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WITCHER [35]
3 years ago
5

For a special event, a restaurant charges a one-time setup fee, plus a charge for each person attending the event. The charge fo

r 5 people is $100. The charge for 10 people is $162.50.
Part 1) Write a linear function that models the cost, y, of the total event cost based on the number of people, x, attending the event.

Part 2) Describe what the rate of change and initial value mean in this situation.
Mathematics
1 answer:
Rashid [163]3 years ago
7 0

Any linear function is of the form y=mx+b

Here m is slope and b is y intercept.

Slope is difference in y divided by different in x values .

In the question for 5 persons cost is $100 and for 10 persons cost is $162.50

So the points are (5,100) and (10,162.50)

Slope m=\frac{162.50-100}{10-5}=12.50

We can find the value of b by taking m=12.50 and (x,y)=(5,100)

Substitute these values in y=mx+b

100=12.50(5)+b

100=62.50+b

Subtracting 62.50 both sides

b=100-62.50

b=37.5

a) Put m=12.50 and b=37.50 to get the equation

y=12.50x+37.50

b)Rate of change is the m value or the slope of the function.

Initial value that is (5,100) gives us one of the points to find the rate of change.

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5 0
3 years ago
Point K is on line JL. given JL =4x, JK= 2x+3, and KL=x, determine the numerical length of kl​
balandron [24]

Hi! I'm happy to help!

Our total line is JL (4x), and it is split into two parts: JK, and KL. We have our values, and we know that JK+KL=JL, so we can substitute our values and solve for x:

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

4x=3x+3

To solve for x, we have to isolate it on one side of the equation.

First, let's subtract 3x from both sides so that we can isolate x:

4x=3x+3

-3x -3x

x=3

<u>So, our x=3, which means that KL=3.</u>

I hope this was helpful, keep learning! :D

5 0
3 years ago
What is x???????need help
gogolik [260]

Answer:

100 degrees

Step-by-step explanation:

The angle x is opposite the angle that is 100 degrees.

Since they are opposite each other, they are vertical angles.

This means that they are congruent, or equal to each other.

Therefore,

x=100

x is 100 degrees

7 0
3 years ago
Find the common difference of the arithmetic sequence 3, -2, -7
svlad2 [7]

Answer:

-5

Step-by-step explanation:

To find the common difference, take the second term and subtract the first term

-2 - 3 = -5

Check with the third term and the second term

-7 - (-2) = -7 +2 = -5

The common difference is -5

4 0
3 years ago
65% of the M&amp;M candies in a package are red. 13 of the M&amp;M candies are red. How many M&amp;M's are there total? *
docker41 [41]
13 = 65%
1% = 13 divided by 65 = 0.2
100% = 0.2 x 100 = 20

There are 20 candies in total^^
8 0
2 years ago
Read 2 more answers
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