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katen-ka-za [31]

2 years ago

13

What number should be added to both sides of the equation to complete the square? x2 + 3x = 6 (StartFraction 3 Over 2 EndFractio

n) squared 3 62

2 answers:

Alex73 [517]2 years ago

3 0

Answer:

$\frac{9}{4}$

Step-by-step explanation:

Given

x² + 3x = 6

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2( $\frac{3}{2}$ )x + ( $\frac{3}{2}$ )² = 6 + ( $\frac{3}{2}$ )²

The number added to both sides is ( $\frac{3}{2}$ )² = $\frac{9}{4}$

Firlakuza [10]2 years ago

3 0

Answer:

b

Step-by-step explanation:

You might be interested in

Find the sum (3.2+4x)+(18.25+6x)=

tatiyna

Answer: -2.145

Step-by-step explanation:

(3.2+4x)+(18.25+6x)=

Simplifying

(3.2 + 4x) + (18.25 + 6x) = 0

Remove parenthesis around (3.2 + 4x)

3.2 + 4x + (18.25 + 6x) = 0

Remove parenthesis around (18.25 + 6x)

3.2 + 4x + 18.25 + 6x = 0

Reorder the terms:

3.2 + 18.25 + 4x + 6x = 0

Combine like terms: 3.2 + 18.25 = 21.45

21.45 + 4x + 6x = 0

Combine like terms: 4x + 6x = 10x

21.45 + 10x = 0

Solving

21.45 + 10x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-21.45' to each side of the equation.

21.45 + -21.45 + 10x = 0 + -21.45

Combine like terms: 21.45 + -21.45 = 0

0 + 10x = 0 + -21.45

10x = 0 + -21.45

Combine like terms: 0 + -21.45 = -21.45

10x = -21.45

Divide each side by '10'.

x = -2.145

Simplifying

x = -2.145

8 0

2 years ago

Read 2 more answers

Nevin made tables of values to approximate the solution to a system of equations. First he found that the x-value of the solutio

prisoha [69]

Answer:

The correct option is B.

Step-by-step explanation:

The given equation are

$y=4x-3$

$y=-5x+9$

On solving both the equation, we get

$4x-3=-5x+9$

$4x+5x=9+3$

$9x=12$

$9x=\frac{12}{9}=\frac{4}{3}$

Put this value in the given equation.

$y=4(\frac{4}{3})-3$

$y=\frac{16}{3}-3$

$y=\frac{16-9}{3}$

$y=\frac{7}{3}$

The solution of the given system of equation is

$(\frac{4}{3},\frac{7}{3})=(1.333,2.333)\approx (1.3,2.3)$

The best approximation of the exact solution is (1.3,2.3). Therefore the correct option is B.

7 0

2 years ago

Read 2 more answers

Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area

Rina8888 [55]

Answer:

11 inches by 11 inches

Step-by-step explanation:

The dimensions of the original photo were 11 inches by 11 inches.

We are informed that the area of the reduced photo is 64 square inches and that In the equation (x – 3)^2 = 64, x represents the side measure of the original photo.

In order to solve for x, we shall first take square roots on both sides of the equation;

The square root of (x – 3)^2 is simply (x - 3).

The square root of 64 is ±8 but we ignore -8 since the dimensions of any figure must be positive.

Therefore, we have the following equation;

x - 3 = 8

x = 8 + 3

x = 11

3 0

2 years ago

Read 2 more answers

The perimeter of the base of a regular quadrilateral prism is 60 cm, the area of one of the lateral faces is 105 cm2.

yawa3891 [41]

For a better understanding of the solution, please follow the diagram in the attached file.

A regular quadrilateral is basically a square.

So, if the base of the prism has a perimeter of 60 cm, then the length of the side of the square will be $\frac{60}{4}=15 cm$ . It is shown of the diagram.

Now, from the diagram, it is clear that the lateral face area, which is given as 105 cm^2, is the product of the side of the square, which is known, and the unknown height, let us call it h. Thus, we will get the following equation:

$15\times h=105$

$\therefore h=\frac{105}{15}=7 cm$

This is depicted on the diagram.

Now, all our required parameters are in place. Thus, let us find what has been asked.

<u>SURFACE AREA</u>

Surface Area (SA) will be the sum of the areas of the two bases (squares) and the areas of the four lateral faces.

Since the side of one square base is 15 cm, therefore, the area of one square base will be $15^2$ .

Likewise, the area of one lateral surface is actually the area of a rectangle with length 15 cm and height 7 cm. Thus, it's area will be given as: $15\times 7$ .

Thus, our equation will be:

$SA=2\times 15^2+4\times 15\times 7=870 cm^2$

Therefore, Surface Area=870 cm^2

<u>VOLUME OF THE PRISM</u>

The volume of the prism will simply be the area of the base times the height of the prism.

Thus, the volume is:

$Volume=15^2\times 7=1575 cm^3$

5 0

2 years ago

A price was increasing at a rate of 15% per month what is the annual growth rate enter your answer rounded to the nearest tenth

Leokris [45]

Hello there! I can help you! The formula for finding the annual growth rate is (1 + r)^t. In other words, you add the rate in decimal form from 1 and raise it to the t power, depending on how many times it is compounded. 15% is 0.15 in decimal form. 1 + 0.15 is 1.15. We have that number. Now, we are looking for the annual growth rate. It increases monthly, annual has to do with 1 year, and there are 12 months in 1 year. Now, let's raise 1.15 to the 12th power. 1.15^12 is 5.350250105. Don't delete it. We can subtract 1 from that number to get 4.350250105. Now, let's multiply it by 100 to get the answer in percent form. When you do, you get 435.0250105 or 435 when rounded to the nearest tenth, because there is a 0 in the tenths place. We can subtract There. The annual growth rate is about 435%.

7 0

2 years ago

Read 2 more answers