Which value must be added to the expression x^2-3x to make it a perfect-square trinomial? a) 3/2 b) 9/4 c) 6 d) 9

Step-by-step explanation:

Here, the given equation,

Let y be the the value after adding the given equation will convert to a perfect square trinomial,

Also, a perfect square trinomial can be written as ( ax + b )² or ax² + 2abx+ b²,

That is,

By comparing,

a = 1, 2ab = -3,

⇒ 2(1)b = -3

⇒ b = -3/2

Hence, the value of y = = =

OPTION B is correct.

it’s supposed to be -4+45=41

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240