Jimmy owns a small engine repair business. The revenue, in dollars, can be modeled by the equation y = 420 + 72x, where x is the number of hours spent repairing small engines. The overhead cost, in dollars, can be modeled by the equation y = 24x + 180 where x is the number of hours spent repairing bikes. After about how many hours does the company break even? Note: The phrase break even refers to the value where the two functions are equivalent.

Mathematics High School

Jimmy owns a small engine repair business. The revenue, in dollars, can be modeled by the equation y = 420 + 72x, where x is the number of hours spent repairing small engines. The overhead cost, in dollars, can be modeled by the equation y = 24x² + 180 where x is the number of hours spent repairing bikes. After about how many hours does the company break even? Note: The phrase break even refers to the value where the two functions are equivalent.

Answers

Answer 1

Answer:

5 hours

Step-by-step explanation:

Given

[tex]y = 420 + 72x[/tex] --- Revenue

[tex]y = 24x^2 + 180[/tex] --- Overhead cost

Required

Determine the hours for break even

To do this, we simply equate both expressions as follows:

[tex]24x^2 + 180 = 420 + 72x[/tex]

Collect Like Terms

[tex]24x^2 - 72x + 180 - 420 = 0[/tex]

[tex]24x^2 - 72x -240 = 0[/tex]

Divide through 24

[tex]x^2 - 3x - 10 = 0[/tex]

Expand:

[tex]x^2 -5x + 2x -10 = 0[/tex]

Factorize:

[tex]x(x -5) + 2(x -5) = 0[/tex]

[tex](x + 2)(x -5) = 0[/tex]

[tex]x + 2 = 0\ or\ x - 5 = 0[/tex]

[tex]x = -2\ or\ x = 5[/tex]

But x can't be negative because it represents time.

So, x = 5 hours

Related Questions

I need help on thiss

Answers

Answer:

1/3

Step-by-step explanation:

Convert the Fractions Into decimal to know the detailed information as almost to whole numbers then use the Integer number system to figure out which is bigger or smaller.

2/8 = 0.25

1/3= 0.33

1/5= 0.2

1/7= 0.14

The largest of them all is 0.33

Hi I’m trying to do 9th grade algebra hw x+(-2)=8

Answers

answer is

x=10 because 10-2=8

-3/4-5/8=
This is a simple math problem
But it’s to hard for me
And I really need help
Not from someone who doesn’t know the answer

Answers

-11/8 because you turn the first one into -6/8 and then subtract to get -11/8

What place do we always round money to?

Answers

Answer:

Hundredths place

50.51

the ones is in the hundredths place

THIS IS VERY URGENT PLS!!!

Answers

Answer:

The answer is A

Step-by-step explanation:

The answer is A because I had the same question and I got it right.

Choose the answer that validates that the rate of change is constant by showing that the ratios of the two quantities are proportional and equivalent to the unit rate (simplified constant rate of change): NUMBER OF TEXTBOOKS Number of Students Number of Textbooks 7 35 14 70 21 105 28 140

Answers

Given:

The table of values is

Number of Students : 7 14 21 28

Number of Textbooks : 35 70 105 140

To find:

The rate of change and showing that the ratios of the two quantities are proportional and equivalent to the unit rate.

Solution:

The ratio of number of textbooks to number of students are

[tex]\dfrac{35}{7}=5[/tex]

[tex]\dfrac{70}{14}=5[/tex]

[tex]\dfrac{105}{21}=5[/tex]

[tex]\dfrac{140}{28}=5[/tex]

All the ratios of the two quantities are proportional and equivalent to the unit rate.

Let y be the number of textbooks and x be the number of students, then

[tex]\dfrac{y}{x}=k[/tex]

Here, k=5.

[tex]\dfrac{y}{x}=5[/tex]

[tex]y=5x[/tex]

Hence the rate of change is constant that is 5.

Plsssssss helpppp meeeee

Answers

Answer:

Step-by-step explanation:

Answer:

(give help)

Step-by-step explanation:

(help) ........................

Can someone please help mee (40 points
brainliest!!!)

Answers

a. $650

b. 50? Not sure about that one

What is the image of (7, -3) after a reflection over the x-axis?

Answers

Answer:(7,3)

Step-by-step explanation:

carley beat the school record for the 400 meter race by 1.3 seconds, if she ran the race in 55.7 seconds, what is the record

Answers

Answer:

57 seconds

Step-by-step explanation:

55.7 + 1.3 = 57 seconds

Answer:

57 seconds

Step-by-step explanation:

Simple math

Work out
3
9
+
2
3
Give your answer in its simplest form
ITS A FRACTON CAN U HELP ASAP

Answers

Answer:

The correct answer is 1.

Step-by-step explanation:

In order to solve the problem [tex]\frac{3}{9}[/tex] + [tex]\frac{2}{3}[/tex], we need can use two methods.

Method 1: Make the denominators the same.

3/9 + 2/3 =

3/9 + 6/9 =

9/9 =

Method 2: Turn both fraction into decimals (by dividing the numerator by the denominator.)

3/9 or 3 ÷ 9 = 0.3 (when rounded to the nearest tenth)

2/3 or 2 ÷ 3 = 0.7 (when rounded to the nearest tenth)

0.3 + 0.7 = 1

Therefore, the answer to this question is 1.

Answer 1 or 9/9

Explanation: First we need to find a common denominator which the easiest would be nine and then multiply those to equal nine and then you will get 3/9+6/9 which is equal to 9/9 which reduces to 1 have a nice day (:

1. Which equation best represents the relationship between x and y
in the graph?

Answers

Answer:

rises down 4 and moves forward 4

The equation y= 1/4x related proportional quantities x and y. What is the value of y when x is 12?

