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2 years ago

2x2 + 2x-4?

Mathematics

1 answer:

nexus9112 [7]2 years ago

6 0

Answer:

2x^2 +2x-4
——————
2x^2-4x+2

Factor out 2 from the expression

2(x^2+x-2)
—————-
2(x^2-2x+1)

Write x as a difference

2(x^2x-x-2)
—————-
2(x^2-2x+1)

Use a^2-2ab+b^2=(ab)^2

2(x^2x-x-2)
—————-
2(x-1)^2

Reduce the fraction with 2

x^2x-x-2
—————-
(x-1)^2

Factor out x from the expression

X*(x^2)-x-2
—————-
(x-1)^2

Factor out negative sign from the expression

X*(x+2)-(x-2)
—————-
(x-1)^2

Factor out x+2 from the expression

(x+2)(x-1)
—————-
(x-1)^2

Simplify the expression

x+2
——
x-1

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A given line has the equation 10x + 2y = −2.

worty [1.4K]

The equation is $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

<h3>Further explanation </h3>

This case asking the end result in the form of a slope-intercept.

<u>Step-1: find out the gradient. </u>

10x + 2y = -2

We isolate the y variable on the left side. Subtract both sides by 10x, we get:

2y = - 10x - 2

Divide both sides by two

y = -5x -1

The slope-intercept form is $\boxed{ \ y = mx + c \ }$ , with the coefficient m as a gradient. Therefore, the gradient is m = -5.

If you want a shortcut to find a gradient from the standard form, implement this:

$\boxed{ \ ax + by = k \rightarrow m = - \frac{a}{b} \ }$

10x + 2y = −2 ⇒ a = 10, b = 2

$\boxed{m = - \frac{10}{2} \rightarrow m = -5}$

<u>Step-2:</u> the conditions of the two parallel lines

The gradient of parallel lines is the same $\boxed{ \ m_1 = m_2 \ }$ . So $\boxed{m_1 = m_2 = -5}.$

<u>Final step:</u> figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)

We use the point-slope form.

$\boxed{ \ \boxed{ \ y - y_1 = m(x - x_1)} \ }$

Given that

m = -5
(x₁, y₁) = (0, 12)

y - 12 = - 5(x - 0)

y - 12 = - 5x

After adding both sides by 12, the results is $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

<u>Alternative steps </u>

Substitutes m = -5 and (0, 12) to slope-intercept form $\boxed{ \ y = mx + c \ }$

12 = -5(0) + c

Constant c is 12 then arrange the slope-intercept form.

Similar results as above, i.e. $\boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }$

$\boxed{Standard \ form: ax + by = c, with \ a > 0}$

$\boxed{Point-slope \ form: y - y_1 = m(x - x_1)}$

$\boxed{Slope-intercept \ form: y = mx + k}$

<h3>Learn more </h3>

A similar problem brainly.com/question/10704388
Investigate the relationship between two lines brainly.com/question/3238013
Write the line equation from the graph brainly.com/question/2564656

Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant

7 0

3 years ago

Read 2 more answers

The length of a rectangle is 2 ft longer than its width.

notsponge [240]

If the length is 2ft longer than it’s width
Let’s assume width as X and so the length will be X+2
Perimeter=40ft
Putting the values into a equation, we get,
X+2+X=40
=2X+2=40
=2X=38
=X=19
Therefore
Length =X+2=19+2
=21ft
Width=X=19ft
Area of rectangle =lxb
= 21x19
3992ft
HOPE IT WAS HELPFUL :)

6 0

3 years ago

Please help! 8 and 9/20, will give brainliest. I do not tolerate spam answers! Offering triple points if you answered both!

horsena [70]

Answer:

hi, quick tip

go to cymath or just screenshot the equations or put it in, and it will automatically solve it for you instead of having to wait for someone to answer.

hope this works :}

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Which of the following is NOT a variation of a Pythagorean identity?

Ipatiy [6.2K]

The expression that is not a variation of the Pythagorean identity is the third option.

<h3>What is the Pythagorean identity?</h3>

The Pythagorean identity can be written as:

$sin^2(x) + cos^2(x) = 1$

For example, if we subtract cos^2(x) on both sides we get the second option:

$sin^2(x) = 1 - cos^2(x)$

Which is a variation.

Now, let's divide both sides by cos^2(x).

$sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x) = 1/cos^2(x)\\\\tan^2(x) + 1 = sec^2(x)\\\\tan^2(x) - sec^2(x) = -1$

Notice that the third expression in the options looks like this one, but the one on the right side is positive. The above expression is in did a variation of the Pythagorean identity, then the one written in the options (with the 1 instead of the -1) is incorrect, meaning that it is not a variation of the Pythagorean identity.

Concluding, the correct option is the third one.

If you want to learn more about the Pythagorean identity, you can read:

brainly.com/question/24287773

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2 years ago

Twice the difference of a number c and forty.

dybincka [34]

Answer:

Equation ----> 2(c - 40)

c = -40

Step-by-step explanation:

2(c - 40)