We have this equation:
First, combine both logarithms using the multiplication property and simplify the expression.
![\log[x(x + 99)] = 2](https://tex.z-dn.net/?f=%5Clog%5Bx%28x%20%2B%2099%29%5D%20%3D%202)
![\log[ {x}^{2} + 99x ] = 2](https://tex.z-dn.net/?f=%5Clog%5B%20%7Bx%7D%5E%7B2%7D%20%2B%2099x%20%5D%20%3D%202)
Now, use the definition of logarithm to transform the equation.
Finally, use the quadratic formula to solve the equation.
With this, we can say that the solution set is:
We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.
Answer:
B
Step-by-step explanation:
Stopping at a stoplight means that Chris's speed would be zero on the graph. The times that his speed is zero are times t = 0, t = 2 min, t = 11 min, and t = 21 min. Because the graph shows his speed from the time he left his house (at t = 0) to the time he arrived at the theater (at t = 21 min), the most likely times he stopped at stoplights are times t = 2 min and t = 11 min.
Lucy used 2 1/3 kilograms of apples for her dessert.
Get the whole fraction.
3 2/3 = ((3*3) + 2) / 3 = 11/3
1 1/3 = ((3*1) + 1) / 3 = 4/3
Original weight of apples = 11/3
Remaining weight of apples = 4/3
weight of apples used = ?
Subtracting fractions:
Step 1. Make sure the denominator are the same
11/3 - 4/3
Step 2. Subtract the numerators and put the difference above the denominator
(11 - 4) / 3 = 7/3
Step 3. Simplify the fraction
7/3 = 2 1/3
Answer:
16 1/3 miles in one hour.
Step-by-step explanation:
12.25 miles in 45 minutes.
How far in 60 minutes?
Set up a proportion: 12.25/45=x/60
45x=735
x=16.3333...
Therefore, Manuel can go 16 1/3 miles in one hour.
I hope this helped and have a good rest of your day!
