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3 years ago

What are the solutions to the equation x2 - 8x = 10

Mathematics

1 answer:

mojhsa [17]3 years ago

5 0

Answer:

x = 4 ±√26

Step-by-step explanation:

Please write this as x^2 - 8x = 10, or x^2 - 8x - 10 = 0. " ^ " indicates exponentiation.

Let's complete the square:

x^2 - 8 x can be rewritten as

x^2 - 8x + 16 - 16, and so

x^2 - 8x = 10 becomes x^2 - 8x + 16 - 16 - 10 = 0, or

(x - 4)^2 = 26

Taking the square root of both sides, we get:

x - 4 = ±√26, or

x = 4 ±√26

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Why aren't the numbers 38 and 40 relatively prime

sergey [27]

Answer:

may be this is helpful!

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2 years ago

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Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=

ladessa [460]

Answer:

(-2, 4, -2)

x=-2, y=4, z=-2.

Step-by-step explanation:

So we have the three equations:

$4x-y-2z=-8\\-2x+4z=-4\\x+2y=6$

And we want to find the value of each variable.

To solve this system, first look at it and consider what you should try to do.

So we can see that the second and third equations both have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all xs.

Therefore, let's first isolate the variable in the second and third equation.

Second Equation:

$-2x+4z=-4$

First, divide everything by -2 to simplify things:

$x-2z=2$

Subtract x from both sides. The xs on the left cancel:

$(x-2z)-x=2-x\\-2z=2-x$

Now, divide everything by -2 to isolate the z:

$z=-\frac{2-x}{2}$

So we've isolated the z variable. Now, do the same to the y variable in the third equation:

$x+2y=6$

Subtract x from both sides:

$2y=6-x$

Divide both sides by 2:

$y=\frac{6-x}{2}$

Now that we've isolated the y and z variables, plug them back into the first equation. Therefore:

$4x-y-2z=-8\\4x-(\frac{6-x}{2})-2(-\frac{2-x}{2})=-8$

Distribute the third term. The -2s cancel out:

$4x-(\frac{6-x}{2})+(2-x)=-8$

Since there is still a fraction, multiply everything by 2 to remove it:

$2(4x-(\frac{6-x}{2})+(2-x))=2(-8)$

Distribute:

$8x-(6-x)+2(2-x)=-16\\8x-6+x+4-2x=-16$

Combine like terms:

$8x+x-2x-6+4=-16\\7x-2=-16$

Add 2 to both sides:

$7x=-14$

Divide both sides by 7:

$(7x)/7=(-14)/7\\x=-2$

Therefore, x is -2.

Now, plug this back into the second and third simplified equations to get the other values.

Second equation:

$z=-\frac{2-x}{2}\\ z=-\frac{2-(-2)}{2}\\z=-\frac{4}{2}\\z=-2$

Third equation:

$y=\frac{6-x}{2}\\y=\frac{6-(-2)}{2}\\y=\frac{8}{2}\\y=4$

Therefore, the solution is (-2, 4, -2)

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3 years ago

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Two cities have nearly the same north-south line of 117 degrees Upper W. The latitude of the first city is 29 degrees Upper N c

Mariulka [41]

Answer:

1117 km

Step-by-step explanation:

Because the two cities are approximately on the same North-South line, they are on the same longitude. The difference in their latitudes is 39° - 29° = 10°. We are subtracting because they are both in the northern hemisphere. The distance between them is

$\dfrac{10}{360}\times2\pi\times6400 \text{ km} = 1117 \text{ km}$

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3 years ago

Emily drew a scale drawing of a house and its lot. The back patio is 42 millimeters long in the drawing. The actual patio is 27

kirill [66]

the scale factor used in Emily scale drawing is K = 1.63 mm/m

<h3>What scale did Emily use?</h3>

We know that Emily drew a scale drawing of a house and its lot.

In the scale drawing, the back patio is 42 millimeters long, and we know that the actual patio is 27 meters long.

Then the scale relates the measures 44mm and 27 meters, such that if the scale is K, we can write:

K*27m = 44mm

Solving for K, we can write:

K = (44/27) mm/m = 1.63 mm/m

So the scale factor used in Emily's scale drawing is K = 1.63 mm/m

If you want to learn more about scale factors:

brainly.com/question/25722260

#SPJ1

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1 year ago

Please help with my homework!

Jobisdone [24]

Answer:

180-123= 57

57+42=99

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3 years ago