The first equation in the following system gives a company's income, in dollars, for selling x baseball caps. The second equation gives the cost of making x baseball caps. Y = 8x y = -0. 01 x2 4x 3,200 The solution of the system is (400, 3,200). How would you interpret this solution?.

Answers

Answer 1

The solution of the equation can be determined by substituting the points in the equation and solving it.

The solution of the given equation would be interpreted by solving the equation for the value of x and y.

The solution of the equation is (400, 3200) and it can be determined by using substitution method.

Given that,

The first equation in the following system gives a company's income, in dollars, for selling x baseball caps.

The second equation gives the cost of making x baseball caps.

[tex]\rm y = 8x\\\\ y = -0.01 x^2 + 4x + 3200[/tex]

The solution of the system is (400, 3,200).

We have to determine,

How would you interpret this solution?

According to the question,

The first equation in the following system gives a company's income, in dollars, for selling x baseball caps.

The second equation gives the cost of making x baseball caps.

[tex]\rm y = 8x\\\\ y = -0.01 x^2 + 4x + 3200[/tex]

On solving both the equation,

Substitute y = 8x in the equation 2,

[tex]\rm y = -0.01 x^2 + 4x + 3200\\\\ 8x = -0.01 x^2 + 4x + 3200\\\\0.01x^2+8x-4x-3200=0\\\\0.01x (x+800) -4(x+800)=0\\\\(x+800)\ (0.01x-4)\\\\When \ \ x +800=0, \ x = -800\\\\And\ \ 0.01x-4 = 0, \ \ x = \dfrac{4}{0.01} \ \ x =400[/tex]

The value of x is not -800 because the cost can not be negative.

Then the value of x is 400.

Substitute the value of x in equation 1,

[tex]\rm y = 8x\\\\y = 8(400)\\\\y = 3200[/tex]

Hence, The solution of the equation is (400, 3200).

For more details about System of Equation refer to the link given below.

https://brainly.com/question/281027


Related Questions

Write an equation that represent the line

Answers

the formula that is needed is y=mx+b, so the answer is y=5/6x+2.5

Round 68,533 to the nearest hundred.

Answers

Answer:

68,500

Step-by-step explanation:

68,533 <- Hundreds place is underlined

[] To round, we look at the number right the place. If it is less than 5, keep it the same. If it is five or greater , round up.

[] In this case it is a 3, so we keep it the same. We get an answer of 68,500

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update  my answer accordingly. (ノ^∇^)

- Heather

The answer is:

68,500

Explanation:

When counting, the digit 5 is in the hundredth place in the entire number.

For example:

$500 (five hundred dollars)
$6,500 (six thousand, five hundred dollars).

Therefore, whatever comes after the number 5 would become a zero.

Test 1 2021-22 19 of 9
The graph represents Samantha's walk in front of a motion detector. Identify two points marked on the graph that define the interval
where her average rate of change was 2/3 meters per second.
Motion Detector Walk

Answers

Given that the shape of the graph is curved, the rate of change can be

estimated by using the average value between specified points.

The points are;

[tex]\underline{(6, \, 6)}[/tex][tex]\underline {(9, \, 8)}[/tex]

Reasons:

The coordinates of the points marked (distances and time) during the walk are;

[tex]\begin{tabular}{|c|c|}Time (seconds), x&Distance from motion detector (meters), y\\0&1\\3&2\\5&4\\6&6\\7&7\\9&8\end{array}\right][/tex]

Required: Identification of two points marked on the graph that define the

interval where Samantha's average rate of change was 2/3 meters per

second.

Solution:

The average rate of change between two points is given by the ratio of

difference in the distance from the motion detector to the difference in

time between the points.

[tex]\displaystyle Average \ rate \ of \ change = \frac{Change \ in \ distance}{Change \ in \ time} = \mathbf{ \frac{\Delta y}{\Delta x}}[/tex]

At the required points, the change in the y-values, will be 2 × a, while the

corresponding change in x-values will be 3 × a, where, a is rational number.

From the above table, at the points where the time is 6 seconds and 9

seconds, we have the following distance time ordered pair;

(6, 6), and (9, 8), from which we have;

[tex]\displaystyle Average \ rate \ of \ change =\frac{\Delta y}{\Delta x} = \mathbf{\frac{8 - 6}{9 - 6}} = \frac{2}{3}[/tex]

Therefore;

The points [tex]\underline{(6, \, 6)}[/tex], and [tex]\underline {(9, \, 8)}[/tex], are two points that represent an interval

where her average rate of change was 2/3 meters per second.

