Answer:
5000
Step-by-step explanation:
Given the following :
Constructed expression used to express size of debt after m, months :
36,700 - (5000 + 500m)
Since it was stated that he his whole signing bonus was dedicated towards paying his debt, then this will be a constant figure or digit.
Then a fixed amount from his monthly pay is also dedicated towards offsetting the loan:
Thus the fixed amount will be the Coefficient of m, where m is the number of months.
Thus total amount paid after m months can be deduced from the expression to be :
(5000 + 500m); where
5000 constant fee is the signing bonus.
Using logarithmic laws: log(a) + log(b) = log(ab)
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
![4^{log_4 (x + 9)(x + 21)} = 4^{3}](https://tex.z-dn.net/?f=4%5E%7Blog_4%20%28x%20%2B%209%29%28x%20%2B%2021%29%7D%20%3D%204%5E%7B3%7D)
![(x + 9)(x + 21) = 64](https://tex.z-dn.net/?f=%28x%20%2B%209%29%28x%20%2B%2021%29%20%3D%2064)
![x^{2} + 9x + 21x + 189 = 64](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%209x%20%2B%2021x%20%2B%20189%20%3D%2064)
Solving the quadratic we get:
![x^{2} + 30x + 125 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%2030x%20%2B%20125%20%3D%200)
![(x + 5)(x + 25) = 0](https://tex.z-dn.net/?f=%28x%20%2B%205%29%28x%20%2B%2025%29%20%3D%200)
![x = -5, -25](https://tex.z-dn.net/?f=x%20%3D%20-5%2C%20-25)
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
Answer:
5.3
Step-by-step explanation:
5 or more raise the score 4 or less let it rest.
3 lets 3 rest so 5.336 rounds down to 5.3.
Answer:
(0, 3)
Step-by-step explanation:
The y-intercept is point on the y-axis that the line passes through.
You can see the line passes through 3 on the y-axis.
On the y-axis, every point has a 0 for the x-coordinate.
The ordered pair for the point that is 3 on the y-axis is (0, 3).