HELP ILL MARK YOU BRAINLIEST (40PTS)!! Which number line best shows how to solve −6 − (−8)? A number line from negative 10 to 10
1 answer:
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Answer:
Length of hypothenuse = 13 inches
Length of other leg = 5 inches
Step-by-step explanation:
A triangle has three sides and three angles. A right angle triangle has 90 degrees as one of the angles. The remaining two angles are complimentary. This means that the sum if the other two angles is 90 degrees.
The longest side is the hypotenuse. The shorter sides are the opposite and adjacent.
In this triangle, the hypotenuse is three inches more than twice the length of one leg. Let the length of one leg be x inches.
Hypothenuse = 2x + 3
The other leg is 12 inches.
The diagram is illustrated in the attached photo.
Applying Pythagoras theorem,
Hypothenuse ^2 = adjacent^2 + opposite ^2
(2x+3)^2 = 12^2 + x^2
(2x+3)(2x+3)= 144 + x^2
4x^2 + 6x + 6x + 9 = 144 + x^2
4x^2 - x^2 + 6x + 6x + 9 - 144 = 0
3x^2 +12x - 135 = 0
3x^2 +27x - 15x - 135 = 0
3x(x+9)-15(x+9)=0
(3x -15)(x+9) = 0
3x -15 = 0 or x+9= 0
3x = 15 or x = -9
x = 15/3 = 5
x = 5inches because it cannot be negative.
Length of hypothenuse = 2x + 3
= 2×5 + 3 = 10 + 3 = 13 inches
Answer:
546 ft³
Step-by-step explanation:
In the figure attached, the top view of the pool is shown. It can be decomposed into a trapezoid which height is 12 ft and which bases are 9 ft and 11 ft; and a rectangle which height is 1.5 ft and and it base is 11 ft.
Area of the trapezoid: (9 + 11)/2 * 12 = 120 ft²
Area of the rectangle: 1.5*11 = 16.5 ft²
Total area: 120 + 16.5 = 136.5 ft²
Volume of the pool: Total area * deep = 136.5 * 4 = 546 ft³