Learn more about average rate of change of a graph here:

https://brainly.com/question/9650454

The area of a triangle is 30 square inches.
The base of the triangle is x - 6 inches,
and the height is x + 5 inches.
Find the value of x, and the dimensions of the triangle.
A = 1/2bh

x=
base=
height=

Answers

Answer:

x=10

base=4inches

height=15inches

Step-by-step explanation:

A=1/2bh

30=1/2(x-6)(x+5)

60= x²+5x-6x-30

x²-x-90=0

x²-10x+9x-90=0

x(x-10) +9(x-10)=0

(x+9)(x-10)=0

x= -9 or 10

x cannot be negative

Therefore x= 10

base= 10-6

=4inches

height=10+5

=15inches

A circumference of the wheel of Victoria is 4.4m. How much distance coill it cover in 500 revolutions?​

Answers

[tex]\huge \bf༆ Answer ༄[/tex]

Total distance covered is equal to ~

Number of revolutions × circumference

[tex] \sf500 \times 4.4[/tex]

[tex] \sf2200 \: m[/tex]

Hence distance covered = 2200 m = 2.2 km

Write the following statements in the form of equations.

a. The sum of five times p and 8 is 23.

b. If you subtract 6 from 3 times a number, you get 18.

c. One third of a number plus 7 is 26.

Answers

Answer:

a. The sum of five times p and 8 is 23.

can hellp me with this plzzzzzzz no links plz

Answers

400? I’m confused what you’re asking me to do !

Find f(2) and f(3).
f(1) = 3
f(n) = 7f(n = 1)

Answers

Answer:

do it got a picture

on the edge2020

Step-by-step explanation:

Ok so how can you tell if 2 angles are complementary, vertical, or supplementary? I don't know how to tell and I have pre-algebra hw due tomorrow. ​

Answers

Complementary angles are two angles that add up to 90°

Supplementary angles are two angles that add up to 180°

Vertical angles are two angles that are opposite of each other and are also congruent

A number is chosen uniformly at random from among the positive integers less than $10^8$. Given that the sum of the digits of the number is 9, what is the probability that the number is prime

Answers

Answer:

 

If the sum of the digits of a number is divisible by 9, then that number is divisible by 9. An..... sorry if this does not help :(

Step-by-step explanation:

Determine whether the graph represents a function. *

Answers

Answer:

Not a function

Step-by-step explanation:

There are two points that correspond to the same variable

Hope this helps

Answer:

not a function

Step-by-step explanation:

There are two points that have the same x and  different y values

This would fail the vertical line test.

#5: Consider the expression below. Which of the following numbers are coefficients? Select all that apply.

9x2 + 5x – 8 + 3x2

A. 9
B. 5
C. 8
D. -8
E. 3

Answers

Answer:

B

Step-by-step explanation:

the 5 in 5X.

The graph shows how the number of hats in your collection increased since you began collecting 6 months ago. How many hats did you collect during the second month? Hat Collection A graph has time (months) on the x-axis, and total number of hats on the y-axis. Lines connect points (0, 0), (1, 3), (2, 5), (3, 8), (4, 9), (5, 10), (6, 12). hats

Answers

Answer:

Step-by-step explanation:

Two hats were collected in the second month (5-3) =2.

You are 5 years less than your older brother express the age of your elder brother in terms of your age using variable​

Answers

Answer:

Step-by-step explanation:

If x represents your age then the age of your elder brother

is x + 5 years.

Answer:

Your age = y

So the variable expressing the age of your elder brother would be y + 5 (years).

Hope that helps?

What is the value of x in the equation 8x – 2y = 48, when y = 4?

Answers

Answer:

x = 7

Step-by-step explanation:

Substitute y = 4 into the equation and solve for x

8x - 2(4) = 48

8x - 8 = 48 ( add 8 to both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Answer:

x = 7

Step-by-step explanation:

8x - 2y = 48

y = 4

First, let's substitute y for it's actual value as we know it.

8x - 8 = 48

Next, add 8 on both sides. (When doing these sort of questions you must do the inverse.)

8x = 56

Divide both sides by 8 to get x.

x = 7

Hope this helps and I hope you have a good day!:)

What is three minus X equals 11

Answers

Answer:

x= -8

Step-by-step explanation:

Subtract 3 from both sides to isolate the variable

Divide the variable by -1 so it can become positive; whatever you do to one side, you have to do to the other.

You'll end up with the equation of x= -8 if you do it correctly

-x=11-3 x=8 this is anwer

hunter has a jar of 368 nickels and dimes. the total value of coins is $28.40. which system of equations below would be the best to use to find the number of nickels and dimes hunter has?

