Here you have a system of 2 equations and 2 unknowns. An easy way to solve this type is to isolate one of the variables.
12a + 2b = 8
2b = 8 - 12a
b =

b = 4 - 6a
Now plug 4 - 6a into equation 1 to solve for a.
a + 5(4 - 6a) = 19
a + 20 - 30a = 19
-29a = -1
a = 1/29 (answer)
Now plug a into the equation for b
b= 4 - 6(1/29)
b= 110/29 (answer)
1) You must add 4 to each side to complete the square.
2) You must add 16 to each side to complete the square.
3) You must add 27 to each side to complete the square.
Explanation:
1) x²-4x=0
To find the number that we add to both sides, we look at b, the cofficient of x. It is -4. We divide it by 2 and square it; -4/2 = -2; (-2)² = 4. This is the value that we add to both sides.
2) x²-8x=6
-8/2 = -4; (-4)²=16
We add 16 to each side to complete the square.
3) 3x²+18x=24
First we can factor a 3 out of the left side:
3(x²+6x) = 24
Our b value is now 6. 6/2 = 3; 3²=9. The 9 would, however, go in the parentheses, so it would be multiplied by 3, which makes 27; this means we would add 27 to both sides.
Answer:
There are as many definitions of empire as there have been empires, but some pretty familiar elements appear in most of them. It starts with working on our “control issues”.
Answer:
f(x + 1) = x² - x
Step-by-step explanation:
f(x) = x² - 3x + 2 when f(x + 1)
f(x + 1) = (x + 1)² - 3(x + 1) + 2
f(x + 1) = (x² + 2x + 1) + (-3x - 3) + 2
f(x + 1) = x² - x + 0
f(x + 1) = x² - x
Best of Luck!
Answer:
The inequality is 
The greatest length of time Jeremy can rent the jet ski is 5 and Jeremy can rent maximum of 135 minutes.
Step-by-step explanation:
Given: Cost of first hour rent of jet ski is $55
Cost of each additional 15 minutes of jet ski is $10
Jeremy can spend no more than $105
Assuming the number of additional 15-minutes increment be "x"
Jeremy´s total spending would be first hour rental fees and additional charges for each 15-minutes of jet ski.
Lets put up an expression for total spending of Jeremy.

We also know that Jeremy can not spend more than $105
∴ Putting up the total spending of Jeremy in an inequality.

Now solving the inequality to find the greatest number of time Jeremy can rent the jet ski,
⇒ 
Subtracting both side by 55
⇒ 
Dividing both side by 10
⇒
∴ 
Therefore, Jeremy can rent for 
Jeremy can rent maximum of 135 minutes.