Question

Can u pls help me with this question ​

Answer 1

Please check the explanation.

Explanation:

We know that when 'y' varies directly with 'x', the equation becomes

y ∝ x

y = kx

where 'k' is called the constant of proportionality.

From the table, it is clear that 'y' varies directly with 'x'

Let us check the value of k for all the points

k = y/x

For the point (130, 9.10)

• k = 9.10 / 130 = 0.07

For the point (145, 10.15)

• k = y/x = 10.15 / 145 = 0.07

For the point (150, 10.50)

• k = y/x = 10.50 / 150 = 0.07

For the point (185, 12.95)

• k = y/x = 12.95 / 185 = 0.07

Thus, the value of proportionality constant is same.

i.e. k = 0.07

Determining the cost of 21 feet of the wire

• And need 21 feet of the wire.

21 feet = 252 inch

Using the equation

y = kx

• where y represents the cost and x represents the length in inches

Thus, the cost of 252-inch wire will be:

y = kx

substituting k = 0.07, and x = 252

y = 0.07 × 252

y = 17.64 Dollars

Thus, the cost of 21 feet wire will be: 17.64 Dollars

Determining the cost of 15 yards of the wire

• Emily needs 15 yards of the wire.

15 yards = 540 inches

Using the equation

y = kx

• where y represents the cost and x represents the length in inches

Thus, the cost of 15 yards of wire will be:

y = kx

substituting k = 0.07, and x = 540

y = 0.07 × 540

y = 37.8 Dollars

Thus, the cost of 15 yards of wire will be: 37.8 Dollars