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Write the expression that can be used to find the slope.
Through (-1, -6) and (-11, 4)

Answer: The slope is -1

Explanation:
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Explanation:
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Find the slope of the line if it is defined.

Through ​(1,9) and ​(1,8)

Explanation:
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Find the​ slope, if it​ exists, of the line containing the pair of points ​(6,-7) and ​(-8,-7)

Explanation:
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Find the slope of the following line
    y = 2.5

 
Explanation:
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Find an equation in the slope-intercept form for the line
Through (3, 9) m = -5

Explanation
Find an equation in​ slope-intercept form for the line (3,9), m=-5
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Find an equation in​ slope-intercept form for the line
Through (1,4), m = -3

Explanation;
Find an equation in​ slope-intercept form for the line (1, 4), m = -3

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Find an equation in​ slope-intercept form for the line that passes through (7,-2) m=0.

Explanation
Note that a line with a slope of zero is a horizontal line and the equation of this line is of the form y = k,

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In 1996​, there were 41,138 shopping centers in a certain country. In 2006, there were 48,908.
a.      Write an equation expressing the number y of shopping centers in terms of the number x of years after 1996.
b.      When will the number of shopping centers reach 70,000?

Explanation:
 
a.         y₂ – y₁ / x₂ – x₁
48908 – 41138 / 10 – 0 =        777
y – 41138 = 777(x-0) =            y = 777x + 41,138
 
​b.         70000 =           777x + 41138
70,000 – 41,138 =       777x =             28,862 =          777x = 28,862 / 777 = x
x =       37.145
1,996 + 37.145 =         2033 To achieve the maximum benefit for the heart when​ exercising, the heart rate​ (in beats per​ minute) should be in the
target heart rate zone. The lower limit of this zone is found by taking​ 70% of the difference between 220 and the
age of the person. The upper limit is found by using​ 85% of the difference. Complete parts a through d.

U = .85(200 - x) = u =
187 - 0.85x
L = .7(220 – x) = L =
154 – 0.70x
 
What is the target heart rate zone for a 40​-year-old?
For a 40-year-old person, the lower limit is ___ and the upper limit is ___ beats per minute.
L = 154 – 0.70(40) = 126
U = 187 - 0.85(40) = 153
 
What is the target heart rate zone for a 60​-year-old?
For a 60-year-old person, the lower limit is ___ and the upper limit is ___ beats per minute
L = 154 – 0.70(60) = 112
U = 187 - 0.85(60) = 136
 
Two women in an aerobics class stop to take their pulse and find that they have the same pulse. One woman is 34 years older
than the other and is working at the upper limit of her target heart rate zone. The younger woman is working at the lower limit
of her target heart rate zone. What are the ages of the two​ women, and what is their​ pulse?
Younger = x + 34
 
154 - .7x = 187 - .85(x + 34)
154 - .7x = 187 - .85x – 28.9
154 - .7x = 158.1 - .85x
Add .85x to both sides =
154 + .15x = 158.1
Subtract 154 from both sides =
.15x = 4.1 = divide both sides by .15 = x = 27.333 (27)
X + 34 = 61
27 and 61
Their pulse is approximately __ beats per minute.
154 - .7(27) = 135.1 (135) Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the past​ century,
life expectancy from age 65 has increased more slowly than life expectancy from​ birth, so eventually these two will be​ equal,
at which​ point, according to these​ scientists, life expectancy should increase no further. In​ 1900, life expectancy at birth was
48 years, and life expectancy at age 65 was 78yr. In​ 2010, these figures had risen to 78.4 and 84.4​, respectively. In both​ cases,
the increase in life expectancy has been linear.
Using these assumptions and the data​ given, find the maximum life expectancy for humans.
Find the linear equations for life expectancy at birth and life expectancy at age 65. Set the​ x-value (time in​ years) for 1900 to 0.
The linear equation for life expectancy at birth is y = __ and the linear equation for life expectancy
at age 65 is y = ___ ​, where y is the life expectancy in years and x is the year ​(1900 = ​0) in both cases.

life expectancy at birth is
The data points are (0,48) (110,78.4)
 

