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aleksklad [387]
3 years ago
15

A certain economy's consumption function is given by the equation C(x) = 0.65x + 9 where C(x) is the personal consumption expend

iture in billions of dollars, and x is the disposable personal income in billions of dollars. Find C(0), C(50), and C(100).
Mathematics
1 answer:
ipn [44]3 years ago
7 0

Answer:

1) C(0) = 9

2) C(50) =41.5

3) C(100) =74

Step-by-step explanation:

Given : A certain economy's consumption function is given by the equation C(x) = 0.65x + 9

where, C(x) is the personal consumption expenditure in billions of dollars, and x is the disposable personal income in billions of dollars.

To find :

1) C(0)

Put x=0 in the given equation,

C(0) = 0.65(0)+ 9

C(0) = 9

2) C(50)

Put x=50 in the given equation,

C(50) = 0.65(50)+ 9

C(50) =32.5+9

C(50) =41.5

3) C(100)

Put x=100 in the given equation,

C(100) = 0.65(100)+ 9

C(100) =65+9

C(100) =74

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Just need help on #7 thru 8(a), b and c
Stella [2.4K]

7

a. The slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

b. The distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

c.  The midpoint of the R(3, 5) and H(-1,2) is  (2, 4)

8.

a. The transformation rule is  (x,y) → (x + 1, y - 1)

b.

  • The x-coordinate is shifted 1 unit to the left and
  • The y - coordinate is shifted 1 unit downwards.

c. The image of B' the pre-image of B(5, 6) is (6, 5)

<h3 /><h3>7 a. How to find the slope of the line?</h3>

The slope of a line passing through the points (x₁, y₁) and (x₂,y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

So, m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 5)/(-1 - 3)

m = -3/-4

m = -3/4

So, the slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

<h3>b. The distance between the points</h3>

The distance between two points (x₁, y₁) and (x₂,y₂) is d = √[(y₂ - y₁)² + (x₂ - x₁)²]

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

d = √[(y₂ - y₁)² + (x₂ - x₁)²]

d = √[(2 - 5)² + (-1 - 3)²]

d = √[(-3)² + (-4)²]

d = √[9 + 16]

d = √25

d = 5 units

So, the distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

<h3>7 c How to find the midpoint of the R(3, 5) and H(-1,2) </h3>

The midpoint of the the points (x₁, y₁) and (x₂,y₂) is (x, y)  = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

So, the midpoint (x, y)  = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(x, y)  = [(3 + (-1))/2, (5 + 3)/2]

(x, y)  = [(3 - 1)/2, (5 + 3)/2]

(x, y)  = [4/2, 8/2]

(x, y)  = (2, 4)

So, the midpoint of the R(3, 5) and H(-1,2) is  (2, 4)

<h3>8. a The rule for the transformation of point A(1, 4) to point B(2, 3)</h3>

Given that point A(1, 4) and point B(2, 3) we see that point B(1 + 1, 4 - 1).

Let pont A be (x,y).

So, point B = (x + 1, y - 1)

So, the transformation rule is  (x,y) → (x + 1, y - 1)

<h3>b. Describe the transformation</h3>

Since the transformation rule is   (x,y) → (x + 1, y - 1), we see that

  • the x-coordinate is shifted 1 unit to the left and
  • the y - coordinate is shifted 1 unit downwards.
<h3>c. The image of B' the pre-image of B(5, 6)</h3>

Since the transformation rule is  (x,y) → (x + 1, y - 1) and point B is (5, 6), thus the image of B' is

(x,y) → (x + 1, y - 1)

(5,6) → (5 + 1, 6 - 1)

(5,6) → (6, 5)

So, the image of B' the pre-image of B(5, 6) is (6, 5)

Learn more about slope of a line here:

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7 0
3 years ago
William has a lemonade stand today he made $17.55 and lemonade sales and one-third that amount in cookie sales how much money di
IgorC [24]

Answer:

Well to find 1/3 of something you have to multiply it by 1/3.

1/3 in decimal form is .33 repeating.

17.55 * .33 = 5.79

17.55 + 5.79 = $23.34

$23.34 is the total profit.


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3 years ago
Question 18 of 25
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2 years ago
Job cashed a check for $1,765. The teller gave him nine hundred-dollar bills, seven fifty-dollar bills, nineteen twenty-dollar b
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Answer:

x = 13

Step-by-step explanation:

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x = 100 (9) + (7) 50 + (19) 20 + (7) 10 - 1765

x = 900 + 350 + 380 + 70 - 1765

x = 1700 - 1765

x = -65

65/5 = 13

x = 13

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2 years ago
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