Longer leg = x + 4
Shorter leg = x
Hypotenuse = x + 8
Using Pythagorean Theorem:
a^2 + b^2 = c^2
(x + 4)^2 + x^2 = (x + 8)^2
x^2 + 8x + 16 + x^2 = x^2 + 16x + 64
2x^2 + 8x + 16 = x^2 + 16x + 64
2x^2 +8x = x^2 + 16x + 48
2x^2 - 8x = x^2 + 48
x^2 - 8x = 48
x^2 - 8x - 48 = 0
You can complete the square from here or use the quadratic formula.
Completing the square:
x^2 - 8x = 48
x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2
x^2 - 8x + 16 = 48 + 16
(x - 4)(x - 4) = 64 or (x - 4)^2 = 64
x - 4 = +√64 OR x - 4 = -√64
x - 4 = +8 OR x - 4 = -8
x = 12 OR x = -4
However, you can't use negative 4 as a length because your length needs to be a positive.
So x will be 12.
Shorter leg: 12
Longer leg: 12 + 4
Hypotenuse: 12 + 8
6 √5
7 π
Both continue on forever and will never have an exact answer - therefore, they're irrational.
16r^2+ 2r -4r
16r^2 - 2r
2r ( 8r -1)
Answer:
0.95
Step-by-step explanation:
Quarter = 0.25
Dime = 0.10
0.25+0.25+0.25= 0.75
0.10+0.10= 0.10
0.10+0.75 = 0.95
There can be no negative in a sqrt
so x+1 must be equal or greater then 0
x+1
0
x
-1
so all answers must be greater then or equal to -1
-1,0,1,2,3,4,5,6,7,8
(-1,infinity) is the domain
