In a 45-45-90 triangle, the hypotenuse = sqrt of 2 times a leg.
Therefore the legs of the 45-45-90 triangle are 6.
That is also the hypotenuse of the 30-60-90 triangle.
In a 30-60-90 triangle, the short leg is one half of the hypotenuse.
Therefore x = 3
The answer would be 7.42
Use desmos online calculator
We can't find explicit values for 
and 
, since there is only one equation, but two variables.
The best we can do is solve for one variable with respect to the other:
Solve for :
subtract 
from both sides:
divide both sides by 
:
Solve for :
subtract 
from both sides:
divide both sides by 
:
Answer:
Step-by-step explanation:
2x^2-6x+10=0
2(x^2-3x)+10=0
2(x-(3/2))^2-9/4)+10=0
2(x-(3/2))^2+10-9/2=0
2(x-(3/2))^2+(20-9)/2=0
2(x-(3/2))^2+11/2=0
2(x-(3/2))^2=-11/2
square is always positive so there is no solution
Answer:
1. 15625
2. 256
3. 46656
Step-by-step explanation:
Simplify the following:
(5^3)^2
Multiply exponents. (5^3)^2 = 5^(3×2):
5^(3×2)
3×2 = 6:
5^6
5^6 = (5^3)^2 = (5×5^2)^2:
(5×5^2)^2
5^2 = 25:
(5×25)^2
5×25 = 125:
125^2
| | 1 | 2 | 5
× | | 1 | 2 | 5
| | 6 | 2 | 5
| 2 | 5 | 0 | 0
1 | 2 | 5 | 0 | 0
1 | 5 | 6 | 2 | 5:
Answer: 15625
_________________________________________
Simplify the following:
(4^2)^2
Multiply exponents. (4^2)^2 = 4^(2×2):
4^(2×2)
2×2 = 4:
4^4
4^4 = (4^2)^2:
(4^2)^2
4^2 = 16:
16^2
| 1 | 6
× | 1 | 6
| 9 | 6
1 | 6 | 0
2 | 5 | 6:
Answer: 256
____________________________________________
Simplify the following:
(6^2)^3
Multiply exponents. (6^2)^3 = 6^(2×3):
6^(2×3)
2×3 = 6:
6^6
6^6 = (6^3)^2 = (6×6^2)^2:
(6×6^2)^2
6^2 = 36:
(6×36)^2
6×36 = 216:
216^2
| | 2 | 1 | 6
× | | 2 | 1 | 6
| 1 | 2 | 9 | 6
| 2 | 1 | 6 | 0
4 | 3 | 2 | 0 | 0
4 | 6 | 6 | 5 | 6:
Answer: 46656
