Answer:
30 square feet
Step-by-step explanation:
The area of a trapezoid is equal to (a+b)/2 * h
In this case, the value of a is 5, b is 10, and h is 4. You can substitute those numbers into the formula and get the answer of 30.
Answer:
1. x + 24 = 3x
24 = 3x - x
24 = 2x
12 = x
3x
3 (12)
36
2. 10x - 27 = 7x
10x - 7x = 27
3x = 27
x = 9
7x
7 (9)
63
3. 5x + 1 = 6x - 13
5x - 6x = -13 - 1
-x = -14
x = 14
5x + 1
5 (14) + 1
71
4. 6x + 3 = 4x + 39
6x - 4x = 39 - 3
2x = 36
x = 18
6x + 3
6 (18) + 3
111
1. B
2. A
3. H
4. E
Answer:
.
Step-by-step explanation:
Step One: Simplify the square roots.
.
The square root of 8
can be simplified as the product of an integer and the square root of 2:
.
As a result,
.
Step Two: Expand the product of the two binomials.
is the product of two binomials:
- Binomial One:
. - Binomial Two:

Start by applying the distributive law to the first binomial. Multiply each term in the first binomial (without brackets) with the second binomial (with brackets)
![({\bf 8} - {\bf \sqrt{2}}) \cdot {(2 + 2\; \sqrt{2})}\\= [{\bf 8} \cdot {(2 + 2\; \sqrt{2})}] - [{\bf \sqrt{2}} \cdot {(2 + 2\; \sqrt{2})}]](https://tex.z-dn.net/?f=%28%7B%5Cbf%208%7D%20-%20%7B%5Cbf%20%5Csqrt%7B2%7D%7D%29%20%5Ccdot%20%7B%282%20%2B%202%5C%3B%20%5Csqrt%7B2%7D%29%7D%5C%5C%3D%20%5B%7B%5Cbf%208%7D%20%5Ccdot%20%7B%282%20%2B%202%5C%3B%20%5Csqrt%7B2%7D%29%7D%5D%20-%20%5B%7B%5Cbf%20%5Csqrt%7B2%7D%7D%20%5Ccdot%20%7B%282%20%2B%202%5C%3B%20%5Csqrt%7B2%7D%29%7D%5D)
Now, apply the distributive law once again to terms in the second binomial.
.
Step Three: Simplify the expression.
The square of a square root is the same as the number under the square root. For example,
.
.
Combine the terms with the square root of two and those without the square root of two:
.
Factor the square root of two out of the second term:
.
Combining the steps:
![(8 - \sqrt{2}) \cdot (2 + 2\; \sqrt{2})\\= [8 \cdot (2 + 2\; \sqrt{2})] - [\sqrt{2} \cdot (2 + 2\; \sqrt{2})]\\= [8 \times 2 + 8 \times 2\;\sqrt{2}] - [\sqrt{2} \times 2 + \sqrt{2} \times 2 \;\sqrt{2}]\\= [16 + 16 \;\sqrt{2}] - [2 \;\sqrt{2} + 2 \times (\sqrt{2})^{2}]\\= [16 + 16 \;\sqrt{2}] - [2 \;\sqrt{2} + 2 \times 2]\\= [16 + 16 \;\sqrt{2}] - [2 \;\sqrt{2} + 4]\\= 16 + 16\;\sqrt{2} - 2\; \sqrt{2} - 4\\= (16 - 4) + (16 \; \sqrt{2} - 2\; \sqrt{2})\\](https://tex.z-dn.net/?f=%288%20-%20%5Csqrt%7B2%7D%29%20%5Ccdot%20%282%20%2B%202%5C%3B%20%5Csqrt%7B2%7D%29%5C%5C%3D%20%5B8%20%5Ccdot%20%282%20%2B%202%5C%3B%20%5Csqrt%7B2%7D%29%5D%20-%20%5B%5Csqrt%7B2%7D%20%5Ccdot%20%282%20%2B%202%5C%3B%20%5Csqrt%7B2%7D%29%5D%5C%5C%3D%20%5B8%20%5Ctimes%202%20%2B%208%20%5Ctimes%202%5C%3B%5Csqrt%7B2%7D%5D%20-%20%5B%5Csqrt%7B2%7D%20%5Ctimes%202%20%2B%20%5Csqrt%7B2%7D%20%5Ctimes%202%20%5C%3B%5Csqrt%7B2%7D%5D%5C%5C%3D%20%5B16%20%2B%2016%20%5C%3B%5Csqrt%7B2%7D%5D%20-%20%5B2%20%5C%3B%5Csqrt%7B2%7D%20%2B%202%20%5Ctimes%20%28%5Csqrt%7B2%7D%29%5E%7B2%7D%5D%5C%5C%3D%20%5B16%20%2B%2016%20%5C%3B%5Csqrt%7B2%7D%5D%20-%20%5B2%20%5C%3B%5Csqrt%7B2%7D%20%2B%202%20%5Ctimes%202%5D%5C%5C%3D%20%5B16%20%2B%2016%20%5C%3B%5Csqrt%7B2%7D%5D%20-%20%5B2%20%5C%3B%5Csqrt%7B2%7D%20%2B%204%5D%5C%5C%3D%2016%20%2B%2016%5C%3B%5Csqrt%7B2%7D%20-%202%5C%3B%20%5Csqrt%7B2%7D%20-%204%5C%5C%3D%20%2816%20-%204%29%20%2B%20%2816%20%5C%3B%20%5Csqrt%7B2%7D%20-%202%5C%3B%20%5Csqrt%7B2%7D%29%5C%5C)
.
The choices E and F are correct.
These two are the only options that form a triangle in their given order.