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All of the questions

All of the questions-example-1

2 Answers

2 votes

Answer:

See below.

Explanation:

A.

The equation of a line is (in slope-intercept form)

y = mx + b

We need to find the slope, m, and the y-intercept for this situation.

Finding the slope:

You already wrote correctly that the difference between each two consecutive values of C(n) is 150. The difference between consecutive values of n is 1. The values we see for n are 2, 3, 4, 5.

n is the number of nights. As the number of nights go up by 1, the cost goes up by $150.

slope = rise/run

For a change of 1 in x (n here, the run), you get a change of 150 in y (C(n) here, the rise)

slope = 150/1 = 150

The slope of the equation is 150.

Now we need to find the y-intercept.

Look at the table.

Here are the first two lines of values.

n C(n)

2 950

3 1100

Since you know that a difference of 1 night creates a difference of $150 in the cost, work backwards, and subtract 1 night and 150 from the top line. You get this new top line (in bold):

n C(n)

1 800

2 950

3 1100

Subtract again 1 night and 150 from the cost, and you get this (new line in bold):

n C(n)

0 650

1 800

2 950

3 1100

For 0 nights, the cost is $650. The y-value at x = 0 is the y-intercept. That means the y-intercept is 650. b = 650

Now that we know the slope and the y-intercept, we can write the equation.

y = mx + b

y = 150x + 650

Since you are using n for x and C(n) for y, your equation is

C(n) = 150n + 650

B.

The slope is the cost per night.

C.

The coordinates of the y-intercept are (0, 650).

It represents the initial fee of $650.

D.

We need to find C(10).

In the function C(n), n represents the number of nights.

Since we have C(10), the 10 is replacing n and represents a stay of 10 days.

To find C(10), we use the function.

C(n) = 150n + 650

C(10) = 150(10) + 650

C(10) = 1500 + 650

C(10) = 2150

Meaning: A 10-day stay costs $2150.

E.

C(n) = 1850

The cost of n nights is $1850.

The question is what is the number of nights that costs $1850?

We use the function set equal to 1850 and solve for n, the number of nights.

C(n) = 150n + 650 = 1850

150n + 650 = 1850

Subtract 650 from both sides.

150n = 1200

Divide both sides by 150.

n = 1200/150

n = 8

Answer: $1850 is the cost of an 8-day stay.

User TheChetan
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5 votes
That's a lot.. I'm so sorry I can't help you. I don't know how to do it. Sorry.
User Adomas Baliuka
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