A cardboard carrying box has the dimensions shown below. How many square inches of cardboard are needed to make the box?
2 answers:
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Answer:
k = 5
Step-by-step explanation:
The formula for coefficient of proportionality is y = kx.
In the given problem, the Area of a rectangle corresponds to "y" in the constant of proportionality formula, and "x" is still the same. Since the formula for the area of a rectangle is: A = L × W, then:
A = y
L = k
W = x
y = kx is the same as A = LW or A = L × W
Thus, we're looking for the value for k, which corresponds to the length (L) (which has a constant value).
Below are the calculations for the missing values in the table:
We'll start with x = 0.14, and A = 0.7 since we're given the values for them. We could plug these values into the formula for the Area of a rectangle to find the constant value of the length (L):
A = L * W
0.7 = L * 0.14
Divide both sides by 0.14 to isolate L:
0.7/0.14 = (L * 0.14)/0.14
5 = L ←← Keep in mind, this is the coefficient of proportionality.
<u>x = 3.1:</u>
A = L * W
A = 5 * 3.1
A = 15.5
x = 2.5:
A = 5 * 2.5
A = 12.5
<u>x = 1.2:</u>
A = 5 * 1.2
A = 6
<u>x = 0.9:</u>
A = 5 * 0.9
A = 4.5
Next, we're given the values for the Area, but we're missing the values for x. However, we already have the value for L = 5. We could still follow the same process by plugging in the values into the formula:
<u>A = 0.3:</u>
A = L * W
0.3 = 5 * W
Divide both sides by 5 to solve for W:
0.06 = W
<u>A = 0.1:</u>
A = L * W
0.1 = 5 * W
Divide both sides by 5 to solve for W:
0.02 = W
Therefore, k = 5.