Ms. Jones wrote the expression below on the chalkboard for her class. 4(3x + 5y + 2z) + 3(x – z)

She asked the students to write an equivalent expression using no more than one set of parentheses.

Tom wrote 12x + 20y + 8z
Jenna wrote 15x + 20y +5z
Chris wrote 40xyz

Which, if any, of the three students wrote an expression that is equivalent to Ms. Jones’ expression? Justify by showing your work!

12x + 20y + 8z + 3(x -z)

12x + 20y + 8z + 3x - 3z

15x + 20y + 5z

15x + 20y + 5z

the answer is:15x + 20y + 5z

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.