How to decide if a point is on a parabola

Mathematics

1 answer:

SVETLANKA909090 [29]3 years ago

5 0

Answer:

All you need is the coordinates of your point (x,y) as well as the function of your parabola (y=x^2 for example).

Then, replace the x and y from the function by the coordinates of your point.

If you end up with the same number on both sides of the equation, then the point is on your curve. If not, it isn't on your curve.

For example, we want to know if K(3,8) is on the parabola y=x^2–1.

8=3^2–1

8=8

So the point K is on the parabola.

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2. Think of the top and middle shelves as two lines cut by a transversal. What type of angles are

nadya68 [22]

Answer:

Angles 1 and 5 are corresponding angles.

Step-by-step explanation:

These are the different types of angles formed by a transversal:

1. Corresponding angles are angles that lie on the <em>same side</em> of the transversal line. Angles 1, 3, 5, 6, 9, and 11 are corresponding angles because they are all on the left side of the transversal (the line that cuts through the other lines). Angles 2, 4, 6, 8, 10, and 12 are corresponding angles because they are all on the right side of the transversal.

2. Alternate interior angles are angles that are nonadjacent angles that lie on opposite sides of the transversal and in between the horizontal lines. Here the alternate interior angles are 3 and 6, 4 and 5, 7 and 10, and 8 and 9.

3. Alternate exterior angles are those that are nonadjacent and lie on the outside of the horizontal lines. In this diagram, angles 1 and 12 and angles 2 and 11 are alternate exterior.

4. Same-side interior angles are angles that lie on the same side of the transversal and in between the horizontal lines. The same-side interior angles in this diagram are angles 3 and 5, 7 and 9, 4 and 6, and 8 and 10.

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A research report claims that 20% of all individuals use Firefox to browse the web. A software company is trying to determine if

Pani-rosa [81]

Answer:

a) The null and alternative hypothesis are:

$H_0: \pi=0.2\\\\H_a:\pi\neq 0.2$

b) Test statistic z = -1.3258

c) P-value = 0.1849

Step-by-step explanation:

a) As the reseracher want to determine if the proportion of their users who use Firefox is significantly different from 0.2, it is a two-tailed test, as a proportion significantly low or significantly high gives evidence to support the alternative hypothesis.

Then the null and alternative hypothesis are:

$H_0: \pi=0.2\\\\H_a:\pi\neq 0.2$

b) The sample has a size n=200.

The sample proportion is p=0.16.

$p=X/n=32/200=0.16$