A client has requested to have a stamped concrete patio put in their backyard. The plan indicates that the patio will be 16 feet
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Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.
Step-by-step explanation: The given system of linear equations is :
We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.
The determinant of the co-efficient matrix is given by
Now, from equations (ii) and (iii), we have
Substituting the value of y and z from equations (iv) and (v) in equation (i), we get
From equations (iv) and (v), we get
Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.
Johnson's will pay by the end of the 20-year loan $326,807.25
Johnson's will pay by the end of the 30-year loan $512,109.68
Step-by-step explanation:
The formula for compound interest, including principal sum is
, where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount (the initial deposit or loan amount)
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per unit t
- t is the time the money is invested or borrowed for
The Johnson's are buying their first home. They are contemplating
two similar loans
The first is a 30-year loan for $150,000 at an interest rate of 4.1% APT
compounded monthly
∴ P = $150,000
∴ r = 4.1% = (4.1/100) = 0.041
∴ n = 12 ⇒ compounded monthly
∴ t = 30
- Substitute all of these values in the formula above
∴
∴ A = $512,109.68
Johnson's will pay by the end of the 30-year loan $512,109.68
The second is a 20-year loan for a $150,000 at an interest rate of 3.9%
APR compounded monthly
∴ P = $150,000
∴ r = 3.9% = (3.9/100) = 0.039
∴ n = 12 ⇒ compounded monthly
∴ t = 20
- Substitute all of these values in the formula above
∴
∴ A = $326,807.25
Johnson's will pay by the end of the 20-year loan $326,807.25
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Answer: Midpoint: (3,-8)
(WORK SHOWN BELOW)
(WORK SHOWN BELOW)
When y = 0,
When x = 0,
Therefore, Ordered pairs are (0,1), (3,0), etc.
