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4 years ago

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)
profit as a percent = 2.75 / 2.50
profit as a percent = 1.1
then we will multiply 1.1 by 100 to get a percentage
profit as a percent = 110%

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