A rectangular carpet has a perimeter of 194 inches. The length of the carpet is 67 inches more than the width. What are the dimensions of the carpet?

The dimensions of the carpet are 15 inches and 82 inches

Step-by-step explanation:

Assume that the width of the carpet is x inches

∵ The width of the carpet is x inches

∵ The length of the carpet is 67 inches more than the width

∴ The length of the carpet is (x + 67) inches

∵ The perimeter of the rectangle = 2(length + width)

∵ The perimeter of the carpet = 194 inches

→ Equate the two right sides of the perimeter

∴ 2(length + width) = 194

→ Divide both sides by 2

∴ length + width = 97

→ Substitute the value of the length and width in the equation above

∵ x + 67 + x = 97

→ Add the like terms in the left side

∴ (x + x) + 67 = 97

∴ 2x + 67 = 97

→ Subtract 67 from both sides

∵ 2x + 67 - 67 = 97 - 67

∴ 2x = 30

→ Divide both sides by 2

∴ x = 15

∵ x represents the width of the carpet

∴ The width of the carpet is 15 inches

∵ The length of the carpet = 15 + 67

∴ The length of the carpet is 82 inches

∴ The dimensions of the carpet are 15 inches and 82 inches

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.

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.