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d1i1m1o1n [39]
3 years ago
13

Alejandra correctly wrote the equation y – 3 = (x – 10) to represent a line that her teacher sketched. The teacher then changed

the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?
Mathematics
1 answer:
Lady bird [3.3K]3 years ago
5 0

Answer:

y-3 = 2(x-10)

Step-by-step explanation:

Given that Alejandra correctly wrote the equation

y - 3 = (x - 10)

to represent a line that her teacher sketched.

This is in point slope form.

Hence the line passes through (3,10) and slope = 1

Now it is given that the teacher then changed the line so it had a slope of 2, but still went through the same point

Using point slope formula we get

y-3 = 2(x-10)

is the equation for the same point with slope =2

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Answer:

The equation of parabola is given by : (x-4) = \frac{-1}{3}(y+3)^{2}

Step-by-step explanation:

Given that vertex and focus of parabola are

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The general equation of parabola is given by.

(x-h)^{2} = 4p(y-k), When x-componet of focus and Vertex is same  

(x-h) = 4p(y-k)^{2}, When y-componet of focus and Vertex is same

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The distance between two points is given by :

L=\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}

For value of p:

p=\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}

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p=\sqrt{(\frac{1}{12})^{2}}

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Since, Focus is left side of the vertex,

p=\frac{-1}{12} is required value

Replacing value in general equation of parabola,

Vertex: (h,k)=(4,-3)

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8 0
3 years ago
Write a solution in Interval Notation - (you don't have to help me on all, 1 or 2 is fine c: )
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QUESTION 1

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(-\infty,-2)\cup (2,+\infty).


QUESTION 2

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We group like terms to get,


|x-4|\:>\:5+3.


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We split the absolute value sign to get,

-(x-4)\:>\:8 or x-4\:>\:8


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x\: or x\:>\:8+4


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We write this in interval notation to get,

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