First we need to define this equation using point slope form.
Point slope form is represented by the following (x₁ and y₁ represent the given points, and m represents slope)
So if we plug in our values, we get
Now, in order to get it into slope-intercept form, we must isolate the Y value
So the equation is
Y = X-7
Given x ^2 −3x+2=0
x ^2 −2x−1x+2=0
(Resolving the expression)
x(x−2)−1(x−2)=0 (Taking common factors)
(x−2)(x−1)=0 (Taking common factors)
∴x−2=0 or x−1=0 (Equating each factor to zero)
∴x=2 or x=1
∴2 and 1 are the roots of x ^2 −3x+2=0
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Answer:
y=1/8(-x^2+4x+44
Step-by-step explanation:
In this question the given focus is (2,4) and a directrix of y = 8 and we have to derive the equation of the parabola.
Let (x,y) is a point on the given parabola.Then the distance between the point (x,y) to (2,4) and the distance from (x,y) to diractrix will be same.
Distance between (x,y) and (2,4)
= √(x-2)²+(y-4)²
And the distance between (x,y) and directrix y=8
= (y-8)
Now √(x-2)²+(y-4)² = (y-8)
(x-2)²+(y-4)² = (y-8)²
x²+4-4x+y²+16-8y = y²+64-16y
x²+20+y²-4x-8y = y²-16y+64
x²+20-4x-8y+16y-64=0
x²+8y-4x-44 = 0
8y = -x²+4x+44
Answer:
1. D
2. B
3. A
4. C
Step-by-step explanation:
1. Vertical angles are a pair of opposite angles formed by the intersection of lines. Choice D has two lines intersecting, and two opposite angles formed by it.
2. Adjacent angles are two angles that have a common vertex and common side but do not overlap. Choice B is two angles with a common vertex and common side, and they don't overlap.
3. Supplementary angles are angles that add up to 180 degrees/make a straight angle. Choice A has two angles that add up to 180 degrees, and the two angles combined make a straight angle/line.
4. Two angles are called complementary angles if they add up to 90 degrees and form a right angle. Choice C has two angles that form a right triangle, meaning it adds up to 90 degrees.
