Is line 1 (1,5) (3,-2) and like 2 (-3,2) (4,0) perpendicular of parallel?

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

7 0

Slope Formula: $\frac{y_2-y_1}{x_2-x_1}$

So remember that perpendicular lines have slopes that are negative reciprocals to each other and parallel lines have the same slope. To find out if they are either parallel or perpendicular, plug the pair of points into the slope formula to find their slopes:

$\textsf{Line 1}\\\\\frac{5-(-2)}{1-3}=-\frac{7}{2}\\\\\textsf{Line 2}\\\\\frac{0-2}{4-(-3)}=-\frac{2}{7}$

Since these slopes aren't the same nor are they negative reciprocals to each other, the lines are neither parallel nor perpendicular.

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3 years ago

PLZ SHOW ALL WORK

lara31 [8.8K]

Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width: w = 12 - 2x
length: l = 18 - 2x
height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x

Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6

Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160

Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224

And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.

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3 years ago

The standard form of the equation of a circle is (x−5)2+(y−6)2=1.

Crank

Answer:

(A) $x^2+y^2-10x-12y+60=0$