78.4 – 48 / 110 – 0 = .276 =
The slope of the linear equation is 0.276.
 
y = 0.276x + 48
 
life expectancy at age 65
 
(0,78) and (110,84.4)
84.4 – 78 / 100 – 0 = .058 =
 
y = .058x + 78
 
0.276x + 48 = 0.058x + 78 = 0.276x =          0.058x + 30 =              x =       138
 
y =       0.276(138) + 48 =        86
   
In 1940, there were 249,849 immigrants admitted to a country. In 2009, the number was 1,177, 091.
a. Assuming that the change in immigration is linear, write an equation expressing the number of immigrants, y, in terms of t,
    the number of years after 1900.
b. Use your result in part a to predict the number of immigrants admitted to the country in 2018.
c. Considering the value of the y-intercept in your answer to part a, discuss the validity of using this equation to model the number of
     immigrants throughout the entire 20th century.
A linear equation for the number of immigrants is y =
 

Explanation:
Let t₁, y₁ = (40,249849) and t₂,y₂ =   (109,1177091)

1177091 – 249849 / 109 – 40 =          13438.29 =      13438.29
y – 249849 = 13438.29(t – 40) =
y – 249849 = 13438.29t – 537531.6 =
y = 13438.29t – 537531.6 + 249849 =
 
A linear equation for the number of immigrants is y =        13438.29t – 287682.6
 
Use your result in part a to predict the number of immigrants admitted to the country in 2018
 
t = 2018 – 1900 =        118
13438.29(t = 118) – 287682.6 =         1298035.62
The answer is:             1,298,036
 
The number of immigrants admitted to the country in 2018 will be approximately 1298036
 
Choose the correct answer below.
A.     The actual model may or may not be linear. More data points would help model the data more accurately.
Using just two data points to create a linear model is not valid.
 
B.      The​ y-intercept gives the number of immigrants in 1900.
The equation in part a is valid to model the number of immigrants throughout the entire 20th century Let f(x) = 8 – 3x

Find f(5)

Explanation

8 – 3(5) = 8 – 15 =       -7

f (5) =   -7

The answer is:          -7

 

Let f(x) = 2 – 3x. Find f(-2)

Explanation

2 – 3(-2) =        8

Let f(x) = 1 – 4x. Find f(t)

Explanation
Simply substitute t for x wherever you see x.

Describe what fixed costs and marginal costs mean to a company.
Choose the correct answer below.

A. Fixed cost is the constant for a particular product and does not change as more items are made.
The number of units at which revenue just equals cost is the marginal cost
B. Fixed cost is the rate of change of cost​ C(x) at the level of production x and is equal to the slope of the cost function at x.
Marginal cost is the constant for a particular product and does not change as more items are made.
C. Fixed cost is the constant for a particular product and does not change as more items are made.
Marginal cost is the rate of change of cost​ C(x) at the level of production x and is equal to the slope of the cost function at x.
D. The number of units at which revenue just equals cost is the fixed cost.

Marginal cost is constant for a particular product and does not change as more items are made.

Explain why a linear function may not be adequate for describing the supply and demand functions.

A. If the rate of change of the price is a​ constant, a linear function may not be adequate for describing the supply and demand functions.
B. If a small enough piece of the supply and demand graph is​ taken, a linear function may not be adequate for describing the supply and demand functions.
C. If the rate of change of the price is not a​ constant, a linear function may not be adequate for describing the supply and demand functions.

Write a linear cost function for the following situation.
A ski resort charges a snowboard rental fee of ​$40 plus ​$5.50 per hour.

Explanation
The answer is given
C(t) = 5.50t + 40

Write a linear cost function for the situation. Identify all variables used.
A parking garage charges 88 dollars plus 85 cents per​ half-hour.
Identify all variables used. Choose the correct answer below.

A. ​C(x) represents the cost for using the parking garage for x​ half-hours.
B. C(x) represents the cost for parking x cars in the parking garage.
C. C(x) represents the number of hours the parking garage was used after paying x dollars.
D.​ C(x) represents the number of​ half-hours the parking garage was used after paying x dollars.

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