The solution to this equation is in the picture i’ve put below!
Answer:
64√2 or 64 StartRoot 2 EndRoot
Step-by-step explanation:
A 45-45-90 traingle is a special traingle. Let's say one of the leg of the triangle is x. The other one is also x because of the isosocles triangle theorem. Therefore, using the pytagorean theorem, you find that x^2+x^2=c^2. 2(x)^2=c^2. You then square root both sides and get c= x√2.
Therefore, the two legs are x and the hypotenuse is x√2. x√2=128 because the question says that the hypotenuse is 128. Solve for x by dividing both sides by √2. X=128/√2. You rationalize it by multiplying the numberator and denominator of the fraction by √2. √2*√2= 2.
X=(128√2)/2= 64√2 cm.
Since X is the leg, the answer would be 64√2
and then there's a line with 2y right under that expression
4 x³ - 8 x² - 12 x =
= 4 x ( x² - 2 x - 3 ) =
= 4 x ( x² - 3 x + x - 3 ) =
= 4 x ( x ( x - 3 ) + ( x - 3 ) ) =
= 4 x ( x - 3 ) ( x + 1 ) ( the factored form )
