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°
Get x by itself
add 16 to both sides, so 4x = 16
divide both side by 4 and x =4
Answer: The mean is 3780
Step-by-step explanation:
Mean is found by adding all values and dividing the sum by how many values were added.
4250+4019+3895+3739+3401+3376=22680
22680/6=3780
Answer: 2x² - 8x + 9
Step-by-step explanation: this is our initial equation:
(4x² – 3x + 2) - (2x² + 5x - 7)
the subtraction sign which is to the left values is multiplying to the values into the parenthesis
(-) * (2x² + 5x - 7)
so this factor change the sign to every value into the parenthesis, then we get the following equation.
-2x² - 5x + 7
after this we get this final equation
4x² – 3x + 2 - 2x² - 5x + 7
then we resolve the equation with the similar values
4x² - 2x² = 2x²
– 3x - 5x = - 8x
+ 2 + 7 = 9
after this we place values in one equation, and we get the form simplified
2x² - 8x + 9
and this the last equation after resolve all the problems into the parenthesis.