Answers

Answer:

Answer is 3

Step-by-step explanation:

[tex] \frac{1}{4} \times 12 = 3[/tex]

please mark me brainliest and 5 star

Solve this equation
m+6=2m-6
2

Answers

Answer: +6=2−62 its =68

Answer:

[tex]m = 12[/tex]

Step-by-step explanation:

[tex]m + 6 = 2m - 6 \\ 2m - m = 6 + 6 \\ m = 12 \\ \\ hope \: it \: helps... \\ pls \: mark \: as \: brainliest[/tex]

HELPPPPPPPPPP 7TH GRADE

Answers

Answer:

2400 m2

Step-by-step explanation:

the eqaution is 40*60

Answer:

2400m²

Step-by-step explanation:

that is the answer

40 x 60 = 2400m²

How many hours do they have to work before they go to the movies

Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's?
I got two different answers last time. One said 25 and the other said 11. Are either of them correct?

Answers

Answer:

25 months

Step-by-step explanation:

Plan A : $70 per month

Plan B : $50 per month + $500 as a one time cost.

So for A $70 a month would take 8 months to be at least $500

And for B it in those 8 months it would cost you $900

But we have to keep going up until they are equal

25*70 = 1750

(25*50) = 1250+500=1750

So yes 25 months is correct

A study of a population of 1,500 moths revealed that 15 out of every 75 moths in the population have gray stripes on their wings. Based on the results of this study, how many moths in the population have gray stripes on their wings?

Answers

Answer: 300 moths

Step-by-step explanation:

Since 15 out of every 75 moths in the population have gray stripes on their wings, this means the fraction of moths that have gray stripes on their wings is 15/75 = 1/5.

Therefore, out of 1500 moths, the number of moths in the population that have gray stripes on their wings would be calculated as:

= 1/5 × 1500

= 300 moths

What is an equivalent equation to 1/4n-16

Answers

Answer:

15/4z+12

Step-by-step explanation:

Help me pls and explain

Answers

Answer:

Step-by-step explanation:

I believe it is A because there is not any repeating X's. There is a repeating y which is 1. Therefore it is A.

Write an equation with variables on each side of the equal sign, at
least one fractional coefficient, and a solution of -6.

Answers

The equation is 1/2x = -9-x

What is the value of 3x+7 when x=3

Answers

Answer:

The answer will be 16

Step-by-step explanation:

If x is 3, then 3x will become 3 * 3 which will get you 9. And then 9 adds 7 and gets 16

Answer:

Step-by-step explanation:

3x+7

3(3)+7

9+7=16

I hope this is correct and have a great day

Can you help me with explanation will give brainiest

Answers

Answer:

Area of rectangular garden = lxb = 10*5

= 50 sq. inch

when area increases by six times

new area = 50*6 = 300 sq inches

now,

let x be increasement in both length and width

(5+x) (10+x) = 300

50 + 5x + 10x + x² = 300

x² + 15x - 250 = 0

x²+ 25x-10x -250 = 0

x(x+25) - 10 (x+25) = 0

( x-10) (x+25) = 0

either x + 25 =0

x = -25 length can be negative

0r x-10 = 0

x = 10

so 10 inches is increase on both side

Step-by-step explanation:

7 apples cost $5. How many apples can i buy with $8?

Answers

Answer:

7 Bc ur gonna b to broke to buy some more

Step-by-step explanation:

8-5

Help HELP HELP HELP HELP- I have 40 missing assignments and I want to make my mom proud!!!!

Answers

Answer:

1. 70

Step-by-step explanation:

2. 105

Answer:

A: 70.311 repeat

B: 105.53

Step-by-step explanation:

im not sure if im correct but hope this helps

Is y=-x+5 proportional

Answers

Answer:

yes

Step-by-step explanation:

I'm not entirely sure what your question is, but x is directly proportional to y, meaning as as x increases at a constant rate, y also increases at a constant rate.

Hunter owns a food truck that sells tacos and burritos. He sells each taco for $3.25 and each burrito for $6.50. Yesterday Hunter made a total of $520 in revenue from selling a total of 120 tacos and burritos. Graphically solve a system of equations in order to determine the number of tacos sold, x,x, and the number of burritos sold, yy.

what are the two equations?

Answers

Answer:

x=80 y=40

Step-by-step explanation:

Statement: At a store, 3 bags of peanuts were sold for $18. Determine if each statement has the same unit rate as the original statement or a different unit rate. Click the box for each statement to indicate "Same unit rate" or "Different unit rate." Same unit rate Different unit rate A jar of jam sold at $25 for 5. Sandwiches sold at $20 for 3. Cups of fruit sold at $48 for 8. Ham sold at $12 for 2.

Answers

Answer:

The original statements unit rate is $6.

A. 25/5=5-Different unit rate

B.20/3=6.67 Different unit rate

C. 48/8=6 Same unit rate

D. 12/2=6 Same unit rate

Step-by-step explanation:

Howie wants to get a $250 loan with a simple interest rate of 4%.

Which expression can be used to find the TOTAL amount that must be repaid on this loan?

1Points
A
250 + 4%

B
250 x 0.04

C
(.04 x 250) + 250

Answers

Answer:

Step-by-step explanation:

i need some help
will someone help me

Answers

Answer:yes

Step-by-step explanation: why not whatcha need

PLEASE ANSWER FAST 33 POINTS

Answers

Answer:

it clearly says 17 points not 33

Step-by-step explanation:

Answer:

(-5)+5=0

Step-by-step explanation:

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