For all positive values of y, the expression \$3/(y + c)\$ is equivalent to \$15/(5y + 30)\$. What is the value of constant c?

A) 4

B) 6

C) 2

D) 8

\$(5x^3 - 3) - (- 4x^3 +8)\$ The given expression is equivalent to \$bx^3 - 11\$, where b is a constant. What is the value of b?

A) -9

B) 6

C) 9

D) -6

Which of the following is equivalent to \$(1 - p) (1 + p + p^2 + p^3 + p^4 + p^5 + p^6)\$?

A) \$1 - p^6\$

B) \$1 - p^3\$

C) \$1 - p^5\$

D) \$1 - p^7\$

Sarah is planning a road trip. She wants to calculate the total cost of gas for the trip. The cost of gas is $3.50 per gallon, and she estimates that her car gets 25 miles per gallon. The total distance of her trip is 400 miles. Sarah wants to know how much she will spend on gas for the entire trip.

A) $56

B) $52

C) $65

D) $25

The expression \$90y^5 - 54y^4\$ is equivalent to \$ry^4(15y - 9)\$ , where r is a constant. What is the value of r?

A) 6

B) 15

C) -6

D) -15

Simplify the given expression: \$(2x^3 y^-(2)) / (4x^(-1)y^4)\$.

A) \$x^4/(2y^6)\$

B) \$x^6/(y^6)\$

C) \$-x^4/(2y^6)\$

D) \$x^4/(2y^4)\$

\$(4x)/(2(x^2 -1)) - (3x) / (3(x^2 -1))\$ Which of the following is equivalent to the given expression for x ≠ -1 and x ≠ 1?

A) \$x /(x^2 -1)\$

B) \$1 /(x^2 -1)\$

C) \$x /(x^2 +1)\$

D) \$1 /(x^2 +1)\$

Find the value of x that makes the expressions \$(x^2 -9)/(x -3)\$​ and \$(x^2− 4)/(x+2)\$​ equivalent.

A) \$3x^2 - 2x +15\$

B) \$3x^2 - 2x -15\$

C) \$3x^2 + 2x +15\$

D) \$3x^2 + 2x -15\$

Which expression represents the product of \$x^(-6) y^3z^5\$ and \$x^4 z^5 + y^8 z^(-7)\$.

A) \$x^2 y^3 z^10 + x^(-6) y^11 z^(-2)\$

B) \$x^(-2) y^3 z^10 - x^(-6) y^11 z^2\$

C) \$x^(-2) y^3 z^10 + x^(-6) y^11 z^(-2)\$

D) \$x^(-2) y^3 z^(-10) + x^6 y^11 z^(-2)\$

Two cars start from the same point and travel in opposite directions. One car travels 20 miles per hour faster than the other. After 3 hours, the distance between the two cars is 270 miles. Find the speed of each car.

A) 35 mph (slower car) 35 mph (faster car)

B) 53 mph (slower car) 55 mph (faster car)

C) 53 mph (slower car) 35 mph (faster car)

D) 35 mph (slower car) 55 mph (faster car)