x^2 - 4
------------------------------
x + 7 | x^3 + 7x^2 - 4x - 28
x^3 + 7x^2
------------------
0 - 4x - 28
-4x - 28
-------------
0
Now we know that
x^3 + 7x^2 - 4x - 28 = (x^2 - 4)(x + 7)
x^2 - 4 can be factored since it is the difference of two squares.
x^2 - 4 = (x + 2)(x - 2)
The complete factoring is:
x^3 + 7x^2 - 4x - 28 = (x +2)(x - 2)(x + 7)
Remark
In order to solve for the Cos(x), you need to find the missing side. You can do that by finding the Sin(x) first and then the Cos of x or you can just use the Pythagorean theorem. I'm going to do the latter.
Formula
a^2 + b^2 = c^2
Givens
a = ???
b = 32
c = 58
Sub and solve
a^2 = ???
b^2 = 1024
c^2 = 3364
a^2 + 32^2 = 58^2
1024 + a^2 = 3364 Subtract 1024 from both sides.
a^2 = 3364 - 1024
a^2 = 2340 Take the square root of both sides.
sqrt(a^2) = sqrt(2340) Break a into its prime factors.
a = sqrt(2 * 2 * 5 * 3 * 3 * 13)
Rule
For every pair of equal factors, one can be brought outside the root sign and the other is discarded.
a = 2 * 3 * sqrt(5*13)
a = 6 sqrt(65)
The cos of an angle = opposite / hypotenuse.
Cos(x) = 6*sqrt(65) / 58 <<<<< This should be the answer
If you are offered choices, you should list them
Another choice would be 6*8.0623 / 58 = 0.8340 <<<<< Answer
Answer:
Substitution property of equality
Step-by-step explanation:
Given
and 
Then
Required
State the property
From the list of options, (d) answers the question.
This is so because:
Substitution property of equality states that
If 
then 
In other words, both can replace one another.
So if , then 2y + 1 can be substituted for x in
So:
becomes
<em>Hence, it is substitution property of equality</em>
Answer:
The answer is 350 sqft
Step-by-step explanation:
terrace 48 sqft
back porch is = 6x6 = 36 sqft
side deck = 3x14 = 42 sqft
playroom = 16x14 = 224 sqft
Total area of the tree house: 48+36+42+224 = 350 sqft
