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.
Answer: 64
Step-by-step explanation:
256 is thesame thing as 2 raise to power of 8.
We then multiply 2 raise to power 8 by the power of 3/4. We will then be left with 2 raise to power 6.
2 raise to power 6 equals:
= 2 × 2 × 2 × 2 × 2 × 2
= 64
Check the attached file for proper explanation.
This is a typical work problem in algebra. The approach to this is using the equation: Rt = 1, where R is the rate per person working, t is the amount of time worked by an individual. All their rates must equal to 1. The solution is as follows:
12/x + 15/x = 1
Solving for x,
x = 27 hours
So, if they work together, they can finish the work in 27 hours.
Answer:
x = -6
Step-by-step explanation:
The solution means to solve for x. To solve for "x", isolate the variable. This means to separate it from everything else. Do this using reverse operations in reverse BEDMAS order.
2/3 x + 5 = 1
2/3 x + 5 - 5 = 1 - 5 Subtract 5 from both sides
2/3 x = -4
(2/3 x) / (2/3) = (-4) / (2/3) Divide both sides by 2/3
x = (-4) / (2/3)
x = -6 Solution