Answers

Answer:

We can't see your answer choices, but it would be n + d = 368 and .05n + .10d = 28.40

Step-by-step explanation:

n+d=368 and 0.05n+0.1d=$28.40 is the system of equations below would be the best to use to find the number of nickels and dimes hunter has

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that hunter has a jar of 368 nickels and dimes.

The total value of coins is $28.40.

We need to find the system of equations below would be the best to use to find the number of nickels and dimes hunter has

The total quantity of nickels and dimes is 328

n+d=368

The value of nickel is 0.05 dollars

The value of dime is 0.10 dollars

0.05n+0.1d=$28.40

Hence, n+d=368 and 0.05n+0.1d=$28.40 is the system of equations below would be the best to use to find the number of nickels and dimes hunter has

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

i needhelp quick will give brainlist

Answers

Answer:

B. y=0.07x

Step-by-step explanation:

Hope this helps! Have a good day:)

HOME WORK DUE SOON PLZ HELP!!!!!

what is the slope of this graph?​

Answers

Answer

16

Step-by-step explanation:

slope go up 16 every time

who wants to help i really dont wanna do this question

Answers

Answer:

71

Step-by-step explanation:

(2x² = 2 × 5² = 2 × 25) + ([4x = 4 × 5 = 20] + 1)

(50) + (21) = 71

Brainliest
Please do one of the above
(I would appreciate if you did more then one)

Answers

Answer:

a) 52.5 ft. b)40.1ft c)12.5ft d) 72.6

Step-by-step explanation:

a) The height of the lighthouse is 84ft, and the angle of elevation is 58 degrees.

tan58=84/x

find x by dividing 84 by tan58, and you get 52.5ft.

b) do the same thing, except 131 is in the base of the right triangle shape. That being said, do tan17=x/131.

multiply 131 by tan17, and you get x=40.1 feet.

c) This question wants you to find the length of the slide, (basically the hypotenuse).

given the angle to be 46, do sin46=9/x

since sin is opp/hyp

9/sin46= 12.5ft

d) Find the angle of elevation by using inverse tan given the base to be 5, and the height to be 16ft.

tan^-1=(16/5)=theta

x=72.6 hope this helps!

Answer:

Step-by-step explanation:

Calculate 3 tonnes 335kg - 905kg and give the answer in tonnes​

Answers

Answer:

2430kg

Step-by-step explanation:

3 tonnes is 3000kg so 3 tonnes 335kg is 3335kg. Take 3335 - 905 you get 2430

How many lines of symmetry does this have it. If none put 0.​

Answers

Answer:

well a line of symmetry is a line that cuts a shape directly in half in this case there is 4

Step-by-step explanation:

(-14,-3) (6,10) find the slope and explain
please

Answers

Answer:

The slope would be 13/20

Step-by-step explanation:

10-(-3) is 13 (numerator) and 6-(-14) is 20 (denominator)

hope this helps!!

G=4ba
Solve for A
Pls

Answers

Answer:

a=g/4b

Step-by-step explanation:

g=4ba

g/4b=a

a=g/4b

Could anyone help out? It's 11pm and I have finals tmrw :/

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). 3 P(x) = 5x? - 2x2 – 3x+ 3; - 4​

Answers

There i hope it help

Stay safe and study hard

Edward deposited ​$6,000 into a savings account 5 years ago. The simple interest rate is 4​%. How much money did Edward earn in​ interest? Need answer in under 10 minutes

Answers

Answer:

,..................... 6000*12*5 %4 =630

Answer:

6240

Step-by-step explanation:

It's it 6,000+4% it's = 6240

kam
An object oscillates as it moves along
the x-axis. Its displacement varies with
time according to the equation
x = 3 cos(6pi t + pi/2)

where t is in seconds

What is the frequency of this motion?

Answers

The frequency of this motion is 3 Hz

The standard equation of an oscillation is given by:

x = A cos(ωt + Ф)

Where x is displacement, A is amplitude, ω is angular frequency = 2πf and Ф is phase difference.

Given the equation:

x = 3 cos(6πt + π/2)

Hence;

ω =

2πf = 6π

f = 3 Hz

The frequency of this motion is 3 Hz

Find out more about frequency at: https://brainly.com/question/254161

I NEED HELP PLEASE! Thank you

Answers

Answer:

A

Step-by-step explanation:

21 -6×3

-6×3=-18

21-18

=3

help with these pleaseee

Answers

Percent Change = (new quantity - old quantity) / old quantity

#2:

(64 - 52) / 52

12 / 52

0.2308

23%

#4:

(12 - 18) / 18

-6 / 18

-0.33

33% decrease

#5:

(10 - 16) / 16

-6 / 16

-0.375

38% decrease

Hope this helps! :)

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