X= shorter leg
x+6= longer leg
(x+6)+6= hypotenuse
Use the Pythagorean theorem to find the length of each side.
a= one leg
b= other leg
c= hypotenuse.
SHORTER LEG:
a^2 + b^2= c^2
substitute each length above
x^2 + (x+6)^2= [(x+6)+6]^2
square each set of parentheses; add inside right side parentheses before squaring
x^2 + (x+6)(x+6)= (x+12)(x+12)
squaring is multiplying each parentheses by itself one time; use the FOIL method: multiply first, multiply outside, multiply inside, multiply last
x^2 + x^2 + 6x + 6x + 36= x^2 + 12x + 12x + 144
combine like terms
2x^2 + 12x + 36= x^2 + 24x + 144
subtract x^2 from both sides
x^2 + 12x + 36= 24x + 144
subtract 24x from both sides
x^2 - 12x + 36= 144
subtract 144 from both sides
x^2 - 12x - 108= 0
factor
(x + 6)(x - 18)= 0
set each parentheses equal to 0
x + 6= 0
x= -6
x - 18= 0
x= 18 cm shorter leg
***Since a side cannot be a negative number, x= 18. Substitute x=18 to find the other sides.
LONGER LEG:
= x+6
= 18 + 6
= 24 cm longer leg
HYPOTENUSE:
= (x+6)+6
= 18 + 6 + 6
= 30 cm hypotenuse
CHECK:
18^2 + 24^2= 30^2
324 + 576= 900
900= 900
ANSWER:
x= 18 cm shorter leg
x+6= 24 cm longer leg
(x+6)+6= 30 cm hypotenuse
Hope this helps! :)
Answer:
36
Step-by-step explanation:
Using the rule of radicals
× 
⇔ 
Simplifying the radicals in the expression
= 
= 
× = 2
= 
= 
× = 4
Thus
4 + 7
= 4 × 2 + 7 × 4
= 8 + 28
= 36
Answer:
AA, AD, AC, AB (or flipped)
BB, BD, BC, BA (or flipped)
CD, CA, CB, CC (or flipped)
DA, DC, DD, DB (or flipped)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Apply rule : ![a^\frac{1}{3}=\sqrt[3]{a}](https://tex.z-dn.net/?f=a%5E%5Cfrac%7B1%7D%7B3%7D%3D%5Csqrt%5B3%5D%7Ba%7D)
![8^\frac{1}{3}=\sqrt[3]{8}](https://tex.z-dn.net/?f=8%5E%5Cfrac%7B1%7D%7B3%7D%3D%5Csqrt%5B3%5D%7B8%7D)
8 is a perfect cube. Evaluate the cube root of 8.
![\sqrt[3]{8}=2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%3D2)
