Answer:
C. 40.2°
Step-by-step explanation:
Cosine rule (real handy to remember): c² = a² + b² - 2·a·b·cos(γ)
If you don't know this yet, look it up but in short: c, a and b are the lengths of the sides of the triangle, the angle opposite side a is called α, for b it is β and for c it is γ. That's the convention I've always used anyway, you can call them whatever of course. Anyhow:
c² = a² + b² - 2·a·b·cos(γ)
⇒ |AC|² = |AB|²+|BC|²-2·|AB|·|BC|·cos(∠B)
⇒ |AC|²-|AB|²-|BC|² = -2·|AB|·|BC|·cos(∠B)
⇒ ( |AC|²-|AB|²-|BC|² ) / ( -2·|AB|·|BC| ) = cos(∠B)
⇒ ∠B = arccos( ( |AC|²-|AB|²-|BC|² ) / ( -2·|AB|·|BC| ) )
= arccos( ( 11²-16²-16² ) / ( -2·16·16 ) )
= 40.21101958°
≈ 40.2°
Equation is 2(3x+24)=9x+18
Answer is x=10
Bisector means it cuts it in half so ABD is the same as DBC. The whole angle is 9x+18 which is the same as doubling 3x+24 since thats half of if hence the equation 2(3x+24)=9x+18
To solve for x you have to distribute 2(3x+24) by multiplying 2 to 3x and 24
New equation is 6x+48=9x+18
Subtract 6x both sides
48=3x+18
Subtract 18 both sides
30=3x
Divide both sides by 3
10=x
Answer:
12 + 3x + 2y
Step-by-step explanation:
14 + 8x + 2y -5x - 2
14 + -2 + 8x -5x + 2y
12 + 3x + 2y
Answer:
15 students. 30%
Step-by-step explanation:
Answer:
Find the volume of the rectangular prism and
divide by the volume of the cube.
Volume of cube = side measure ^3
Cube = (1/8)3 = 1/512
Volume of prism = Ixwxh
Prism (1/4)(1/2)(3/8) =3/64
3/64/1/512
3/64 x 512/1
3x 512/64
1536/64
24
