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.


1 h

5 h

2 h

10 h

Answers

Answer 1
y₁ = 420 + 72x
y₂ = 24x² + 180

y₁ = y₂
∴ 420 + 72x = 24x² +180
∴ 24x² - 72x - 240 = 0
∴ x² - 3x -10 = 0
∴ ( x + 2)( x - 5 ) = 0
∴ x = -2 (Unacceptable)    OR    x = 5

∴ The correct answer is the second ⇒⇒⇒⇒⇒ 5h

Related Questions

answer these questions. Number 1 and number 2.

Answers

It would kinda make a triangle shape the others doesn't match and for the second one i'd be out of both cones.
1) The shape of the cross section is a triangle.

2) A cone, the top right one, is being formed by the rotation.

Today an exercise equipment store took 15% off the price of a treadmill, and for the next 2 days, it will take 15% off the previous day's price. If the price of the treadmill yesterday was $4000, what will be the price of the treadmill 2 days from now? (5 points: Part I – 1 point; Part II – 1 point; Part III – 1 point; Part IV – 2 points)

Answers

To find the price of the treadmill, you can calculate the amount you will pay after each day and then multiply by the percentage that you will pay for each additional day.

You should use 85% (100% - 15%) as the part you will pay for a quicker calculation.

$4000 x 0.85 = $3400 (after the first day)
$3400 x 0.85 = $2890 (after the second day)
$2890 x 0.85 = $2456.50 (after third day)

If the price of the treadmill yesterday was $4000, what will be the price of the treadmill 2 days from now?  I interpreted this as the discount would be applied for 3 days.

A line passes through (-7, -5) and (-5, 4). a. Write an equation gor the line in point-slope form. b. Rewrite the equation in standard form using integers.
A. Y-5=9/2(x+7);-9x+2u=-53
B. Y+5=9/2(x-7);-9x+2y=53
C. Y+5=9/2(x+7);-9x+2y=53
D. Y+7=9/2(x+5);-9x+2y=31

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -7 &,& -5~) % (c,d) &&(~ -5 &,& 4~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-5)}{-5-(-7)}\implies \cfrac{4+5}{-5+7}\implies \cfrac{9}{2}[/tex]

[tex]\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=\cfrac{9}{2}[x-(-7)] \\\\\\ \boxed{y+5=\cfrac{9}{2}(x+7)}\implies y+5=\cfrac{9}{2}x+\cfrac{63}{2}\impliedby \begin{array}{llll} \textit{and now we multiply}\\ \textit{both sides by }\stackrel{LCD}{2} \end{array} \\\\\\ 2y+10=9x+63\implies \boxed{\stackrel{\textit{standard form}}{-9x+2y=53}}[/tex]

just a quick note, multiplying both sides by the LCD, whatever it may be, simply gets rid of the denominators.

How do I do this? Please help

Answers

with intersecting chord lengths multiplying the 2 given lengths of one chord needs to equal the multiplication of the 2 lengths of the 2nd chord

so on chord FH you have 3.5 and 4.8
 multiply those:  3.5 x 4.8 = 16.8

so now chord GI needs to equal 16.8
 to find Y divide 16.8 by 2.4

y = 16.8 / 2.4 = 7

y = 7


The chord AB is a diameter of O. True or false.

Answers

Answer:

False.

Step-by-step explanation:

We have been given a graph and a statement. We are asked to determine whether the given statement is true or false.

Statement: The chord AB is a diameter of O.

We know that diameter of a circle is a chord that passes through the center of the circle.

Upon looking at our given graph, we can see that chord AB doesn't pass through the center at point 'o', therefore, AB is not a diameter of circle O.

Therefore, the given statement is false.

Answer: False

Step-by-step explanation:

I just got it right on the quiz

What percent of 51 is is 40?

Answers

the answer is 78.43%

Someone please help me?

Answers

because both AP and BP are tangent lines they are the same length so we will set them to equal each other to solve for x

AP = BP

3x-4 = 2x +12

subtract 2x from each side:

x-4 = 12

add 4 to each side:

x = 16

now we know x, replace x with 16 in the equation for AP:

AP = 3(16) -4
AP = 48 -4
AP = 44 meters

Complete the solution of the equation. Find the value of Y when X equals 2. 2x - 2y = 22

Answers

2x - 2y = 22

substitute 2 as the value of x.

we get;

2*2 -22 = 2y
4 - 22 = -18 = 2y
y = -9

The value of Y when x = 2 is y = -9

If the reserve rate is 6% and a bank receives a deposit of $14,000, how much of the $14,000 is the bank free to loan out?

