRECT.

A train travels 128 km in 2 hours and 30 minutes. What is its average speed in km/min?

Answers

1 hour = 60 minutes

2 hours = 120 minutes +30 = 150 minutes total

128 / 150 = 0.853 km/min

What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2, 4)?

Answers

The answer to this question is -y=10x-8

The equation of the line parallel to [tex]$5x + 2y = 12$[/tex] and passing through the point (-2, 4) is given as [tex]$y = -\frac{5}{2}x - 1$.[/tex]

To find the equation of a line parallel to [tex]$5x + 2y = 12$[/tex] and passing through the point (-2, 4), we need to follow these steps:

1. Convert the given equation[tex]$5x + 2y = 12$[/tex] into slope-intercept form [tex]$y = mx + b$.[/tex]

2. Determine the slope of the given line.

3. Use the slope and the given point to find the equation of the parallel line using the point-slope form.

4. Convert the equation into slope-intercept form if needed.

Let's start with step 1:

1. Convert [tex]$5x + 2y = 12$[/tex] into slope-intercept form [tex]$y = mx + b$:[/tex]

Subtract [tex]$5x$[/tex] from both sides:

[tex]\[2y = -5x + 12\][/tex]

Divide both sides by 2:

[tex]\[y = -\frac{5}{2}x + 6\][/tex]

Now, we know that the slope of the given line is [tex]$-\frac{5}{2}$[/tex] . Since the line we're looking for is parallel to this line, it will have the same slope.

2. The slope [tex]($m$)[/tex] of the parallel line is [tex]$-\frac{5}{2}$.[/tex]

Next, we use the point-slope form[tex]$y - y_1 = m(x - x_1)$,[/tex]where [tex]$(x_1, y_1)$[/tex] is the given point (-2, 4) and [tex]$m$[/tex] is the slope.

3. Substitute the values into the point-slope form:

[tex]\[y - 4 = -\frac{5}{2}(x - (-2))\][/tex]

[tex]\[y - 4 = -\frac{5}{2}(x + 2)\][/tex]

Now, distribute[tex]$-\frac{5}{2}$:[/tex]

[tex]\[y - 4 = -\frac{5}{2}x - 5\][/tex]

4. Convert to slope-intercept form:

Add 4 to both sides:

[tex]\[y = -\frac{5}{2}x - 5 + 4\][/tex]

[tex]\[y = -\frac{5}{2}x - 1\][/tex]

So, the equation of the line parallel to [tex]$5x + 2y = 12$[/tex] and passing through the point (-2, 4) is [tex]$y = -\frac{5}{2}x - 1$.[/tex]

Complete question:

What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2, 4)?

Help I can’t answer this math question!!!

Answers

I hope this will help you
The probability is 6 out of 16

Find an equation of a line whose graph intersects the graph of the parabola y=x^2 at (a) two points, (b) one point, and (c) no point.

Answers

(a) y = x + 2

(b) y = 2x - 1

(c) y = 2x - 3

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