Answer:
X is 22.5°
Step-by-step explanation:
» Let's assume our diagram is as above, from trigonometric ratio:
- theta is X
- opposite is a
- hypotenuse is c
First, you have to imagine that you cut the upper triangle. If you do that, then this is how the inner angles are added to 180°:
180° = 90° + (x/2) + (7x - 90°)
180° = x/2 + 7x
180° = x *(1/2 + 7)
180° = x*(15/2)
2/15 * 180° = x
24 = x
Angle A:
A= x/2
A = 24/2
A = 12°
Angle B:
B = 7x
B = 7*24
B = 168°
The two bottom angles are both worth 90°.
Y₂-y₁ ÷x₂-x₁ =
(7.5 - 24) ÷ (36-5) =
-16.5 ÷ 31 = -16.5/31 ≈ -0.5322480
Or as a fraction: -33/62
1. Using c=2pi(r), plug in 7 for r and solve. Then using a=pi(r)^2, plug in 7 for r once again and solve.
2. First, the diameter (d) is 12 so to get the radius (r), divide 12 by 2 and you should get 6. Then use c=2pi(r) for circumference and a=pi(r)^2 for area to solve.
3. To get the area of the semicircle, divide 16 by 2 to get the radius (r), plug it into a=pi(r)^2, and divide the answer you get for a by 2. To get the area of the triangle, use a=1/2bh, plugging in 16 for b and 10 for h. Finally, add your two answers (the a's from the semicircle and triangle problems).
4. Multiply 20 by 5.5 to get the area of the triangle. Then multiply 4.5 by 20 to get the area of the parallelogram and add your two quotients.
5. Use a=1/2bh and plug in 4 for b and 3 for h and solve. Then multiply the quotient by 10 and there's your volume. To find the surface area, solve SA=(10×4)+(10×3)+(10×5)+12. All I did there was find the area of all the sides and added them together.
6. To find the triangle's volume, use a=1/2bh (b=4, h=1.5) and then multiply the quotient of that by 2.5. To find the rectangle's volume, use v=lwh (l=4, w=2.5, h=2) and solve. Finally, add the triangle's volume and the rectangle's volume to get the total volume. To get its surface area, start with the rectangle. Find the areas of all the sides and add them together but then subtract the 2.5×4 rectangle as it is not on the surface. It should look like this: SA=2(4×2)+2(2.5×2)+10. Again, all I did was find the areas of all the rectangle's sides on the surface and added them. Next, find the triangle's areas on the surface and it should look like this: SA=2(1.5×4)+2(2.5×2.5). Finally, add both values of SA from the triangle and rectangle and there's your surface area.
Answer:
12 x 3 , 2 x 18
Step-by-step explanation:
9x4= 36. You need to find two numbers that multiply to equal 36. In this case, you can do 12 x 3, and 2 x 18
