1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dima020 [189]
2 years ago
5

100 POIntsSarah has been running a dog-walking business since 2010. She walks dogs twice a day, takes them to the park, and retu

rns them to their homes. Each year, she has increased her fee by the same amount. The table shows what Sarah charged each customer for two given years of her business:
Year Annual Dog-walking Fee
2010 $350
2014 $750
A. What is the rate of change and initial value for Sarah's business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Sarah charges each year. (10 points)
Mathematics
1 answer:
Svetach [21]2 years ago
7 0

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

Problem (a):  \textsf{Rate of change = \$100 per year, Initial value = \$350}

Problem (b):  \textsf{y = 100x + 350}

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

The first step that we must take before attempting to solve the problem is to understand what the problem is asking us to do and what is given to us to help do so.  So in the first part we are asked what the rate of change and initial value for Sarah's business.  Using that information we would be able to complete the second part which asks us to write an equation in slope-intercept form.  In this problem we are given two points which resemble how much Sarah charged each customer for the given years.

Now that we know what we must accomplish, we can move onto actually solving the problem.  So first we must determine what the rate of change is and this is basically like finding the slope.  This can be done by subtraction the y-values in the numerator and the x-values in the denominator.

<u>Determine the rate of change</u>

  • m = \frac{y_2 - y_1}{x_2 - x_1}
  • m = \frac{750 - 350}{2014 - 2010}
  • m = \frac{400}{4}
  • m = 100

Now we can see that the rate of change would be an increase of $100 per year after calculating the slope.  The next part was to determine the initial value for Sarah's business and this can be easily done because we know that she has had this business since 2010 and we are given that the price in 2010 was $350.

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

We now have completed part (a) and we can move onto the next part which is to create an equation in slope-intercept form to represent the fees that Sarah charges each year.

So we know that the slope is an increase of $100 per year which means that we will have a positive slope.  We also know the initial price that Sarah charged in her first year which will represent the y-intercept or the first point on the graph.

  • m ⇒ This represents the slope of the line that is being written.
  • b ⇒ This represents the y-intercept of the line that is being written.

<u>Plug in the values</u>

  • y = mx + b
  • y = 100x + 350

After plugging in the values we have a finished expression in slope-intercept form which represents the scenario that is going on with Sarah's business. We see that that initial price was 350 and we increase that by 100 each year. Therefore, the final equation in slope-intercept form is y = 100x + 350.

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

You might be interested in
What is the value or x?
Romashka [77]

From the given figure

\cos x=\frac{XY}{XZ}

Since XY = 5.1 and XZ = 7.7, then

\cos x=\frac{5.1}{7.7}

To find x, use the inverse of cos

x=\cos ^{-1}(\frac{5.1}{7.7})

Use the calculator to find x

x=48.522

The answer is

4 0
1 year ago
PLEASEE HELP!! &lt;3 100 POINTSS
iris [78.8K]

To tell isf a table is proportional, divide y by x,

if all sets are the same it is proportional.

First table:

3 / -3 = -1

2 / -4 = -2


-1 and -2 are not the same


Table 2:

1/-1 = -1

3/-3 = -1

5/-5 = -1


These are all the same.


Table 2 is correct.

6 0
3 years ago
Read 2 more answers
Please answer with explanation
aksik [14]
Itttttttsssssssss A...........
8 0
3 years ago
Find the volume of the cylinder in terms of . The diagrams are not drawn to scale.
hoa [83]

Answer:

43.35pi m cubed

Step-by-step explanation:

Volume of a cylinder

= pi r^2 h

Where r = radius

h = height

Given r = 1.7m and

h = 15m

Volume = pi x (1.7)^2 x 15

= pi x 1.7 x 1.7 x 15

Multiply through

Volume = 43.35 pi m cubed

7 0
2 years ago
Which equation can pair with x 2y = 5 to create an inconsistent system?
mr Goodwill [35]

The equation that can be paired with x + 2y = 5 to create an inconsistent system is given by:

2x + 4y = 3.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

An inconsistent system is a system that has no solutions, and it happens when the coefficients of x and y are multiples, and the independent terms are not.

Hence:

x + 2y = 5.

2x + 4y = 3.

Is inconsistent, as the variables are each multiplied by 2, but the independent term is not.

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

5 0
2 years ago
Read 2 more answers
Other questions:
  • What is the slope of the line from point (-4,2) to (-2,2)?
    7·1 answer
  • Jack spent $40 on new shoes then he spent half of what he had left on clothes finally he gave five dollars to his brother now he
    12·1 answer
  • How many times can 10go in to 2,135,468
    12·1 answer
  • 1. Un conjunto de tablero de baloncesto que se vende por $ 79 tiene un descuento del 15%. ¿Cuál es el precio de venta?
    14·1 answer
  • Solve the literal equation ab+c=d in terms of a
    9·1 answer
  • Which option is equivalent to log 7 - log 2? A. log 5 7 B. log O C. log 9 OD. log 72​
    7·1 answer
  • Solve the expression. 0.02 × 0.3<br> A. 0.6<br> B. 0.06<br> C. 0.006
    9·1 answer
  • In a school election, 2/5 of the 30 candidates are girls and the rest are boys. How many candidates are boys?
    7·2 answers
  • Find the missing dimension of the cylinder. round your answer to the nearest whole number
    12·1 answer
  • The ratio of cement to water is 4:1. Choose the other ways to write the ratio.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!