9514 1404 393
Answer:
D. 43 degrees
Step-by-step explanation:
The sum of angles in a triangle is 180°. If x represents the measure of the third angle, then ...
75° +62° +x = 180°
137° +x = 180° . . . . . . . . . collect terms
x = 180° -137° = 43° . . . . subtract 137° from both sides of the equation
The third angle measures 43°.
Given expression is
![\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B%5Cfrac%7B16x%5E%7B11%7Dy%5E8%7D%7B81x%5E7y%5E6%7D%7D)
Radical is fourth root
first we simplify the terms inside the radical


So the expression becomes
![\sqrt[4]{\frac{16x^4y^2}{81}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B%5Cfrac%7B16x%5E4y%5E2%7D%7B81%7D%7D)
Now we take fourth root
![\sqrt[4]{16} = 2](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B16%7D%20%3D%202)
![\sqrt[4]{81} = 3](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B81%7D%20%3D%203)
![\sqrt[4]{x^4} = x](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E4%7D%20%3D%20x)
We cannot simplify fourth root (y^2)
After simplification , expression becomes
![\frac{2x\sqrt[4]{y^2}}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5Csqrt%5B4%5D%7By%5E2%7D%7D%7B3%7D)
Answer is option B
Volume of Solids
The volume of the solid is 758.83 in³
Step-by-step explanation:
Given that the cone and half sphere is hollow
The volume of the cone =
The Volume of the sphere = 
So the Volume of the half sphere =
The volume of solid = volume of cone + volume of the half sphere

Given
height h = 19 in
radius r = 5 in
= 
= 1/3 × 3.14 × 5 × 5 × 19
= 497.16 in³

= 2/3 × 3.14 × 5 × 5 × 5
= 261.67 in³
V = 497.16 in³ + 261.67 in³
= 758.83 in³
Hence the volume of the solid is 758.83 in³
Answer:
ST = x = 1.8 (to the nearest tenth)
Step-by-step explanation:
STU is a right triangle right angled at T with S =61° and hypotenuse SU=3.7 units.
ST = x = SUcos(61°) = 3.7cos(61°) = 3.7*0.48481 = 1.7938
Answer:
Graph A
Step-by-step explanation:
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