The total area of the polygon is 176 square feet. Find the value of x.
2 answers:
Answer:
x = 6 ft
Step-by-step explanation:
Total area of the given polygon = Area of triangle 1 + Area of rectangle 2 + Area of triangle 3
Area of triangle 1 = Area of triangle 3 =
=
= 4x square feet
Area of rectangle 2 = Length × Width
= 16 × 8
= 128 square feet
Total area of the given polygon = 4x + 128 + 4x
176 = 8x + 128
8x = 176 - 128
x =
x = 6 ft
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From the information given,
x represents number of small boxes while y represents number of large boxes.
If each small box can hold 6 books and each large box can hold 10 books, it means that the expression for the number of books that x small boxes and y large boxes can hold is
6x + 10y
If James can pack up to 110 books, it means that the number of books that he can pack is less than or equal to 110. The inequality representing this scenario is
6x + 10y ≤ 110
10y ≤ - 6x + 110
Dividing both sides of the equation by 10, we have
y ≤ - 6x/10 + 110/10
y ≤ - 3x/5 + 11
The graph is shown below
The inequality that represents this sitaution is 6x + 10y ≤ 110
The graph of the inequality wil have solid boundary at y = - 3x/5 + 11
and will be shaded below the line.
