Answer for the first one - it's complicated, but that maths is correct
I kind of cheated and did it a different way than they'd expect. By doing 24 squared, that gives you 576.
since both angles are 45 degrees, then the sides are equal lengths. Therefore x squared times 2 = 576.
Because of this, x squared = 576 divided by 2, which equals 288.
Therefore the square root of 288 = 12 square root 2
If 4x = 8x - 1 then 4x must be equivalent to 1. So that means x is .25 or 1/4.
Hope this helps!
(I assumed your trying to solve for x, please word the question better next time)
Answer:
a) x=2
b)x=12
c)x=5/4
Step-by-step explanation:
a)5x-2=8
5x=8+2
5x=10
x=2
b)4x-3=2x+9
4x-2x=9+3
2x=12
x=6
c)6x+3=2x+8
6x-2x=8-3
4x=5
x=5/4
Proof:
a)5x-2=8
5(2)-2=8
10-2=8
8=8
b)4x-3=2x+9
4(12)-3=2(12)+9
48-3=24+9
45=45
c)6x+3=2x+8
6(5/4)+3=2(5/4)+8
30/4+3=10/4+8
15/2+3=5/2+8
10.5=10.5
Hope this helps ;) ❤❤❤
Answer:
The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.
Step-by-step explanation:
Given a function y, the average rate of change S of y=f(x) in an interval
will be given by the following equation:

In this problem, we have that:

Find the average rate of change in the balance over the interval t = 0 to t = 5.


Then

The average rate of change in the balance over the interval t = 0 to t = 5 is of $20.82 a year. This means that the balance increased by $20.82 a year over the interval t = 0 to t = 5.
Question:
Howard is designing a chair swing ride. The swing ropes are 4 meters long, and in full swing they tilt in an angle of 23°. Howard wants the chairs to be 3.5 meters above the ground in full swing. How tall should the pole of the swing ride be? Round your final answer to the nearest hundredth.
Answer:
7.18 meters
Step-by-step explanation:
Given:
Length of rope, L = 4 m
Angle = 23°
Height of chair, H= 3.5 m
In this question, we are to asked to find the height of the pole of the swing ride.
Let X represent the height of the pole of the swing ride.
Let's first find the length of pole from the top of the swing ride. Thus, we have:

Substituting figures, we have:
Let's make h subject of the formula.

The length of pole from the top of the swing ride is 3.68 meters
To find the height of the pole of the swing ride, we have:
X = h + H
X = 3.68 + 3.5
X = 7.18
Height of the pole of the swing ride is 7.18 meters