A recipe requires a mixture of juice and water in a 3:2 ratio. Write two equivalent expressions for the total amount of liquid (j for juice, w for water).

A) \$ L = (1/3) ​j \$ and \$ L = (5/2) ​w \$

B) \$ L = (5/3) ​j \$ and \$ L = (5/2) ​w \$

C) \$ L = (5/3) ​j \$ and \$ L = (1/2) ​w \$

D) \$ L = (2/3) ​j \$ and \$ L = (1/2) ​w \$

Simplify the expression:
\$ (\sqrt(x^2 + 10x + 16)) + (\sqrt(x^2 - 2x + 1)) \$

A) \$ |x - 8| + |x - 1| \$

B) \$ |x - 4| + |x - 2| \$

C) \$ |x + 4| + |x - 1| \$

D) \$ |x - 1| + |x + 2| \$

Simplify the expression and find an equivalent expression: \$ (x^2 + 5x + 6)/(x + 2) times (x + 3) \$

A) \$ (x + 1)^2 \$

B) \$ (x + 3)^2(x + 1)^2 \$

C) \$ (x + 3)^2(x + 3)^2 \$

D) \$ (x + 3)^2 \$

Simplify the expression :\$ (x^2)^(1/2) * x^(3/2) \$.

A) \$ x^(5/2) \$

B) \$ x^(3/2) \$

C) \$ x^(7/2) \$

D) \$ x^(9/2) \$

The area of a rectangle is given by the product of its length (l) and width (w). Write two equivalent expressions for the perimeter (p) of the rectangle when the length is 2 units more than twice the width.

A) \$ p = 6w + 4, p = 6w + 4 \$

B) \$ p = 2w + 4, p = 6w + 2 \$

C) \$ p = 6w + 3, p = 4w + 4 \$

D) \$ p = 7w + 4, p = 7w + 4 \$

Simplify the expression \$2(2x^2 - 3x + 1) + 2(x^2 - 1)\$.

A) \$4(x^2 - 3x + 2)\$

B) \$4(x^2 - x + 3)\$

C) \$4(x^2 - x + 2)\$

D) \$(x^2 - 3x + 2)\$

Simplify the expression and determine if it is equivalent to \$2(x^2 - 3x + 4) - (x^2 - 5x + 6)\$: \$2x^2 - 6x + 8 - x^2 + 5x - 6\$ is it Equivalent to:

A) \$x^2 - x + 6\$

B) \$x^2 - x + 4\$

C) \$x^2 - x + 2\$

D) \$x^2 - 3x + 6\$

Prove or disprove that the following expressions are equivalent:
\$(4x^2 - 16)/(2x + 4)\$ and 2(x - 2)

A) Equivalent for all x.

B) Equivalent only if \$x ne -2\$ and \$x ne 2\$.

C) Equivalent only if \$x ne -2\$.

D) Not Equivalent.

Simplify the expression and check if it is equivalent to \$(3x − 2)^2 − (3x − 2) (2x + 1)\$:
\$(9x^2 − 12x + 4) − (6x^2 + 3x − 4x − 2)\$ is equivalent to:

A) \$3x^2 − 11x + 6\$

B) \$3x^2 − 7x + 6\$

C) \$3x^2 − 11x + 2\$

D) \$3x^2 − 7x + 2\$

Are the expressions \$(\sqrt((x + 2))^2)\$ and x + 2 equivalent?

A) Equivalent for all x.

B) Equivalent only if \$x ge - 2\$.

C) Equivalent only if \$x ge 0\$.

D) Equivalent only if \$x ge - 2\$ and \$x ge 0\$.