We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2.
Answer:
7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg
8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg
Step-by-step explanation:
Law of Cosines

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.
Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.
7.
We use the law of cosines to find C.






Now we use the law of sines to find angle A.
Law of Sines

We know c and C. We can solve for a.


Cross multiply.





To find B, we use
m<A + m<B + m<C = 180
40.8 + m<B + 78.6 = 180
m<B = 60.6 deg
8.
I'll use the law of cosines 3 times here to solve for all the angles.
Law of Cosines



Find angle A:





Find angle B:





Find angle C:





Answer: her sales last week was $4300.
Step-by-step explanation:
Let x represent her her sales in a week.
Danielle earns a 8.25% commission on everything she sells at the electronics store where she works. This means that the commission she gets if she makes sales of $x is 0.0825x
She also earns a base salary of $675 per week. The expression for the total earnings for a week in which she made sales of $x would be
0.0825x + 675
if her total earnings for last week were $1,029.75, it means that
0.0825x + 675 = 1029.75
0.0825x = 1029.75 - 675
0.0825x = 1029.75 - 675
0.0825x = 354.75
x = 354.75/0.0825
x = $4300