The length of a side of a pentagon is 69 units.
Since the hexagon on the left has 6 sides, and all of the sides have an equal length, if you multiply the number of sides(6) by the length of one side (3x+5) you will get the perimeter of the hexagon, 6(3x+5)
This is the same for the pentagon as well, since the pentagon on the right has 5 sides, and all of the sides have an equal length, if you multiply the number of sides(5) by the length of one side (4x-1) you will get the perimeter of the pentagon, 5(4x-1)
Now we have the equation for the perimeter of the hexagon, 6(3x+5), and the pentagon 5(4x-1). Since we know that the perimeters are the same length for each shape, we can set these two formulas equal to each other
Here is how I set up my equation
6(3x+5)=5(4x-1)
Now that you have the equation, you must solve for x, which I will demonstrate the steps down below
6(3x+5)=5(4x-1)
18x+30=20x-5 (subtract 18x on both sides)
30=2x-5 (subtract -5 on both sides)
35=2x (divide 2 on each side)
17.5=x
Now that you have determined that x is 17.5, all that is left to do is plug in 17.5 into the equation that solves for one side of the pentagon(4x-1) to get the length of a side of a pentagon, which is your answer.
Here is the work if needed
4(17.5)-1
70-1
69
The length of a side of a pentagon is 69 units.
I hope this helped!
Leave a comment on my answer if you have any questions on what I said here or need any more help with math.
7/8 of an hour is 52.5 minutes. 3/10 of 52.5 minutes is 15.75 minutes. They spent 15.75 minutes warming up and cooling down.
The approximate value of x will be approximately equal to 3.4
<h3>Area of triangle and circle</h3>
The formula for calculating area of rectangle is expressed as:
A = lw
- l is the length
- w is the width
Ar = (3x-1)(x+2)
Ar = 3x^2+6x-x-2
Ar = 3x^2 + 5x - 2
For the circle
Ac = πr²
Ac = 3.14(x-3)²
Ac = 3.14(x²-6x+9)
Ac = 3.14x² - 18.84x + 28.26
If the area are equal;
3x² + 5x - 2 = 3.14x² - 18.84x + 28.26
3.14x² - 3x² - 5x - 18.84x + 30.26 = 0
0.14x²-23.84x+30.26 = 0
On factorizing the equation, the approximate value of x will be approximately equal to 3.4
Learn more on area of rectangle here; brainly.com/question/25292087
Answer:

Step-by-step explanation:
We are given:

Separation of Variables:

So:

Integrate:

Integrate:

Raise both sides to e:

Simplify:

So:

Simplify:
