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DedPeter [7]
4 years ago
12

Solve the equation x^2 + 5x = -1 by completing the square.

Mathematics
1 answer:
8090 [49]4 years ago
3 0

Answer:

The answer to your question is: the third option

Step-by-step explanation:

              x² + 5x = - 1

              x² + 5x + (\frac{5}{2}) ^{2} = -1  + (\frac{5}{2} )^{2}

             (x + \frac{5}{2})² =   - 1 + 25/4

            (x + \frac{5}{2})²  =  (-4 + 25) / 4

            (x + \frac{5}{2})² = 21/4

            (x + \frac{5}{2}) = ± \sqrt{\frac{21}{4} }

            x = \frac{5}{2} ±   \frac{\sqrt{21}}{2}

            x = \frac{-5 ± \sqrt{21} }{2}

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10. What is the value of x in the solution to the system of equations?
RUDIKE [14]

Solve for x in first equation:

x-2y=7

Add “2y” to both sides

x=2y+7

Put this in to second equation:

3(2y+7)+2y=21

Solve for y:

Distribute the 3 into the ()

6y+21+2y=21

Combine the like y terms

8y+21=21

Subtract 21 from both sides

8y=0

Divide by 8 on both sides

y=0

Put this into the first solved equation:

x=2(0)+7

Solve for x:

Multiple 2(0)

x=0+7

Add 0 and 7

x=7

So the value of x is positive 7.

3 0
3 years ago
The store paid 2.50 for a book and sold it 5.25%. What is the percent?
Mandarinka [93]
To find the profit as a percentage:

profit as a percent = (price sold - purchase price) / (purchase price)

profit as a percent = (5.25 - 2.50 ) / (2.50)
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3 0
3 years ago
1. Pool Dimensions. The area of a rectangular
Irina18 [472]

Answer: I think the length is 60.25 yd and the width is 19.75 yd

Step-by-step explanation: I formed a equation using the information that has been given.

Width : X

length : 1 + 3x

equation : (1 + 3x) + x = 80

Then, I added the like pairs ( 3x+x ). After, I subtracted 1 from 80 and got 79. Then I divided 79 and 4 (79/4) to get 19.75, which is my x value. later, I substituted the x value to the equation and received my answer.

5 0
3 years ago
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified l
Sloan [31]

Answer:

The integral of the volume is:

V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy

The result is: V = 78.97731

Step-by-step explanation:

Given

Curve: x^2 + 4y^2 = 4

About line x = 2 --- Missing information

Required

Set up an integral for the volume

x^2 + 4y^2 = 4

Make x^2 the subject

x^2 = 4 - 4y^2

Square both sides

x = \sqrt{(4 - 4y^2)

Factor out 4

x = \sqrt{4(1 - y^2)

Split

x = \sqrt{4} * \sqrt{(1 - y^2)

x = \±2 * \sqrt{(1 - y^2)

x = \±2 \sqrt{(1 - y^2)

Split

x_1 = -2 \sqrt{(1 - y^2)}\ and\ x_2 = 2 \sqrt{(1 - y^2)}

Rotate about x = 2 implies that:

r = 2 - x

So:

r_1 = 2 - (-2 \sqrt{(1 - y^2)})

r_1 = 2 +2 \sqrt{(1 - y^2)}

r_2 = 2 - 2 \sqrt{(1 - y^2)}

Using washer method along the y-axis i.e. integral from 0 to 1.

We have:

V = 2\pi\int\limits^1_0 {(r_1^2 - r_2^2)} \, dy

Substitute values for r1 and r2

V = 2\pi\int\limits^1_0 {(( 2 +2 \sqrt{(1 - y^2)})^2 - ( 2 -2 \sqrt{(1 - y^2)})^2)} \, dy

Evaluate the squares

V = 2\pi\int\limits^1_0 {(4 +8 \sqrt{(1 - y^2)} + 4(1 - y^2)) - (4 -8 \sqrt{(1 - y^2)} + 4(1 - y^2))} \, dy

Remove brackets and collect like terms

V = 2\pi\int\limits^1_0 {4 - 4 + 8\sqrt{(1 - y^2)} +8 \sqrt{(1 - y^2)}+ 4(1 - y^2)  - 4(1 - y^2)} \, dy

V = 2\pi\int\limits^1_0 { 16\sqrt{(1 - y^2)} \, dy

Rewrite as:

V = 16* 2\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy

V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy

Using the calculator:

\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy = \frac{\pi}{4}

So:

V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy

V = 32\pi * \frac{\pi}{4}

V =\frac{32\pi^2}{4}

V =8\pi^2

Take:

\pi = 3.142

V = 8* 3.142^2

V = 78.97731 --- approximated

3 0
3 years ago
What is the height of the triangular prism below if the volume equals 1,638 cubic millimeters? 65 mm 63 mm 26 mm 28 mm.
sergejj [24]

Answer:

The height of the triangular prism is 26\ mm

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the triangular prism is equal to

V=Bh

where

B is the area of the triangular base

h is the height of the prism

<em>Find the area of the base B</em>

B=\frac{1}{2}(7)(18)=63\ mm^{2}

we have

V=1,638\ mm^{3}

h=x\ mm

substitute and solve for x

1,638=(63)x

x=1,638/(63)=26\ mm

6 0
4 years ago
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