ANSWER

EXPLANATION
The general term for the sequence is

To find the 55th term, we have to substitute

in to the general term and simplify.
This implies that,




Therefore the 55th term is 161.
Answer:
(-12,11)
Step-by-step explanation:
x + 2y = 10
3x + 4y = 8
(-2)x + (-2)2y = (-2)10
3x + 4y = 8
-2x - 4y = -20
3x + 4y = 8
Add to eliminate:
x = -12
Substitute x to solve y:
x + 2y = 10
(-12) + 2y = 10
-12 + 2y = 10
2y = 10 + 12
2y = 22
y = 22 ÷ 2
y = 11
Check:
x + 2y = 10
(-12) + 2(11) = 10
-12 + 22 = 10
10 = 10
Set up the following equations:


x represents car A's speed, and y represents car B's speed.
We'll use elimination to solve this system of equations. Multiply the first equation by 7:


Combine both equations:

Divide both sides by 28 to get x by itself:

The speed of car A is
80 mph.Since we now know the value of one of the variables, we can plug it into the first equation:


Subtract 160 from both sides.

Divide both sides by 2 to get y by itself:

The speed of car B is
60 mph.
Answer:
197,8879 N.
Step-by-step explanation:
The magnitude of the horizontal force exerted on the statue can be calculated using trigonometric functions.
The question given says that <em><u>Nancy</u></em> is <em><u>pushing</u></em> the statue with a force of<em><u> 120 N at a 60° angle to the horizontal</u></em> and <em><u>Harry</u></em> is <em><u>pulling</u></em> the statue with a force of <u><em>180 N at a 40° angle with the horizontal</em></u>.
With that information can be calculated the horizontal force exerted on the statue by Nancy, the horizontal force exerted on the statue by Harry and, adding that results, the total horizontal magnitude can be calculated.
The cosine function can be used to calculate the horizontal component of the forces exerted by Nancy and Harry, to determine the horizontal component of the force exerted on the statue.
F= (120 N cos 60°) + (180 N x cos 40°)
F= 197,8879 N