Felix has $1,000 in his savings account. He wants to purchase a motorcycle for $5,000. The seller has agreed to take a payment of $250 a month without interest. Felix saves an extra $300 each month, plus paying for the motorcycle. What system of equations could Felix use to determine when he will have enough money to completely pay for his motorcycle?

The system of equations is

(1) Amount balance to buy the motorcycle = Cost of motorcycle - Balance in savings

(2) Number of months Felix would need to make up the amount balance to buy the motorcycle = When Felix will have enough money to completely pay for his motorcycle

(3) Number of months Felix would need to make up the amount balance to buy the motorcycle = When Felix will have enough money to completely pay for his motorcycle

(4) The period it will take for Felix to have enough money to completely pay for his motorcycle is 8 months

Step-by-step explanation:

Here we have

Balance in savings = $1,000

Amount available to Felix each month = $500

Amount balance to buy the motorcycle = Cost of motorcycle - Balance in savings

= $5,000 - $1,000 = $4,000

Number of months Felix would need to make up the amount balance to buy the motorcycle = When Felix will have enough money to completely pay for his motorcycle

The above is given by

Number of months = Amount balance to buy the motorcycle ÷ Amount available to Felix each month

∴ Number of months = $4,000 ÷ $500 = 8 Months

That is Felix will have enough money to pay for his motorcycle in 8 months.

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)