Answer:
8 grams
Step-by-step explanation:
The balance is in equilibrium, so the weights of the two sides are equal.
Let the weight of a square be s.
Left side: 2s + 4
Right side: s + 3(4) = s + 12
The weights are equal, so we set the two expressions equal.
2s + 4 = s + 12
s = 8
Answer: The weight of a square is 8 grams.
The length of the diagonal of the canvas is approximately 27 degrees.
The height of the rectangular canvas must reach 18 inches. It must form a 48 degrees angle with the diagonal at the top of the canvas.
<h3>Length of the diagonal Canvas</h3>
Therefore, the length of the diagonal can be found as follows:
Using trigonometric ratio,
- cos ∅ = adjacent / hypotenuse
where
∅ = 48°
adjacent side = Height of the rectangle = 18 inches
hypotenuse = Length of the diagonal
Therefore,
cos 48° = 18 / h
cross multiply
h = 18 / cos 48°
h = 18 / 0.66913060635
h = 26.9005778976
length of the diagonal ≈ 27 inches
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Answer:
B=45
Step-by-step explanation:
310+50=360
360/8=45
:)
The perimeter of the rectangle based on the factors given is 46.
<h3>How to calculate the perimeter?</h3>
The area of the rectangle is given as (x² + 13x - 90). This will be:
= (x² + 13x - 90)
= x² + 18x - 5x - 90
= x(x + 18) - 5(x + 18)
= (x - 5)(x + 18)
The sides of the rectangle are 5 and 18. The perimeter will be:
= 2(l + w)
= 2(5 + 18)
= 46
The area of the rectangle is given as (x² + 24x - 81.
= (x² + 24x - 81)
= x² + 27x - 3x - 81
= x(x + 27) - 3(x + 27)
= (x - 3)(x + 27)
The sides are 3 and 27. The perimeter will be:
= 2(l + w)
= 2(27 + 3)
= 60
= (x + 1)² + 3(x + 1) + 2
= (x + 1)(x + 1) + 3x + 3 + 2
= x² + x + x + 1 + 3x + 5
= x² + 5x + 6
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Answer:
151
Step-by-step explanation:
