The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10lb watermelon on a hanging scale, the spring stretched 5in. Write an equation that relates the length L that the spring stretches to the weight w. How many pounds does a watermelon weigh if it stretch the spring 6in?

A watermelon weighs 12 lb if it stretches the spring 6in.

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that length, L varies directly with weight, W, if we introduce a constant of proportionality, k, the expression becomes

L = kW

When W = 10 and L = 5, then

5 = 10k

k = 5/10 = 0.5

Therefore, the equation that relates the length L that the spring stretches to the weight W is

L = 0.5W

Therefore, if L = 6 inch, then

6 = 0.5W

W = 6/0.5 = 12 lb

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