In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to
tan θ =m, where m is the slope of the equation
In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.
<span>y-2x=7
y = 2x+7
dy/dx = 2 =m
So,
tan </span>θ = 2
θ = tan⁻¹(2)
θ = 63.43°
Answer: k = -1 +/- √769
<u>Step-by-step explanation:</u>
48x - ky = 11
<u>-48x </u> <u> -48x</u>
-ky = -48x + 11
Slope: 
*************************************************************************
(k + 2)x + 16y = -19
<u>- (k + 2)x </u> -<u>(k + 2)x </u>
16y = -(k + 2)x - 19
Slope: 
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and are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.
* 
= -1
= 1
Cross multiply, then solve for the variable.
(k + 2)(k) = 16(48)
k² + 2k - 768 = 0
Use quadratic formula to solve:
k = -1 +/- √769
G(2)= -2-2
g(2)= -4
r(g(2))= r(-4)
r(-4)= 2(-4)^2 -1
r(-4)= 31
ANSWER=31
Angle 3: 24 degrees- the angle across from it is 24 which makes this one 24 so it’s congruent.
Angle 1 and 4: 78 degrees- on one side of these angles (the line the seperates it running parallel) the angles total to 180 degrees, we take angle 3 which was 24 and subtract that from 180. That equals 156 which we then divide into two because we have two angles left to solve for which makes 78 each.
Angle 2: 71 degrees- We know angle 3 is 24 and we have a written angle as 85. Knowing each side of these angles equals 180 degrees, we add 85 and 24 to get 109. We then will subtract 180 from 109 to get our missing angle which is 71 degrees.
I hope I could help :)
