A ramp 17 1/2 feet in length rises to a loading platform that is 3 1/2 feet off the ground. Find the angle that the ramp makes with the ground.
Answers
Answer:
The angle that the ramp makes with the ground is 11.54°
Step-by-step explanation:
From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.
We can use the fact that the sin(θ) = to find the angle that the ramp makes with the ground.
The angle is equal to
Final answer:
The angle that the ramp makes with the ground can be found using the concept of tangent in trigonometry. By dividing the height of the loading platform by the length of the ramp and taking the inverse tangent of the result, we find the angle to be approximately 11.3 degrees.
Explanation:
This question can be solved by using trigonometric principles, specifically the tangent of an angle in a right triangle. The tangent of an angle θ (theta) can be defined as the ratio of the side opposite the angle to the side adjacent to it.
In this scenario, the ramp forms a right triangle with the ground and the vertical line from the loading platform to the ground directly below it. The height of the platform, or the 'opposite' side, is 3 1/2 feet, and the ramp, or the 'adjacent' side, is 17 1/2 feet.
Therefore, we can say that: tan θ = (3.5 / 17.5)
To find the value of θ, we take the inverse tangent (or arc tangent) of the quotient. Using a calculator to do this (remember to set your calculator to degree mode), we find θ to be approximately 11.3 degrees.
Thus, the angle that the ramp makes with the ground is about 11.3 degrees.
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\dfrac{3}{4} =
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Answer:
9/12
Step-by-step explanation:
First you multiply 3x12 which equal 36 then you divide 36 by 4 which equal 9 so your answer is 9/12
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__ is the answer hope that i helped
12
Answers
Answer:
I think the answer is "6" but I could be wrong.
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The solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).
Given:
Brody can work a maximum of 13 hours: x + y ≤ 13
Brody must earn at least $150: 10x + 15y ≥ 150
These are the two inequalities we need to solve graphically.
Graph the first inequality: x + y ≤ 13
This inequality represents the total number of hours Brody can work, which cannot exceed 13 hours. We'll plot the line x + y = 13 and shade the region below it.
Graph the second inequality: 10x + 15y ≥ 150
This inequality represents the total earnings Brody needs to make, which should be at least $150. Let's simplify it to 2x + 3y ≥ 30. We'll plot the line 2x + 3y = 30 and shade the region above it.
Now, let's find the point where the shaded regions of both inequalities overlap. This point will represent the feasible solution where Brody's working hours and earnings satisfy both conditions.
Solving the system of inequalities graphically, you will find the point of intersection. However, since I can't create a graphical representation here, I'll explain how to calculate the solution point algebraically:
First, solve the equation x + y = 13 for y:
y = 13 - x
Now substitute this value of y into the equation 2x + 3y = 30:
2x + 3(13 - x) = 30
2x + 39 - 3x = 30
-x = -9
x = 9
Now substitute the value of x back into the equation y = 13 - x:
y = 13 - 9
y = 4
So, the solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).
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Graph y≤13−x (shading down)
graph y≥10− 3/2x (shading up)
Answers
The number is 442 which is obtained after decreasing 520 by 15% the answer is 442.
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Let x be the number that is obtained after decreasing 520 by 15%
= (100 - 15)% of 520
= 85% of 520
= 0.85×520
= 442
Thus, the number is 442 which is obtained after decreasing 520 by 15% the answer is 442.
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Answer:
442
Step-by-step explanation:
If you want to decrease 520 by 15%, you have to multiply 15% by 520 first, which is 78. Next, you have to minus 78 from 520. Now you get 442!
Answers
Answer:
8 <b
Step-by-step explanation:
5 < b - 3
Add 3 to each side
5+3< b-3+3
8 <b
Answer:
8 < b
Step-by-step explanation:
1. Add 3 by both sides to eliminate the -3 on b - 3.
2. You get 8 < b.