Answer: width = 5 units
Step-by-step explanation:
Let L represent the length of the rectangle.
The width of a rectangle is the length minus 2 units. It means that the width of the rectangle is (L - 2) units.
The formula for determining the area of a rectangle is expressed as
Area = length × width
The area of the rectangle is 35 units. It means that
L(L - 2) = 35
L² - 2L = 35
L² - 2L - 35 = 0
L² + 5L - 7L - 35 = 0
L(L + 5) - 7(L + 5) = 0
L - 7 = 0 or L + 5 = 0
L = 7 or L = - 5
Since the length cannot be negative, then
L = 7 units
Width = 7 - 2 = 5 units
The answer to your question is 15
Let S = number of small yogurts ($2 each).
Let M = number of medium yogurts ($3 each)
Let L = number of large yogurts ($5 each)
Total yogurts is 27, therefore
S + M + L = 27
Total revenue generated is $98, therefore
2S + 3M +5L = 98
There are five more large yogurts than small yogurts, therefore
L = S + 5, or
-S + L = 5
These three equations may be written as the matrix equation
[ 1 1 1 | |S| |27|
| 2 3 5 | |M| = |98|
| -1 0 1 | |L| | 5|
The determinant of the matrix is
D = 3 - (2+5) + 3 = -1.
Solve with Cramer's Rule to obtain
S = -[27*3) - (98-25) - 15]
= 7
M = -[(98-25) - 27(2+5) + (10+98)]
= 8
L = -[15 - (10+98) + 27(3)]
= 12
Answer: 7 small, 8 medium, 12 large yogurts.
From 0g to 494.7g are rejected as well as those heavier than 505.3grams.
You calculate this by subtracting and adding 5.3 to 500
