What is the value of y

Step-by-step explanation:

step 1. there are 3 right triangles!

step 2. 8/6 = 6/x (definition of right triangle with an altitude)

step 3. 8x = 36 (cross multitude)

step 4. x = 9/2 (divide both sides by 8)

step 5. 6^2 + x^2 = y^2 (pythagorean theorem)

step 6. 6^2 + (9/2)^2 = y^2

step 7. 144/4 + 81/4 = y^2

step 8. 225/4 =y^2

step 9. y = 15/2 = 7.5.

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step-by-step explanation:

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let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0