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
Answer:44
Step-by-step explanation:11=1/4 of what?
11=1/4 of 44
#9 is answer A) yes,
#10 the answer is A) (n,j)
Just multiply w*l*h
1.89m cubed
Using Gauss's method
Total number of terms = [15-(-129)]/4+1=36+1=37
Add
S=15+11+7+....-125-129
S=-129-125-...+7+11+15
--------------------------------
2S=-114-114-114...(37 times)
=>
sum=S=(1/2)*(-114)*37=-2109
Using AP, T(n)=15+11+7+....-129
T(n)=19-4n => T(1)=15, T(37)=-129
S(n)=(1/2)(37)(T(1)+T(37)=(1/2)37(15-129)=2109
