1. 25n + 0.08 (25n) + 17, simplified is 27n + 17
2. 6c + (0.05 + 0.20) (6c) - 10, simplified is 7.5c - 10
Below is the solution, I hope it helps.
<span>i) tan(70) - tan(50) = tan(60 + 10) - tan(60 - 10)
= {tan(60) + tan(10)}/{1 - tan(60)*tan(10)} - {tan(60) - tan(10)}/{1 + tan(10)*tan(60)}
ii) Taking LCM & simplifying with applying tan(60) = √3, the above simplifies to:
= 8*tan(10)/{1 - 3*tan²(10)}
iii) So tan(70) - tan(50) + tan(10) = 8*tan(10)/{1 - 3*tan²(10)} + tan(10)
= [8*tan(10) + tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}
= [9*tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)}
= 3 [3*tan(10) - tan³(10)]/{1 - 3*tan²(10)}
= 3*tan(30) = 3*(1/√3) = √3 [Proved]
[Since tan(3A) = {3*tan(A) - tan³(A)}/{1 - 3*tan²(A)},
{3*tan(10) - tan³(10)}/{1 - 3*tan²(10)} = tan(3*10) = tan(30)]</span>
Answer:
10
Step-by-step explanation:
(x−a)(x−b)=x2−(a+b)x+ab
Hope this was helpful----
Answer:
1. 28
2. b = 7.06
2. c = 3.76
Step-by-step explanation:
1. m < C = 90 - B = 90 - 62 = 28 degrees
2. sin B = opposite/hypotenuse
sin (62o) = b/8
b = 8 x sin (62o) = 8 x 0.883 = 7.06
3. sin C = opposite/hypotenuse
sin (28o) = c/8
c = 8 x sin (28o) = 8 x 0.4695 = 3.76
Answer:
$2,065
Step-by-step explanation:
The computation of the commission earned by Sam is shown below:
For each sale, he gets 7% commission
So,
For $12,000, the commission amount is
= $12,000 × 0.07
= $840
And, for another sale i.e. $17,500, the commission amount is
= $17,500 × 0.07
= $1,225
So, the total commission he earned is
= $840 + $1,225
= $2,065
