Let A and B be the two complementary angles.
A = smaller angle = 2x
B = larger angle = 13x
x = some unknown number
Note how the ratio A:B turns into 2x:13x which simplifies to 2:13
A+B = 90 ... because the angles are complementary
2x+13x = 90 ... substitution
15x = 90
x = 90/15
x = 6
A = 2*x = 2*6 = 12 degrees
B = 13*x = 13*6 = 78 degrees
The two angles are 12 degrees and 78 degrees.
Check:
A/B = 12/78 = (2*6)/(13*6) = 2/13, so A:B = 2:13
A+B = 12+78 = 90
Answer:
−
10
x
^3
−
4
x
^2
+
4
x
+
3
Step-by-step explanation:
Answer:
34.78 feet
Step-by-step explanation:
1) using the cosine function, I did cos(43)=x/51
This is because cosine is equal to adjacent over hypotnuse
Once I found x, I used the pythagorean theorem to get 34.78 feet
Answer:
x = 1 or x = -3/2
Step-by-step explanation:
Solve for x over the real numbers:
2 x^2 + x - 3 = 0
The left hand side factors into a product with two terms:
(x - 1) (2 x + 3) = 0
Split into two equations:
x - 1 = 0 or 2 x + 3 = 0
Add 1 to both sides:
x = 1 or 2 x + 3 = 0
Subtract 3 from both sides:
x = 1 or 2 x = -3
Divide both sides by 2:
Answer: x = 1 or x = -3/2
Total distance 5 km; at 5km / 0.65 h =
Second part distance: x; at 6 km/h, during t2
First part distance: 5 - x; at 8.75 km/h, during t1
V = d/t ⇒ t = d/V
t2 = x/6
t1=[5-x]/8.75
t2 + t1 = 0.65
x/6 + [5-x]/8.75 = 0.65
x/6 + 5/8.75 - x/8.75 = 13/20
x/6 - x/8.75 = 13/20 - 5/8.75
x/6 - 4x/35 =13/20 - 20/35
35x - 24x = (35*6)(35*13 - 20*20)/(20*35)
11 x = 16.5
x = 16.5/11 = 1.5 km
