Answer:
12 units
Step-by-step explanation:
Point H is the intersection of the medians, so divides each median into parts with the ratio 2:1. Here, that is ...
CH : HG = 2 : 1 = CH : 6
Then CH = 2×6 = 12.
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Alternatively, you could determine altitude CG from the Pythagorean theorem applied to triangle BCG. You would compute ...
CG² +GB² = BC²
CG = √(BC² -GB²) = √(19.8² -8²) = √146.7 ≈ 12.1
This is an approximation based on the fact that the value 9.9 for BF is an approximation. Based on BG and GH being integer values, the appropriate measure of BF is (√388)/2 ≈ 9.8489.
(The triangle shown cannot exist.)
The ladder will reach 122 ft up the building.
The 120 feet of the extended ladder, since it will be leaning against the building, will be the hypotenuse of the right triangle. x will be the height from the top of the fire truck to the point where the ladder hits the building. 75° is the angle the ladder will make with the fire truck.
We have an angle, the side opposite the angle, and the hypotenuse. Opposite/hypotenuse is the ratio for sine, so we set up our equation as such:
x/120 = sin 75
Multiply both sides by 120:
120(x/120) = 120*sin 75
x = 120*sin 75
x ≈116
However, this is just from the top of the fire truck to the point where the ladder hits the building. We still add the 6 feet from the top of the truck to the ground. 116+6 = 122.
Let the original 2-digit number be xy.
Because 5 times the sum of the digits is 13 less than the number, therefore
5(x + y) = 10x + y - 13
5x + 5y = 10x + y - 13
-5x + 4y = - 13 (1)
The number with reversed digits is yx.
Because 4 times the sum of the digits is 21 less than the reversed 2-digit number, therefore
4(x + y) = 10y + x - 21
4x + 4y = 10y + x - 21
3x - 6y = -21
x - 2y = -7
x = 2y - 7 (2)
Substitute (2) into (1).
-5(2y - 7) + 4y = -13
-10y + 35 + 4y = -13
-6y = -48
y = 8
From (3), obtain
x = 2*8 - 7 = 9
Answers:
The original 2-digit number is 98
The reversed 2-digit number is 89
The difference between the original and the reversed 2-digit numbers is
98 - 89 = 9
Don’t at me I think it’s B
