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adoni [48]
3 years ago
9

What is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –(x – 6) and passes through

the point (−2, −2)? y = –x – y = –x + y = x – 1 y = x + 1
Mathematics
1 answer:
Mkey [24]3 years ago
4 0
Let's convert the equation in point-slope form to slope-intercept form.

y - 4 = -(x - 6)
Multiply everything out.
y - 4 = -x + 6
Add 4 to both sides.
y = -x + 10

To be perpendicular, the slope of the new has to be the reciprocal of the other line. To slope in this equation is -1/1. To get the reciprocal, flip the numerator and denominator and change the sign too.

-1/1 becomes 1/-1, and changes to 1/+1, or 1.

y = x + b

Input the coordinate point and solve for b.

-2 = -2 + b
Add 2 to both sides.
0 = b

y = x
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Read 2 more answers
5x^2-2x=2<br>help plsmmm​
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Answer:

Presumably you're solving for x here?  Without further information we'll assume that.

With that in mind, x is approximately equal to 0.86 and -0.46

Step-by-step explanation:

Let's start by putting it in the usual ax² + bx + c format.

5x^2- 2x = 2\\5x^2 - 2x - 2 = 0\\

let's solve it.  First we'll multiply both sides by five, making the first term a perfect square:

25x^2 - 10x - 10 = 0\\

Now we'll add 11 to both sides:

25x^2 - 10x + 1 = 11\\

Which makes the left side a perfect square:

(5x - 1)^2 = 11

And now we can solve for x:

(5x - 1)^2 = 11\\\\5x - 1 =  \sqrt{11} \\\\5x = 1 + \sqrt{11}\\\\x = \frac{1 + \sqrt{11}}{5}

Note that there's no apparent way of drawing the ± symbol when editing equations, so take that + sign as actually being ±.

That gives us two answers:

x = \frac{1 + \sqrt{11}}{5}\\\\x \approx \frac{1 + 3.32}5\\\\x \approx \frac{4.32}5\\\\x \approx 0.86             x = \frac{1 - \sqrt{11}}{5}\\\\x \approx \frac{1 - 3.32}5\\\\x \approx \frac{-2.32}5\\\\x \approx -0.46

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