Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $24.50. The oil change for the other car required 7 quarts of oil and cost $29.00. How much is the labor fee and how much is each quart of oil?


The labor fee is $____
and each quart of oil costs $___

Answers

Answer 1

The labor fee is $16.75, each quart of oil costs $1.75.

Let $x be thee price of each quart of oil and $y be a flat fee for labor.

1. If the oil change for one car required 5 quarts of oil,

then these 5 quarts cost $5x and together with a flat fee for labor it cost $25.50.

Thus,

5x + y = 25.50.

2. If the oil change for another car required 7 quarts of oil, then these 7 quarts cost $7x and together with a flat fee for labor it cost $29.00.

Thus,

7x + y = 29.00.

3. Subtract from the second equation the first one, then

2x = 29 .00 - 25.50

2x = 3.5

x = 3.5/2

x = 1.75

Substitute it into the first equation:

5x + y = 25.50.

8.75 + y = 25.50.

y = 16.75

Thus, The labor fee is $16.65, each quart of oil costs $1.75

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Related Questions

Joe needs to get to his house, which is 106 miles away in 2 hours. How fast does he need to drive? 48 mph 104 mph 0.019 mph 53 mph

Answers

Answer:

53 mph

Step-by-step explanation:

We need to give the answer in terms of miles per hour. This means that we need to find out how many miles Joe needs to travel in one hour. Therefore, this is a ratio problem.

We can set up a proportion where the unknown variable is the number of miles driven in one hour:

[tex]\frac{106}{2} =\frac{x}{1}[/tex]

x is just 106/2, or 53. Therefore, Joe needs to travel 53 mph

Identify the property being demonstrated for each expression.
3+ (5 + 7) = (3+5)+7
(3)[5(7)] = (3)[7(5)]
Intro
5+0=5
Dor

Answers

The answer of this is 3•5•8 I did the math now I need to pass my test

Can someone please help me on this problem and show work pleasee I’m having trouble doing this!!!

Answers

Let’s start by stating the formula for the area of a rectangle,

A=LW

the letter a represents area, l represents length, and w represents width.

Next let’s substitute known values.

A=x(x+10)

Next let’s use the distributive property

A=(x(x))+(10(x))

Now simplify.

A=x^2 + 10x

So the equation for the area of this rectangle is A=x^2+10x

I believe this is the most simplified answer, please tell me if I am wrong and I will redo my work.

Answer here
x^2 + 10x

Find the length of JN

Answers

The length of JN from the figure is 108

Measure of segment of a line

A line is the shortest distance between two points. Given the following parameters

Required

We need the length of JN

JN = JK + KN

JN = 59 + 49

JN = 108

Hence the length of JN from the figure is 108

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Question 5 of 15
What would be the best first step in solving this system
x²-3x + 2y = -4
y = 3x + 2

Answers

Isolate y on both equations then equate

x²-3x+2y=-42y=-x²+3x-4y=-x²/2+3/2x-2

Now you can equate it with second one to get x

Answer:

Substitute y = 3x + 2 into x² - 3x + 2y = -4

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x^2-3x+2y=-4\\y=3x+2\end{cases}[/tex]

Since y is already isolated in the second equation, the best first step would be to substitute the second equation into the first equation, then solve for x.

Substitute equation 2 into equation 1:

[tex]\implies x^2-3x+2(3x+2)=-4[/tex]

Expand the brackets and simplify so that the equation equals zero:

[tex]\implies x^2-3x+6x+4=-4[/tex]

[tex]\implies x^2+3x+4+4=0[/tex]

[tex]\implies x^2+3x+8=0[/tex]

Now use the Quadratic Formula to solve for x.

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Define the variables:

[tex]\implies a=1, \quad b=3, \quad c=8[/tex]

Substitute the values into the formula and solve for x:

[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(8)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-23}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-1 \cdot 23}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-1}\sqrt{23}}{2}[/tex]

Remember that [tex]i^2=-1[/tex]

[tex]\implies x=\dfrac{-3 \pm i\sqrt{23}}{2}[/tex]

Therefore, the solutions to the system of equations are:

[tex]x=\dfrac{-3 + i\sqrt{23}}{2}, \quad \dfrac{-3 - i\sqrt{23}}{2}[/tex]

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A recent survey at a local company showed that 300 employees, or 66⅔% of the company’s employees, carpool to work each day. How many employees work at this company?
I'm sorry for all this trouble just really need help I'm in summer school because I was gone most of the school year and its all online so i don't understand anything

Answers

Answer:

450 employees work at this company.

