Completing the square is done as follows:
1. Write the equation in a way that the constants are in the right side while the terms with x are on the left.
<span>9x2 +54x = 7
</span>
2. Make sure that the coefficient of the x^2 term is 1.
<span>9(x2 + 6x) = 7
</span>
3. Adding a term to both sides that will complete the square in the left side. This is done by dividing the coefficient of the x term by 2 and squaring it. Note: The same amount should be added to the right side to balance the equation.
<span>9(x2 + 6x + 9) = 7 + 81
9(x+3)^2 = 88
</span>
The value of x is 3, while the length of the rectangle is 30 units and the width is 24 units.
<h3>How to determine the dimensions?</h3>
The given parameters are:
Base = 5(x+3)
Height = 2(x+9)
Perimeter = 108
The perimeter of a rectangle is
P = 2 *(Base + Height)
So, we have:
2 *(5(x + 3) + 2(x + 9)) = 108
Divide both sides by 2
5(x + 3) + 2(x + 9) = 54
Open the brackets
5x + 15 + 2x + 18 = 54
Evaluate the like terms
7x = 21
Divide by 7
x = 3
Substitute x = 3 in Base = 5(x+3) and Height = 2(x+9)
Base = 5(3+3) = 30
Height = 2(3+9) = 24
Hence, the value of x is 3, while the length of the rectangle is 30 units and the width is 24 units.
Read more about perimeter at:
brainly.com/question/24571594
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Rents his place for $125 per day and his goal has to be in 5 days. Lets use 125 times 5 days then each chime sold is $12 and we need the number of chimes sold so we use "x" as our variable. Equation 125(5) + 12x = 3500. Hope this helps.
Answer: 25.2361459992ft
This question can be solved by a trigonometric equation. Shadow formed when something with height like a tree, so it can be pictured as a vertical line. Shadow is a length of and can be pictured as a horizontal line.
In trigonometric, to find the vertical line length with horizontal line you need tan function. The sun angle will be used in the function, so the calculation would be: tan(31) x 42ft = 25.2361459992ft
