Which expression is equivalent to C^2-4/c+3 divided by c+2/3(c^2-9)

What must be added to both sides in 4x² + 24x + 8 = 32 in order to complete the square?

Sergeu [11.5K]

Answer:

16

Step-by-step explanation:

To solve a quadratic equation by using the completing the square method, the coefficient of the square term i.e x² must be one (1).

Therefore, we would have to first make the coefficient of x² to be equal to 1.

4x² + 24x + 8 = 32

We would simplify the equation;

4x² + 24x = 32 - 8

4x² + 24x = 24

Divide all through by 4;

x² + 8x = 24

The value to be added = (8/2)² = 4² = 16

x² + 8x + 16 = 8 + 16

x² + 4x + 4x + 16 = 24

x(x + 4) + 4(x + 4) = 24

(x + 4)² = 24

Taking the square root of both sides;

x + 4 = ± 4.9

x = -4 ± 4.9

x = -4 + 4.9 = 0.9

or

x = -4 - 4.9 = - 8.9

Therefore, 16 must be added to solve the quadratic equation by completing the square method.

6 0

3 years ago

A, b, c, and d please

DIA [1.3K]

<h2>Answers / Step-by-step explanation:</h2><h3>a. What is the length of one side of the square.</h3>

Looking at the image, the radius (r) of the circle appears to cover half of the length of a side of the square. Hence, the side of the square has a length of 2r.

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<h3>b. The formula A= πr² is used to find the area of a circle. The formula A=4r² can be used to find the area of the square. Write the ratio of the area of the circle to the area of the square in the simplest form.</h3>

$Ratio=\frac{\pi r^{2} }{4r^2} =\frac{\pi}{4}$ .

Notice that the value "r²" disappears from the expression because is being multiplied and divided by it at the same time.

$Ratio=\frac{4\pi }{16} =0.7854.$

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c. Complete the table.

To complete each cell of the table, simply take the equation of the asked parameter and substitute the value of r by the number indicated in the title of the column. For example, column 3 should be filled out like this:

Area of Circle (units²): π(3)²or 9π.

Length of 1 Side of the Square: 2r= 2(3)= 6.

Area of Square (units²)= 4r²= 4(3)²= 36.

Ratio: $\frac{\pi}{4}$ .

Do the same for all the other columns.

The answers to the table are presented on the attached image.

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d. What can you conclude about the relationship between the area of the circle and the square?

They will always have the same value, π/4, regardless of the size of the square and circle. As long as the circle borders meet the square's at the middle of each side of the square, the relationship will be the same.

4 0

2 years ago

John and Jennifer are both basketball players. John made 5 out of 8 shots and Jennifer made 8 out of 12 shots. Who made the high

Natasha2012 [34]

Answer:

Jennifer made the higher percentage of shots

4 0

3 years ago

If 2x - 3y = 24 and 3x + 4y = 2, what is the value of x - y?

ruslelena [56]

Answer:

10

Step-by-step explanation:

y = -4

x = 6

x-y = 6-(-4) = 6+4 = 10

8 0

3 years ago

42x^2 + 32 - 18 =6062

Elenna [48]

Okay, we start with 42x^2 + 32 - 18 = 6062. To solve single-variable equations like this one, we want to isolate the x by moving all of the other numbers to the other side of the equation. We need to first subtract 32 and 18, and that equals 14. Now our problem looks like this, 42x^2 + 14 = 6062. Since 14 is the only other number on the left side, we subtract four from both sides! This gives us 42x^2 + 14 - 14 = 6062 - 14, so 42x^2 = 6062. Now to find x, we want to just have one x on the left side instead of 42, so we divide the equation by 42 to find that 42x^2/42 = 6048/42, so x = 12

4 0

3 years ago