Step-by-step explanation:

300 = 2/3 of x
300 × 3 = 2x
900 = 2x
450 = x

If a problem is 8(2x+4) = 2(1x+3) is the first step done of PEMDAS for THIS SPECIFIC PROBLEM parentheses or multiplication?

Answers

The first step is the parenthesis

How to determine the first step?

The equation is given as:

8(2x+4) = 2(1x+3)

Using PEMDAS, the first step is to open the brackets by multiplication.

So, we have:

16x + 32 = 2x + 6

Hence, the first step is the parenthesis

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A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32. 1. How much do you think a bus containing 30 people would be charged?

Answers

The charges of entrance fee for a bus containing 30 people is $98

Equation

let

Fixed charge = xAdditional charge per person = yNumber of person = m

Charges For 2 people = mx + y

14 = 2x + y

Charges For 4 people = mx + y

20 = 4x + y

14 = 2x + y

20 = 4x + y

subtract both equation

20 - 14 = 4x - 2x

6 = 2x

x = 6/2

x = 3

Substitute x = 3 into

14 = 2x + y

14 = 2(3) + y

14 = 6 + y

14 - 6 = y

8 = y

Charges For 8 people = mx + y

= 8(3) + 8

= 24 + 8

= $32

Therefore,

Charges For 30 people = mx + y

= 30(3) + y

= 90 + 8

= $98

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PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!

Answers

Answer:

Option D is correct

Step-by-step explanation:

there were no corn muffins sold.

Answer:

No corn muffins were sold at the bake sale :)

Step-by-step explanation:

Lets go thru each answer choice to see why it is incorrect/correct :)

A.

A is incorrect because more cookies were sold than muffins! that is why A is incorrect :)

B.

This calls for adding! lets do that now :)

Chocolate chip: 5

Oatmeal: 1

Peanut: 3

6 + 1 + 3 = 10

10 < 11

10 is not greater than 11 so B is incorrect!! :)

C.

We need to add again so lets do that now!

Corn: 0

Muffin: 2

2 + 0 = 2

2 < 3

2 is less than 3 so C is incorrect!! :)

D.

It is true that 0 corn muffins were sold at the bake sale so D is our answer!! :D

Have an amazing day!!

Please rate and mark brainliest!!

The perimeter of a rectangle is 96 ft and the width is 22 ft what is the length of the rectangle

Answers

The length of the rectangle is 26ft.

What is the perimeter of a rectangle?

The sum of all sides of a rectangle is the perimeter of the rectangle.A rectangle has two equal lengths and two equal widths.Therefore, the perimeter 'P' of a rectangle is the sum of two equal lengths and two equal widths. That is, 'P=2l+2w' where 'l' is the length and 'w' is the width of the rectangle.

What is the length of the rectangle with perimeter 96ft and the width 22ft?

The perimeter of a rectangle is, P = 96 ft.

The width of the rectangle is, w = 22ft.

As we know the perimeter P of a rectangle is given by the formula, P=2l+2w

Therefore, substituting the values in the equation we get,

P = 2l + 2w

96 = 2l + 2*22

96 = 2l + 44

2l = 96 - 44

2l = 52

l = 52/2

l = 26

Hence, the length of the rectangle is 26ft.

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What is the value of x? Show your work.

(Please hurry and see image for details.)

Answers

Answer:

7

Step-by-step explanation:

By the AA Postulate, triangles JKL and MNP are similar. Segment JK corresponds to segment MN, and segment JL corresponds to segment MP.

JK/MN = JL/MP

25/30 = 20/(4x-4)

25(4x-4) = 20*30

100x - 100 = 600

100x = 700

x = 7

Which type of arc requires another entity to specify its start point?

Answers

The type of arc that requires entity to specify its start point is the tangent arc.

Copy DEF to the line so that S is the
vertex.
This task will be complete when you have
constructed an angle with vertex S that is
congruent to ZDEF.

Answers

Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.

How to construct an angle with vertex?

To copy an angle we observe the subsequent steps,

1). Mark a working line with the help of a straightedge.

2). Now we set a point S as the vertex of the angle.

3). Create an arc with a radius 'r' (any length ) from vertex S which bisects the working line V.

4). With the exact radius we mark an arc from point E which bisects the line ED and EF at G and H respectively.

5). Mark an arc from point G which bisects line EF at I.

6). Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.

7). Now join the points S and U.

Therefore we copy any angle.

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Identify the recursive formula for the sequence -3, 9, -27, 81, ....

Answers

Answer:

A

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 3

this indicates the sequence is geometric.

the recursive formula allows a term in the sequence to be found by multiplying the previous term by the common ratio r , that is

f(n) = - 3f(n - 1) if n > 1 : f(1) = - 3

If the value the discriminant is exactly O,
what is true about the graph of the
quadratic equation?