Answers

Apex said $13160 was the right answer

The bank must keep 6% of the $14,000 deposit as a reserve, which amounts to $840. Therefore, it is free to loan out the remaining $13,160.

If the reserve rate is 6% and a bank receives a deposit of $14,000, the bank is required to keep 6% of that deposit as reserves. To calculate the amount the bank needs to keep in reserves, we multiply the total deposit by the reserve rate:

Reserve amount = Total deposit x Reserve rate

Reserve amount = $14,000 x 0.06 = $840

Now, to find out how much the bank is free to loan out, we subtract the reserve amount from the total deposit:

Amount available for loans = Total deposit - Reserve amount

Amount available for loans = $14,000 - $840 = $13,160

The bank can loan out $13,160 of the initial $14,000 deposit.

Miguel’s teacher asked him to color 4/8 of his grid. He must use 3 colors: red, blue, and green. There must be more green sections than red sections. how can Miguel color the sections of his grid to follow all the rules.

Answers

color 2/8 of grid in green, 1/8 grid in red and 1/8 grid in blue

The population of a town increased from 5,400 to 6,000 people. What was the percent of the increase?

Answers

increase = 6000 - 5400 = 600

percentage increase = 600/5400 x 100 = 11.11%

Answer: 11.11%

What is the eleventh term in the sequence 17, 24, 31, 38…?

Answers

I got 87. hope this helps!

Michelle will be 72 years old in eighteen years. How old is Michelle now?

Answers

Michelle would be 54 years old. 

72-18=54
She is 54 years old, since you would subtract 18 from 72.

Two apples and three peaches cost $1.65. three apples and two peaches cost $1.60. what is the cost of one peach

Answers

Let a = cost of an apple and p = cost of a peach

From the two statements we can create the following system of equations:
2a + 3p = 1.65
3a + 2p = 1.60

Since we want to know the cost of a peach, let's eliminate the "a" terms by creating opposites.  The LCM for 2 and 3 is 6 so I will multiply the top equation by 3 and the bottom equation by -2. This will create opposites to cancel "a" terms.
3(2a + 3p = 1.65)  →  6a + 9p = 4.95
-2(3a + 2p = 1.60) → -6a - 4p = -3.20
The result of adding →       5p = 1.75
The result of ÷ 5 →              p = .35
This means one peach cost .35 or 35 cents
Let number of apples be a and peaches be p.
Number of apples = a
Number of peaches = p

Two apples and three peaches cost $1.65
⇒2a + 3p = 1.65

Three apples and two peaches cost $1.60
⇒3a + 2p = 1.60

System Equations :
[tex]\begin{cases}&2a + 3p = 1.65 ---- (1) \\&3a + 2p = 1.60 ---- (2)\end{cases}[/tex]

[tex]\begin{cases}&\text{Equation (1}) \times3: 6a + 9p = 4.95 ---- (1a) \\&\text{Equation (2}) \times2: 6a + 4p = 3.20 ---- (2a)\end{cases}[/tex]

Equation (1a) - (2a) :
[tex] \begin{aligned} &5p = 1.75 \\&p = 0.35&\end{aligned} [/tex]

Answer: $0.35

{3, 4, 7} list all the subsets.

Answers

A subset is a collection of items drawn from the original larger set. A subset can have the same number of items as the original set or the count can be smaller. 

Subsets that have 3 items: {3, 4, 7} which is the original set. Any set is a subset of itself. 

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

Subsets that have 2 items
{3, 4}, {3, 7}, {4, 7}

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

Subsets that have 1 item
{3}, {4}, {7}

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

Subsets that have 0 items: the empty set which we write { } or using the symbol [tex]\varnothing[/tex]

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

So all together we have 8 subsets
{3, 4, 7}
{3, 4}, {3, 7}, {4, 7}
{3}, {4}, {7}
{ }

Side Note: There are n = 3 items in the original set so there are 2^n = 2^3 = 8 subsets possible. The collection of all subsets is known as a power set.

