Answer:
x4+7x3-2x2-9x-3 remainder -10
or we could write it as
x4+7x3-2x2-9x-3 - 10/(x+8)
Step-by-step explanation:
x+8 ) x5+15x4+54x3−25x2−75x−34 (x4+7x3-2x2-9x-3 <--- Quotient.
x5+ 8x4
7x4+54x3
7x4+56x3
-2x3-25x2
-2x3-16x2
-9x2-75x
-9x2-72x
-3x-34
-3x-24
-10 <--- Remainder.
Do Area = (base 1 + base2) × H
Answer:
θ = (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = , so
θ = ( ) = ( or 60° )
In 1 hour she earns $7.25
18 hours she earns $130.5
18 times 17.25 it’s $130.5
Answer:
679
Step-by-step explanation:
The goal of this exercise is to find a three digit number given five statements.
1 - We can conclude that two digits out of 964 are correct but in the wrong place.
2 - One digit out of 147 is correct, but in the wrong place
3 - One digit out of 189 is correct and in the right place. Since 1 is on the same place in 147 and 189, 1 is not the correct digit. The correct digit is either 8 or 9.
4 - One digit out of 286 is correct, but in the wrong place. Since 8 is on the same place in 189 and 286, 8 is not the correct digit. We can then conclude that 9 is correct (statement 3) and in the right place (third) and that either 2 or 6 are correct but in the wrong place.
5 - 523 are all wrong. We can then conclude that 6 is correct and that is not in the third or second place, which leaves it in the first place.
If 1 and 4 are incorrect, from the second statement, we infer that 7 is the remaining correct digit at the second place.
Therefore the number is 679