The following rectangle has an area of 3x^2-5x-12. What are the possible side lengths, in terms of x? Explain your answer and justify how you know that the sides you found are possible lengths

the possible side lengths:

3x+4 and x-3

Step-by-step explanation:

factorize the the expression and you will get two expressions in terms of x. those expressions are the lengths of the rectangle

1) write -5x as a difference

2) factor out x from the expression 3x²+4x

3) factor out -3 from the expression -9x-12

4) factor out 3x+4 from the expression

the possible lengths are 3x+4 and x-3

to check whether the answer is correct, you can just multiply the both lengths using the area of rectangle formulae

area of rectangle formulae

(3x+4)(x-3)

= 3x²-9x+4x-12

= 3x²-5x-12 ( proven )

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

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