Final answer:

The subsets of {3, 4, 7} are {}, {3}, {4}, {7}, {3, 4}, {3, 7}, {4, 7}, {3, 4, 7}

Explanation:

When listing all the subsets of {3, 4, 7}, we include the empty set {}, as well as all the subsets that can be formed by selecting one or more elements from the original set. In this case, the subsets are:

{}{3}{4}{7}{3, 4}{3, 7}{4, 7}{3, 4, 7}

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Peaches varied directly as apples. when there were 40 peaches, there were 120 apples. how many apples went with 500 peaches?

Answers

Given that peaches varied directly as apples. then:
let the number of peaches be p and that of apples be a
hence
p=ka
where
k is constant of proportionality given by:
k=p/a
when:
p=40, a=120
thus
k=40/120=1/3
thus the equation will be:
p=1/3a
thus the number of apples where there are 500 peaches will be:
500=1/3a
multiplying both sides by 3 we get:
500×3=1/3a×3
a=1500

2x-14y= -16 solve for x ..

Answers

The first step for solving this expression is to move the variable to the right side of the equation and then change its sign.
2x = -16 + 14y
Now divide both sides of the equation by 2.
x = -8 + 7y
Since we cannot simplify this equation any further,, the correct answer will be that x = -8 + 7y.
Let me know if you have any further questions.
:)

2x - 14y = -16

Move all the terms without the variable on the other side of the equation. Add 14y to both sides of the equation.

2x = -16 + 14y

Divide both sides by 2.

x = -8 + 7y is your answer.

Craig is designing a new cylinder-shaped can for a pet food company. He wants the height of the can to be 40 mm and the radius of the can to be 1 3/8 times the height of the can. He models the can on a coordinate grid as a rectangle in the first quadrant that will be rotated around the y-axis to create the 3-dimensional can. What will be the diameter of the can?

Answers

The height of the can for this case is given by:
 h = 40 mm
 The radius of the can is given by:
 r = (1 3/8) * h
 Substituting values:
 r = (1 3/8) * 40
 r = 55 mm
 Therefore, the diameter of the can is:
 d = 2 * r
 d = 2 * 55
 d = 110 mm
 Answer:
 The diameter of the can will be:
 d = 110 mm

two negative integers have a sum of -18 and a product of 80. what are the integers?

Answers

The two integers your looking for are -8, and -10. -8+-10=-18
                                                                               -8*-10=80
Please rate brainliest if this helped you.
Hello!

The most reasonable answer would -8 and -10.

-8 * -10 = 80

-8 + -10 = 18

Hope I helped!

A translation is applied to the rectangle formed by the points A(−2, 6) , B(2, 6) , C(2, 4) , and D(−2, 4) . The image is the rectangle that has vertices ​ A′(1, 6) ​, ​ B′(5, 6) ​, C′(5, 4) and D′(1, 4) . Select the phrase from the drop-down menu to correctly describe the translation. The rectangle was translated .

Answers

The triangle was translated 3 units to the right horizontally. (x+3, y)
You can just move one of the points to see how it moved. 

Answer:

The answer is 3 units to the right.

Step-by-step explanation:

A school play cost $1,200 to produce. if tickets sold for $5 each, the profit, p, made on the play by selling x tickets is given by the equation shown. p=5x−1,200 what is the slope of the line representing this equation?

Answers

5. 

Slope is always the number attached to x. 

The slope of the line representing this equation will be;

⇒ $5

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The tickets sold for $5 each, the profit, p, made on the play by selling x tickets is given by the equation shown,

⇒ p = 5x - 1,200

Now,

We know that;

The slope - intercept form of an equation is,

y = mx + c

Where, 'm' is slope of the line and 'c' is y - intercept.

Here, The equation is,

⇒ p = 5x - 1200

By comparing, we get;

⇒ Slope (m) = 5

Thus, The slope of the line representing this equation = 5

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A total of 589 tickets were sold for a play. They were either adult tickets or student tickets. There are 61 fewer student tickets sold than adult tickets. How many adult tickets were sold?

HELLLPP ASAPPP

Answers

Adult tickets: 325
Student Tickets: 264

You can get this by setting adult tickets equal to x and student tickets equal to x - 61. Then you can set equal  to 589 and solve for x. 

