Three seventh-grade students, Rudy, Beth, and Diego, collect aluminum cans for recycling. They receive 1.7 cents for each can they collect. The student who collects $40 worth of cans receives a special prize from the school. The prize is a gift certificate equal to 1/2 of the dollar value of the cans they collect. If Rudy collects 1,500 cans, Beth collects 2,750 cans, and Diego collects 4,000 cans, which of them will win the prize and how much will it be? a) Rudy will win and receive $75 in prize money

b) Beth will win and receive $50 in prize money

c) Beth will win and receive $46.75 in prize money

d) Diego will win and receive $34 in prize money ​

b

Beth will win and receive $50 in prize money

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl