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zavuch27 [327]
3 years ago
12

Find the value of n so that the following points will lie on a line. (3,5), (−1,3), and (7,n)

Mathematics
1 answer:
crimeas [40]3 years ago
4 0

Answer:

We get value of n=7

Step-by-step explanation:

If points lie on same line, they have same slope.

First we will find slope of points (3,5), (−1,3)

Using formula: Slope=\frac{y_2-y_1}{x_2-x_1}

We have x_1=3, y_1=5, x_2=-1, y_2=3

Finding slope

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{3-5}{-1-3} \\Slope=\frac{-2}{-4} \\Slope=\frac{1}{2}

Using slope 1/2 and points (−1,3), and (7,n) we can find value of n

Slope=\frac{y_2-y_1}{x_2-x_1}\\\frac{1}{2} =\frac{n-3}{7-(-1)}  \\\frac{1}{2} =\frac{n-3}{7+1} \\\frac{1}{2} =\frac{n-3}{8}\\Cross\:Multiply\\1(8)=2(n-3)\\8=2n-6\\2n=8+6\\2n=14\\n=\frac{14}{2}\\n=7

So, we get value of n=7

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She put in 40 pennies. Hope this helps ;)


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Read 2 more answers
Cost, Revenue, Profit
Anika [276]

Answer:

1. C(n) = 2.25n + 120

2. R(n) = 3.51n

3. P(n) = 1.26n - 120

1. 96 frozen bananas must be sold in order to make a positive profit.

2. In order to make a profit, I have to sell a minimum of <u>96 frozen bananas</u>.

Step-by-step explanation:

1. Write a function, C(n), to represent your total costs for the week if you sell n frozen bananas.

Total cost is the addition of total variable cost and total fixed cost. Therefore, the function is as follows:

C(n) = 2.25n + 120

Where 2.25n is the total variable cost while 120 is the total fixed cost.

2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week.

Revenue is equal to selling price per unit multiplied by the number of units sold. Therefore, the function is as follows:

R(n) = 3.51 * n

R(n) = 3.51n

Where 3.51 is the selling price per unit while n the number of units sold.

3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week.

Profit is equal to total revenue minus total cost. Therefore, the function can be derived as follows:

P(n) = R(n) - C(n)

P(n) = 3.51n - 2.25n + 120

P(n) = 1.26n - 120

1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number.

This can be obtained by equating the profit function to zero and solve for n as follows:

P(n) = 0 => 1.26n - 120 = 0

Therefore, we have:

1.26n = 120

n = 120 / 1.26

n = 95.2380952380952 frozen bananas

Writing it as a whole number, we have:

n = 95 frozen bananas

However, using this whole number will result in a negative profit by substituting it into the profit function as follows:

P(n) = (1.26 * 95) - 120 = -$0.30

Therefore, n has to be increased by one to 96 which is also a whole number to have a positive profit as follows:

P(n) = (1.26 * 96) - 120 = $0.96

Therefore, 96 frozen bananas must be sold in order to make a positive profit.

2. Complete the following sentence to explain the meaning of #1:

In order to make a profit, I have to sell a minimum of <u>96 frozen bananas</u>.

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3 years ago
Betty and Adam are playing cards. Betty has won 6 hands and Adam has won 24 hands. What is the ratio of the number of hands Bett
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Betty : Adam
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Hope this helps.
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