9514 1404 393
Answer:
x = -7, x = 9
Step-by-step explanation:
We presume your equation is ...
x² -2x -63 = 0
Factors of -63 that have a sum of -2 are -9 and +7. Then the factored equation is ...
(x -9)(x +7) = 0
Solutions make the factors zero.
x -9 = 0 ⇒ x = 9
x +7 = 0 ⇒ x = -7
The solutions to the quadratic equation are x = -7 and x = 9.
Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees
<h3>Trigonometry identity</h3>
Trigonometry identities are expressed as a function of cosine, sine and tangent.
Given the trigonometry expression shown
4cos2θ+9=−14cosθ
Equate to zero
4cos2θ+9 + 14cosθ = 0
According to trig identity
cos2θ = 2cos²θ - 1
Substitute to have:
4(2cos²θ - 1)+9 + 14cosθ = 0
Expand
8cos²θ - 4 + 9 + 14cosθ = 0
8cos²θ+ 14cosθ + 5 = 0
let P = cosθ to have;
8P² + 14P + 5 = 0
Factorize the result
8P² + 10P + 4P + 5 = 0
2P(4P+5)+1(4P+5)=0
(2P+1) = 0 and 4P+5 = 0
2P = -1 and P = -5/4
P = -1/2 and -5/4
Recall that P = cosθ
If P = -1/2
cosθ = -1/2
θ = -60
Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees
Learn more on trigonometry identity here: brainly.com/question/24349828
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The unknown number is - 2.5
Let the number = n
The equation will be formed as follows;
- eight times a number plus two = 8n + 2
- Two times the quantity of eight times a number plus two = 2(8n + 2)
- two times the same number minus seven = 2n - 7
- three the quantity of two times the same number minus seven = 3(2n-7)
Our final equation becomes;
2(8n + 2) = 3(2n-7)
Simplify as follow, to determine the unknown number;
16n + 4 = 6n - 21
16n - 6n = -25
10n = -25
n = -2.5
Thus, the unknown number is - 2.5
Learn more here: brainly.com/question/13818690
Answer:
10
Step-by-step explanation: because if you get 45$ for breaking 1 and lose 20$ for paying for it you will just get 25$ for breaking each board