Answers

The last option seems correct

Circle O is shown. Line segments B O and O C are radii. Point A is on the circle and is not within angle B O C.

The measure of Arc B A C is 240. What is the ratio of the measure of the major arc to the measure of the minor arc?
3:1
1:3
2:1
1:2

Answers

The ratio of major to minor arc = 2 : 1

What is a Circle?

A circle is the locus of a point such that its distance from a fixed point (center) is always constant.

Calculation

The length of an arc (L) with center angle θ is given by:

                                          L = (θ/360) * 2πr

where r is the radius.

Putting the values in the above formula.

For the major arc:

L = (240/360) * 2πr

For the major arc:

l = ((360-240)/360) * 2πr

l = (120/360) * 2πr

The ratio of major to minor arc = [(240/360) * 2πr] / [(120/360) *2πr] = 2 : 1

The ratio of major to minor arc = 2 : 1.

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Answer:c

Step-by-step explanation:

What is the midpoint of the segment shown below?

Answers

Answer:

The correct answer choice is D

I'LL GIVE YOU BRAINIEST!
1 1/5 · x/3 = 9/10 solve for x

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\huge\textbf{Solve:}[/tex]

[tex]\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\mathbf{\rightarrow \dfrac{1\times5+1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\mathbf{\rightarrow \dfrac{5 + 1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\mathbf{\rightarrow \dfrac{6}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{\rightarrow \dfrac{2}{5}x = \dfrac{9}{10}}[/tex]

[tex]\huge\textbf{Multiply \boxed{\bf \dfrac{5}{2}} to both sides:}[/tex]

[tex]\mathbf{\rightarrow \dfrac{5}{2}\times \dfrac{2}{5}x = \dfrac{5}{2}\times \dfrac{9}{10}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{5}{2}\times \dfrac{9}{10}}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{5\times9}{2\times10}}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{45}{20}}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{45\div5}{20\div5}}[/tex]

[tex]\mathbf{\rightarrow x = \dfrac{9}{4}}[/tex]

[tex]\mathbf{x \approx 2 \dfrac{1}{4}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = }\frak{2 \dfrac{1}{4}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Question :

1 1/5 . x/3 = 9/10 Solve for x

Solution :

>> (5 × 1 + 1 / 5) × (x / 3) = 9 / 10

>> (5 + 1 / 5) × (x / 3) = 9 / 10

>> (6 / 5) × (x / 3) = 9 / 10

>> 6 × x / 5 × 3 = 9 / 10

>> 6x / 15 = 9 / 10

>> 2x / 5 = 9 / 10

>> 2x × 10 = 5 × 9

>> 20x = 45

>> x = 45 / 20

>> x = 9 / 4

Therefore,

Value of x is 9 / 4 !!

Jenna collects stamps. She puts the same number of stamps on each page and then inserts each page into one of her two stamp books. One of her stamp books has a total of 840 stamps. The other has 1008. What is the largest number of stamps that Jenna could be putting on each page

Answers

168 is  the largest number of stamps that Jenna could be putting on each page

What is the Greatest Common Factor?

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

So the largest number of stamps that Jenna could be putting on each page

would be gcd of 1008 and 840.

840 = 2 x 2 x 2 x 3 x 5 x 7

1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7.

∴ The Gcd = 2 x 2 x 2 x 3 x 7 = 168.

Hence 168 is  the largest number of stamps that Jenna could be putting on each page

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To solve the equation 1. 75n = 7 for n, what operation must be applied to both sides in order to isolate the variable n?

Answers

Answer: Division
Divide both sides by 75 to isolate N

Jasmine wants to buy a car marked at $5200 at a second hand car dealer. The deposit is two-fifth of the price of the car
for the next weck's delivery. Jasmine's father helped her in the deposit by paying 30% of the price. Will jasmine have
enough for her car deposit? If not, how much more does she need to add to get the deposit?

Answers

Jasmine will not have enough for the car. The amount more that she needs is $520.

Will Jasmine have enough for the car?

The first step is to convert the fraction that represents the amount needed as a deposit to percentage.

