We are assuming A, C and B are on the same line segment AC, of length 17, with B a point in the segment.
|AC|=|AB|+|BC|
17= (4x-9)+(3x+5)
17= (4x+3x)+(-9+5)
17=7x-4
7x=17+4
7x=21
x=21/7=3
Answer: x=3
1-3 are about trigonometric ratios (SOH CAH TOA). 4, 5 are about the Law of Cosines, and 6 uses the Law of Sines.
1. Sin = Opposite/Hypotenuse
x = 10*sin(40°) ≈ 6.428
2. Sin = Opposite/Hypotenuse
x = arcsin(7/12) ≈ 35.69°
3. Tan = Opposite/Adjacent
x = 18/tan(52°) ≈ 14.063
4. b^2 = a^2 +c^2 -2ac*cos(B)
B = arccos((a^2 +c^2 -b^2)/(2ac)) = arccos((7^2 +13^2 -8^2)/(2*7*13))
B = arccos(11/13) ≈32.20°
5. Same formula.
x = √(a^2 +c^2 -2ab*cos(B)) = √(157-132cos(42°)) ≈ 7.675
6. The ratio of side lengths is the same as the ratio of the sines of the opposite angles.
6/10 = sin(x)/sin(100°)
x = arcsin((6/10)*sin(100°)) ≈ 36.22°
I’m not 100% about this answer but i’m pretty sure it’s going to be 40/120. i hope this helped a little
First, we need to calculate 80% of what they earned before:
50,000 * 0.80 = 40,000 per year
Social Security = 1200 a month x 12 months ( 1 year) = 14,400 per year
Additional income = 40,000 - 14,400 = $25,600 per year
Answer:
5/9
Step-by-step explanation:
Let's begin by determining the factors of the problem. We know that Robert ran a race that is 2/3 of a mile long. Therefore, we know that 2/3 is a factor in the equation. We also know that, of the 2/3 mile, he ran 5/6 of it. Now the tricky part is deciding how the two fractions are related.
To make this easier, let's substitute a different number for 5/6. We'll say 2.
If he has completed TWICE the length of the race, how would you determine how far he ran?
You would multiply 2/3 by 2! This same principle can be applied to the problem.
To determine the total distance run in miles, we can write it as 2/3 * 5/6
(NOTE that * is known as "times" or "multiplied by")
With this, you multiply the numerators (2 * 5 = 10) and the denominators (3 * 6 = 18) and then make your fraction... 10/18!
But you're not done yet. Always remember to simplify when possible. Both terms are divisible by 2. Therefore, it can be written as 5/9.
Hope this helped!