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Pavel [41]
3 years ago
12

Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay,

due to the crowding and smaller lot sizes. In fact, if it builds 20 houses in this particular development, it can sell them for $540,000 each, but if it builds 50 houses, it will only be able to get $450,000 each. Obtain a linear demand equation. HINT [See Example 3.] (Let p be the price of a house and q the number of houses
Mathematics
1 answer:
Alona [7]3 years ago
3 0
We are assuming that p is the price of the house and that q is the number of the houses.

The points given (q,p) , therefore, are:
(20 , 540000) and (50 , 450000)

The general form of the linear straight line is:
y = mx+c where m is the slope and c is the y-intercept.

(1) Calculating the slope:
The formula used to calculate the slope is:
m = (y2-y1) / (x2-x1) where:
y2 is the y-coordinate of the second point = 450000
y1 is the y-coordinate of the first point = 540000
x2 is the x-coordinate of the second point = 50
x1 is the x-coordinate of the first point = 20
Therefore:
m = (450000-540000) / (50-40) = -3000

(2) Calculating the y-intercept:
After getting the slope, the equation now is:
y = -3000x + c
To get the value of thec, use any point that belongs to the line and substitute with it in the equation above. I will use the point (20, 540000).
y = -3000 + c
540000 = -3000(20) + c
c = 540000 + 3000(20) = 600000

Based on the above calculations, the equation of the line is:
y = -3000x + 600000

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Vladimir79 [104]

Answer:

2/5

Step-by-step explanation:

The slope is given by

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5 0
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The nth term of a sequence is 3n²-1
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Answer: The number is 26.

Step-by-step explanation:

We know that:

The nth term of a sequence is 3n²-1

The nth term of a different sequence is 30–n²

We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.

we get:

3n²- 1 =  30–m²

Notice that as n increases, the terms of the first sequence also increase.

And as n increases, the terms of the second sequence decrease.

One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.

if m = 1, then:

3n²- 1 =  30–1²

3n²- 1 = 29

3n² = 30

n² = 30/3 = 10

n² = 10

There is no integer n such that n² = 10

now let's try with m = 2, then:

3n²- 1 =  30–2² = 30 - 4

3n²- 1 = 26

3n² = 26 + 1 = 27

n² = 27/3 = 9

n² = 9

n = √9 = 3

So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.

the number is:

3*(3)² - 1 = 26

30 - 2² = 26

The number that belongs to both sequences is 26.

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Fittoniya [83]

Answer:

a

Step-by-step explanation:

6 0
3 years ago
An average of 20 pears were sold from Monday to Friday. After the sales on Saturday and Sunday, the average pears sold per day w
Fittoniya [83]

Answer:

5 pears

Step-by-step explanation:

Given that

The  average of 20 pears were sold from Monday to Friday

But after the sales on Saturday and Sunday, the average pears sold per day were increased to 25

We need to determine the number of pears sold on Saturday and sunday

So, it is

= 25 pears - 20 pears

= 5 pears

4 0
3 years ago
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