9514 1404 393
Answer:
FH = 16
Step-by-step explanation:
ΔGHE is a 5-12-13 triangle.
ΔEHF is a 3-4-5 triangle with a scale factor of 4, so side FH is 4·4 = 16 units.
_____
(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) are all commonly used Pythagorean triples. The first two on the list are used in these triangles.
If you like, you can work out the numbers using the Pythagorean theorem, which tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.
For ΔEHG, that is ...
GE² = EH² + HG²
13² = EH² + 5²
EH² = 13² -5² = 169 -25 = 144
And for ΔEHF, ...
FE² = EH² +HF²
20² = 144 + HF²
400 -144 = HF² = 256
HF = √256 = 16
The length of side FH is 16 units.
Answer:
12 ft
Step-by-step explanation:
it's either 12 or 18, I have no idea :/
Answer:
Too much money
Step-by-step explanation:
To take out terms outside the radical we need to divide the power of the term by the index of the radical; the quotient will be the power of the term outside the radical, and the remainder will be the power of the term inside the radical.
First, lets factor 8:
Now we can divide the power of the term, 3, by the index of the radical 2:
![\frac{3}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B2%7D%20)
= 1 with a remainder of 1
Next, lets do the same for our second term
![x^{7}](https://tex.z-dn.net/?f=%20x%5E%7B7%7D%20)
:
![\frac{7}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B2%7D%20)
= 3 with a remainder of 1
Again, lets do the same for our third term
![y^{8}](https://tex.z-dn.net/?f=y%5E%7B8%7D%20)
:
![\frac{8}{2} =4](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B2%7D%20%3D4)
with no remainder, so this term will come out completely.
Finally, lets take our terms out of the radical:
![\sqrt{8x^{7} y^{8} }= \sqrt{ 2^{3} x^{7} y^{8} } =2 x^{3} y^{4} \sqrt{2x}](https://tex.z-dn.net/?f=%20%20%5Csqrt%7B8x%5E%7B7%7D%20y%5E%7B8%7D%20%20%7D%3D%20%5Csqrt%7B%202%5E%7B3%7D%20x%5E%7B7%7D%20y%5E%7B8%7D%20%20%20%7D%20%20%3D2%20x%5E%7B3%7D%20%20y%5E%7B4%7D%20%20%5Csqrt%7B2x%7D%20)
We can conclude that the correct answer is the third one.
Seven units long. The distance between 2 sides, in this example is 6, and -1. The distance between 6 and -1 is 7, so when you add units, you get 7 units.