From the given info (and the linked question) we find
![\cos\alpha=-\dfrac5{13}](https://tex.z-dn.net/?f=%5Ccos%5Calpha%3D-%5Cdfrac5%7B13%7D)
![\sin\alpha=\dfrac{12}{13}](https://tex.z-dn.net/?f=%5Csin%5Calpha%3D%5Cdfrac%7B12%7D%7B13%7D)
![\sin\beta=-\dfrac45](https://tex.z-dn.net/?f=%5Csin%5Cbeta%3D-%5Cdfrac45)
Then using the angle-sum identity for cosine, we have
![\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha-%5Cbeta%29%3D%5Ccos%5Calpha%5Ccos%5Cbeta%2B%5Csin%5Calpha%5Csin%5Cbeta)
![\cos(\alpha-\beta)=\left(-\dfrac5{13}\right)\dfrac35+\dfrac{12}{13}\left(-\dfrac45\right)=-\dfrac{63}{65}](https://tex.z-dn.net/?f=%5Ccos%28%5Calpha-%5Cbeta%29%3D%5Cleft%28-%5Cdfrac5%7B13%7D%5Cright%29%5Cdfrac35%2B%5Cdfrac%7B12%7D%7B13%7D%5Cleft%28-%5Cdfrac45%5Cright%29%3D-%5Cdfrac%7B63%7D%7B65%7D)
80% of x = 0.80x or 4x/5
Any fraction equivalent to 80/100 can be used to multiply x. You could also divide x by any equivalent to 5/4 or 1.25.
Answer:
23
Step-by-step explanation:
7*3 is 21. 5*5 is 25. 23 is the only odd number in between
Answer:
7 hours
Step-by-step explanation:
$247.50 - $45.00 (how much he charges for the first hour) = $202.50
$202.50 ÷ $33.75 (how much he charges for the additional hours) = 6 hours
But he charges 45 dollars for the first hour so he 7 hours in total
Answer:
(x + 1)(3x - 10)
Step-by-step explanation:
Given
3x² - 7x - 10
Consider the factors of the product of the x² term and the constant which sum to give the coefficient of the x- term.
product = 3 × - 10 = - 30 and sum = - 7
The factors are + 3 and - 10
Use these factors to split the x- term
3x² + 3x - 10x - 10 ( factor the first/second and third/fourth terms )
3x(x + 1) - 10(x + 1) ← factor out (x + 1) from each term
(x + 1)(3x - 10), thus
y = (x + 1)(3x - 10) ← in factored form