An acrobat was launched toward a water tank, with an upward velocity of 48 feet per second. The launch point was 32 feet below the water level in the tank. Use the quadratic equation 0 = -16t2 + 48t – 32 to find how much time, t, it took for her to reach the water level in the tank.

Answers

Answer:

1 or 2 seconds

Step-by-step explanation:

Math papa

Answer:

B. 1 or 2 seconds

Step-by-step explanation:

ttm

An item is priced at $13.04. If the sales tax is 5%, what does the item cost including sales tax? If necessary, round to the nearest cent.
A.
$13.56
B.
$13.24
C.
$12.39
D.
$13.69

Answers

The answer would be D
to find 5% you have to multiply by 0.05 

13.04 * 0.05 = 0.652
When you round it to the nearest cent you get 69 cents
so the answer is D) 13.69 

A rectangle has a length that is 3 times the width. Use the formula P = 2l +2w to determine the length if the perimeter is 32 and the width is 4 a. 12 c. 32 b. 8 d. 4

Answers

Let the width be 4
Let the lenght be 3x because it is 3 times the width
P = 2L + 2W
32= 2(3X)+2(4) Combine like terms
32 = 6x+ 8 solve for x
24=6x divide
x= 4
Answer: D

Graph the equations to solve the system Y equals 1/3 X +6 and why equals 1/3 X +4

Answers

For this case we have the following functions:
 y = (1/3) x + 6
 y = (1/3) x + 4
 We note that both lines have the same slope in this case given by:
 m = 1/3
 Therefore, the lines are parallel. As they are parallel, they are not cut at any point.
 Thus, the system of equations has no solution.
 Answer:
 The system has no solution (parallel lines)
Graph the equations to solve the system Y equals 1/3 X +6 and y equals 1/3 X +4

Following the formula: y=mx+b,
where:
m= slope
b=y-intercept
As observed in the given equations, they have the same slope which is equal to 1/3 but each have different y-intercept which is 6 and 4.

Note that two lines are parallel if their slopes are equal and they have different y-intercepts. 

Upon graphing, it had seen that the two functions are parallel.
See attached picture for the graph.

A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. one flower is chosen at random and given to a woman. another flower is then chosen at random and given to a different woman. what is the probability that both flowers are pink roses?

Answers

0.267 should be right 

Answer:

Step-by-step explanation:

The probability that the first flower is a pink rose is  4 /15.

The probability that the second flower is a pink rose is  3 /14 .

Therefore, the probability that both flowers are pink roses is  

4 /15  ·  3 /14 = 0.057

Robin says that polynomials are closed under division. Brad adamantly disagrees. Who is correct? Justify your answer.

Answers

Brad is correct.

Polynomials do not include negative exponents; this means there can be no variables in the denominator.  If two polynomials do not divide evenly, the remainder is written as a fraction with the divisor (which can include a variable) in the denominator.  This is not a polynomial.

A function has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}. Which set of ordered pairs represents this function?

A.{(1, 2), (3, 4), (5, 6), (7, 2)}
B.{(1, 2), (3, 6), (5, 4), (5, 2)}
C.{(1, 2), (3, 2), (5, 2), (7, 2)}
D.{(1, 4), (3, 4), (5, 6), (7, 6)}

Answers

For this case we have the following domain:
 {1, 3, 5, 7}
 We have the following range:
 {2, 4, 6}
 A value of the range belongs to each value of the domain.
 Therefore, the ordered pairs are:
 (1, 2)
 (3. 4)
 (5, 6)
 Answer:
 A. {(1, 2), (3, 4), (5, 6), (7, 2)}

Which of the following segments is a radius of O?
Please help

Answers

Possibly B. RO. maybe even
ANSWER

The segment that is a radius is

[tex]\bar{RO} [/tex]

EXPLANATION

A radius is any line segment from the center of a circle to the circumference.

From the above diagram, the center of the circle is O.

The points on the circumference are A, R S and T.

The only line from the circumference to the centre in the options above is the line segment RO.

The correct answer is B.

Note however that

[tex]\bar{AS}[/tex]
is a diameter, which is a special chord.

[tex]\bar{RA}[/tex]

is a chord.

[tex]
\bar{ST}[/tex]
is also a chord.
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