Answer:
Part 1: (n÷2)-7 = -12
Part 2: n = -10
Step-by-step explanation:
Part 1:
Let's first write "the quotient of a number and 2" using numbers and variables. Let "n" represent "a number". The key word that we see here is quotient, meaning we have to divide something by something else. "The quotient of a number and 2 means that "a number" is the dividend (number that is divided) and "2" is the divisor (number that divides the dividend). Therefore we obtain:
n÷2
The first part says "seven less than the quotient of a number and 2". The keyword here is less, meaning we have to use subtraction. Therefore:
(n÷2)-7
The last part says "is equal to -12". Therefore the whole expression we just wrote is equivalent to -12:
(n÷2)-7 = -12
Part 2
Remember the Order of Operations:
Parentheses
Exponents
M/D: Multiplication/Division (whichever comes first in the equation)
A/S: Addition/Subtraction (whichever comes first in the equation)
Start by adding 7 to both sides
(n÷2) = -5
Then, multiply both sides by 2
Note: I used a fraction to display the division because it is easier to see why we have to multiply both sides by 2; to cancel out the denominator.
X = 3 and x = -1 are the answers for both. They are exactly the same equation.
FOR COMPLETING THE SQUARE
Make in terms of ()^2 which you can do by adding numbers to both sides. Eventually it will look like this:
(2x - 1)^2 - 7 = 0
Add to both sides, take a square root and then solve.
USE THE QUADRATIC FORMULA
Be sure to solve for zero and be aware of negatives when plugging in.
Answer:
AP is 11.25 so the answer is F
Step-by-step explanation:
Since they are similar triangles (due to the ~ symbol)
You can write this:
AC/XZ = AP/XQ
since XZ=12
XQ=5
AC=27
you can write:
27/12=AP/5
then cross multiply:
27x5=135
135/12=11.25
AP is 11.25