(2/5) x 100 = 40%

Difference in the deposit and the amount Jasmine's father deposited: 40% - 30% = 10%

Amount more that she needs : 10% x 5200 = $520

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Which of the following ordered pairs is a solution of the system?
x + 3y = 12
y-x=12

Answers

Answer:

Step-by-step explanation:

Answer is ( -6, 6 )
Step by step
We have two equations
I like to label them first
x + 3y = 12 we will call A
y - x = 12 we will call B

I like to have the equations be in y intercept form to make the math easier
So I will change equation A to
3y = -x + 12
and change B to
y = x + 12

Now we will substitute the value of y of equation B into equation A

3(x + 12) = -x + 12
distribute
3x + 36 = -x + 12
now Isolate x on one side by adding x to both sides
3x + x + 36 = -x + x + 12
Combine like terms
4x + 36 = 12
Now subtract 36 from both sides to isolate x
4x +36 -36 = 12 - 36
Combine terms
4x = -24
Now solve for x by dividing both sides by 4
4/4x = -24/4
x = -6

Now to find y
Substitute your x value into equation B
y = x + 12
y = -6 + 12
y = 6

So your answer is (-6 , 6)

Check your work with equation
x + 3y = 12 from the original question
Substitute x and y values

-6 + 3(6) = 12
-6+18 = 12
12 = 12

Now do the same with the other equation
y - x = 12
6 - (-6) = 12
6 + 6 = 12
12 = 12

Both are Correct, so problem solved

Solve to find the value for x in the linear equation: 3(−4x 5) = 12. 1. use the distributive property: 2. use the subtraction property of equality: 3. division property of equality: 3(−4x) 3(5) = 12 −12x 15 = 12 −12x 15 − 15 = 12 − 15 −12x = −3 x =

Answers

Answer:

1/4

Step-by-step explanation:

I think that you forgot the addition or the subtraction sign between -4x  and 5.  I will assume that it was an addition sign

3(-4x+5) = 12  Multiply everything in the parentheses by 3

-12x + 15 = 12  Subtract 15 from both sides

-12x = -3  Divide both sides by -12

x = -3/-12 = 3/12 =1/4


A scientist measured the water pressure at different depths. She made a table showing her findings. The x-values
represent the depth, in meters. The y-values represent the pressure in atmospheres (atm).
0
15
30
0
3
6
Assuming there is a proportional relationship, which additional set of values could be included in the table?
(10,2)
(40,9)
(50,38)
(100, 76)
Mark this and return
Save and Exit
TIME REMAINING
51:28
Next
Submit

Answers

The additional set of values which could be included in the table is; (10,2).

Which additional set of values can be included in the table?

As evident in the task content, it follows that for a 15 unit increase in x, depth, there is a 3 unit increase in y, pressure.

On this note, it follows that with each 5 unit increase in x corresponds to 1 unit increase in y.

And ultimately, at x = 10, y = 2 × 1 = 2.

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Find the volume of the sphere.

Answers

Answer:

268.08 (268)

Step-by-step explanation:

The volume of a sphere is 4/3*pie*r^3

Which graph represents the circle given by the equation x + y - 4x + 9y -7 = 0?

Answers

The graph of the circle equation is graph (d)

How to determine the circle?

The equation is given as:

x^2 + y^2 - 4x + 9y -7 = 0

Rewrite as:

x^2 - 4x + y^2 + 9y = 7

Express (x^2 - 4x) and (y^2 + 9y) as perfect squares.

So, we have:

(x - 2)^2 + (y + 3)^2 = 7 + 4 +  20.25

Evaluate the sum

(x - 2)^2 + (y + 3)^2 = 31.25

A circle equation is represented as:

(x - h)^2 + (y - k)^2 = r^2

Where

Center = (h, k)

Radius = r

So, we have:

(h, k) = (2, -3)

r^2 = 31.25

r = 5.5

The circle that has a center of (2, -3) and a radius of 5.5 is graph d

Hence, the graph of the circle equation is graph (d)

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Measure the length of AD & D B what is the ratio of AD to DB ​

Answers

Based on the calculations, the ratio of AD to DB ​ is equal to 0.6.

What is a ratio?

A ratio is a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

From the graph, we have:

Length of AD = 1.5

Length of DB = 2.5

Ratio = AD/DB

Ratio = 1.5/2.5

Ratio = 0.6.

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What is the range of the function shown on the graph

Answers

Answer:

[tex]y \geq - 6[/tex]

Step-by-step explanation:

the range is all the y values shown in the graph, so as you can see, the y values are all those greater than or equal to -6

During the month of May there were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths. The newborn death rate is

Answers

During the month of May, there were 130 births, of which the newborn death rate is 38.4615.

According to the question,

There were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths.

In order to find the newborn death rate we have the formula:

=  [tex]\frac{number of death under 28 days of age }{Total live births in the same year}[/tex]  × 1000

= [tex]\frac{5}{130}[/tex] × 1000

=[tex]\frac{5000}{130}[/tex]

=38.4615

Hence, the new born death rate is 38.4615.

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An interior wall is made up of metal studs with 5/8 gypsum board on each side if the actual width of a stud is 3 5/8 what is the total thickness of the wall

Answers

Add em to get the answer
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