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

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

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

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

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

A) Equivalent for all x.

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

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

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

\$\sqrt(2x + 6) + 4 = x + 3\$
What is the solution set of the equation above?

A) {- 1}

B) {5}

C) {- 1, 5}

D) {0, - 1, 5}

\$5x^2 + 10x + 16 = 0\$
How many distinct real solutions does the given equation have?

A) Infinitely many

B) Exactly one

C) Zero

D) Exactly two

A company mixes two types of nuts, one with a protein content of 10 grams per 100 grams and the other with 20 grams per 100 grams. They need to create a mixture with a protein content of 15 grams per 100 grams. What are the possible ratios of the two types of nuts they can use?

A) x : y = 100 : 75 and x : y = 100 : 25

B) x : y = 100 : 75 and x : y = 75 : 100

C) x : y = 25 : 100 and x : y = 100 : 25

D) x : y = 100 : 75 and x : y = 75 : 25

- 15x + 25y = 65
One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which of the following could be the second equation in the system?

A) 12x + 20 y = 52

B) 12x + 20 y = - 52

C) - 12x + 20 y = 52

D) - 12x + 20 y = - 52

48x - 72y = 30y + 24
\$ ry = 1/6 - 16x \$
In the given system of equations,r is a constant. If the system has no solution, what is the value of r?

A) - 34

B) 34

C) 23

D) - 23

\$ y = 6x + 18 \$
One of the equations in a system of two linear equations is given. The system has no solution. Which equation could bethe second equation in the system?

A) - 12x + y = 18

B) - 6x + y = 18

C) - 12x + y = 36

D) - 6x + y = 22

The given system is:
x + 2y = 4 (Equation 1)
mx + (2m - 1)y = n (Equation 2)
For what values of m and n will the system have infinitely many solutions?

A) m = 1, n = 2

B) m = any real number, n = a multiple of 4

C) m = any even integer, n = any real number

D) m = - 2, n = 0

Find the values of u and v for which the following system of linear equations has no solutions:
ux + 3y = 4
​2x + vy = 5
3x + (u + v)y = 9​

A) \$ u = 3/v \$​, v ≠ 1 ​ ​

B) \$ u = v/3 \$​, v ≠ 0

C) \$ u = 6/v \$​, v ≠ 0

D) \$ u = v/6 \$​, v ≠ 1