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Delvig [45]
3 years ago
5

Determine if the following equations form a perpendicular line or not

Mathematics
1 answer:
GREYUIT [131]3 years ago
5 0
  • Slope-Intercept Form: y = mx + b, with m = slope and b = y-intercept.

If two lines are perpendicular, then they will have slopes that are <u>negative reciprocals</u> to each other. An example of negative reciprocals are 2 and -1/2

<h2>6.</h2>

Now with line 2, I have to convert it to slope intercept form. Firstly, subtract 2x on both sides of the equation: -5y=-2x+8

Next, divide both sides by -5 and your slope-intercept form is y=\frac{2}{5}x+\frac{8}{5}

Now since 2/5 is <em>not</em> the negative reciprocal of -2/5, <u>these lines are not perpendicular.</u>

<h2>7.</h2>

It's pretty much the same process; convert to slope-intercept and determine if negative reciprocal. This time I'll brush through them:

6x-3y=15 \\-3y=-6x+15\\y=2x-5\\\\2x+4y=-12\\4y=-2x-12\\y=-\frac{1}{2}x-3

Now since 2 <em>is</em> the negative reciprocal of -1/2, <u>these lines are perpendicular.</u>

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Hopefully this helps

is it ten or tenth?

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7x+5+ 54 how you do this
KonstantinChe [14]

Answer:

7x+59

Step-by-step explanation:

Add 5 and 54

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How to solve this system of equal: x+y+z=1;x^2+y^2+z^2=1
swat32

There are infinitely many solutions.

Algebraically, we can eliminate z and try to solve for x,y:

x+y+z=1\implies z=1-x-y

Then

x^2+y^2+(1-x-y)^2=1

\implies x^2+y^2+1-2x+x^2-2y+y^2+2xy=1

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which is the equation of an ellipse.

5 0
3 years ago
Triangles abc, dbe, and fbg are all symmetric about the y-axis. what are the coordinates of the centroid?
Drupady [299]

Answer:

The coordinates of the centroid are (0, 5)

Step-by-step explanation:

The coordinates of the centroid of a triangle whose vertices (x1, y1), (x2, y2), and (x3, y3) are (\frac{x1+x2+x3}{3} , \frac{y1+y2+y3}{3})

In Δ ABC

∵ A = (-20, 0), B = (0, 15), C = (20, 0)

∴ x1 = -20, x2 = 0, x3 = 20

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-20+0+20}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ ABC are (0, 5)

In Δ DBE

∵ D = (-15, 0), B = (0, 15), E = (15, 0)

∴ x1 = -15, x2 = 0, x3 = 15

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-15+0+15}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ DBE are (0, 5)

In Δ FBG

∵ F = (-5, 0), B = (0, 15), G = (5, 0)

∴ x1 = -5, x2 = 0, x3 = 5

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-5+0+5}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ FBG are (0, 5)

∵ The three triangles are symmetric about the y-axis

→ That means they have the same centroid and it lies on the y-axis

∴ The coordinates of the centroid are (0, 5)

8 0
2 years ago
What is point A on the coordinate plane
Zinaida [17]

Answer:

4,1

Step-by-step explanation:

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