Answer:
Step-by-step explanation:
Given that:
- x represents the number of months of ownership; and
- y represents the total paid for the car after ‘x' months.
<u>First Option (Leasing)</u>
250x - y + 4000 = 0
Expressing the equation in the Slope-Intercept Form y=mx+b, we have:
y=250x+4000
<u>Second Option (Financing)</u>
$400 for 0 months of ownership, (0,400), and $4400 for 10 months of ownership, (10, 4400).
First, we determine the slope of the line joining (0,400) and (10,4400)

We have:
y=400x+b
When y=400, x=0
400=400(0)+b
b=400
Therefore, the Slope-Intercept Form of the second option is:
y=400x+400
<u>Significance</u>
- In the first option, there is a down payment of $4000 and a monthly payment of $250.
- In the second option, there is a down payment of $400 and a monthly payment of $400.
<u>Part B</u>
We notice from the graph that after 24 months, the cost for leasing and financing becomes the same ($10,000). Therefore, a consumer will be better off financing since the downpayment for leasing is higher.
<u>i.e </u>
- When x=0, y=$4000 for leasing
- When x=0, y=$400 for financing
That’s a irrational number
Answer:
4(x^2 +10 +21)
4(x+3)(x+7) = 0
Smaller
4(x+7) = 0
4x +28 = 0
4x = -28
x = -28/4
x = -7
Larger
4(x+3) = 0
4x + 12 = 0
4x =-12
x = -12 / 4
x = -3
Step-by-step explanation:
In order to be continuous everywhere, we only need to satisfy continuity at
. For that to happen, we need to have

By the function's definition,
. Compute the limits:


So we must have

Answer: x is 12
Step-by-step explanation:
For directly proportional relationship, both variables change in the same direction. It means that an increase in one variable will result to an increase in the other variable. A decrease in one variable will result to a decrease in the other variable.
y and x have a proportional relationship,
We will introduce a proportionality constant and replace the proportionality symbol with an equal to symbol. Thus
y = kx
When y is 12, x is 8
Substituting into the equation,
12 = k × 8
k = 12/8 = 1.5
The equation becomes
y = 1.5x
The value of x when y is 18 will be
18 = 1.5x
x = 18/1.5 = 12