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
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.

You might be interested in
What 2 numbers multiply to -36 and add to 16​
KatRina [158]

Answer:

Step-by-step explanation:

I understand

6 0
2 years ago
This figure is made up of a rectangle and parallelogram.
ivann1987 [24]

The area of the figure is 40 units. (rounded off from 39.998 units)

Step-by-step explanation:

1. Area of the figure = Area of Rectangle + Area of Parallelogram.

2. Naming points:

Let the rectangle consist of points A(-6,-1), B(-5,-5), C(3,-3) and D(2,1).

Let the parallelogram consist of points C(3,-3), D(2,1), E(2,7) and F(3,3).

3. Each coordinate has a point on the x-axis and a point on the y-axis. We shall refer to these points as x', x'' ,x''' and so on corresponding to the x-axis values of A, B, C and so on in that order till F. For the y-axis points, we will name them in the series of y', y'', y''' and so on.

In simple words, in A(-6,1), x' = -6; y' = -1

4. Formula for finding area:

Area of a rectangle = length (l) × width (w)

Area of a parallelogram = base (b) x height (h)

5. Finding area of the rectangle:

l = AD = \sqrt{[x'''' - x']^{2} - [y'''' - y']^{2}}

, i.e. AD = \sqrt{[2 - (-6)]^{2} - [1 - (-1)]^{2}}

, i.e. AD = √68 = 8.246 (rounded to 3 decimals) = l

Now, w = AB = \sqrt{[x'' - x']^{2} - [y'' - y']^{2}}

, i.e. AB = \sqrt{[(-5) - (-6)]^{2} - [(-5) - (-1)]^{2}}

, i.e. AB = √17 = 4.123 (rounded to 3 decimals) = w

Area of rectangle = l x w = 8.246 x 4.123 = 33.998 units.

6. Finding area of the parallelogram:

b = DE = 6 units (we can observe this from the graph, i.e. points from 1 to 7 on the y axis)

h = Height is the line drawn perpendicular to the base from point F, which as we can see is 1 unit long.

Hence, Area of parallelogram = b x h = 6 x 1 = 6 units.

7. Now, adding both, we can arrive at the final answer.

Area of the figure = Area of rectangle + Area of parallelogram,

i.e. 33.998 units + 6 units = 39.998 units. (can be rounded off to 40 units)

4 0
2 years ago
A clothing design company pays two different people to design its T-shirts.
irina [24]

Answer: D

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Write an expression that represents the height of a tree that begins at 10 feet and increases by 3 feet per year. Let t represen
mestny [16]
  • t represents number of years
  • initial height=10ft
  • Increases per year=3ft

Expression:-

\\ \sf\longmapsto 10+3t

3 0
3 years ago
What is the difference between log(x/y) and log(x)/log(y)?
Yuliya22 [10]
They are different equations lol. If you plug in the same x and y for both you wont get the same answer. Do you have answer choices? 
6 0
2 years ago
Other questions:
  • A golfer hits a ball from a starting elevation of 4 feet with a velocity of 70 feet per second down to a green with an elevation
    7·1 answer
  • Complete the objective function. P = x + y
    9·1 answer
  • The side lengths of different triangles are given. Which triangle is a right triangle? A. 6,7,13 B. 21−−√,99−−√,11 C. 10,60,61 D
    6·1 answer
  • Solve the inequality. q/2 ≤ -8
    8·1 answer
  • Put the equations in slope-intercept form and identify the equations as parallel orperpendicular lines.
    5·1 answer
  • Get brainiest if right!! <br> 10 points!!
    8·1 answer
  • The temperature outside is currently 10°F. It will fall at a constant rate of 3°F per hour. Which temperature will it be in 4 ho
    5·1 answer
  • Help me plz i’ll give extra points
    12·1 answer
  • Please help!! I'm super confused:(
    15·1 answer
  • This is algebra 1 id appreciate it if you could help me thx!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!