Factor out the common term; 3
(3(x + 1))^2 = 36
Use the Multiplication Distributive Property; (xy)^a = x^ay^a
3^2(x + 1)^2 = 36
Simplify 3^2 to 9
9(x + 1)^2 = 36
Divide both sides by 9
(x + 1)^2 = 36/9
Simplify 36/9 to 4
(x + 1)^2 = 4
Take the square root of both sides
x + 1 = √4
Since 2 * 2 = 4, the square root of 2 is 2
x + 1 = 2
Break down the problem into these 2 equations
x + 1 = 2
x + 1 = -2
Solve the first equation; x + 1 = 2
x = 1
Solve the second equation; x + 1 = -2
x = -3
Collect all solutions;
<u>x = 1, -3</u>
Answer:
see explanation
Step-by-step explanation:
Given
a = ![\left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
To obtain -3a multiply each of the elements of a by -3
3a = ![\left[\begin{array}{ccc}-3(3)\\-3(2)\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%283%29%5C%5C-3%282%29%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}-9\\-6\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-9%5C%5C-6%5C%5C%5Cend%7Barray%7D%5Cright%5D)
To obtain 1.5a multiply each element by 1.5
1.5a = ![\left[\begin{array}{ccc}1.5(3)\\1.5(2)\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1.5%283%29%5C%5C1.5%282%29%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}4.5\\3\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4.5%5C%5C3%5C%5C%5Cend%7Barray%7D%5Cright%5D)
It took 12 days for all the 60 gallons of water to leak out of the barrel. If you divide 60 by 5 you will get 12.
Answer: 56 degrees
Step-by-step explanation:
We know that angle between b and c is 90 degrees. Because there is a line dividing angles a and b from 124 and c, we also know that each side is 180 degrees (a and b add to 180, and 124 and c add to 180).
124 and c are supplementary angles. We can represent this in an equation to solve for c:
Divide the population of 65 or older by the percentage:
30.2 million / 0.122 = 247.54 million total population. (Round answer as needed)
