1.
, then
and triangles ADC and ACB are similar by AAA theorem.
2. The ratio of the corresponding sides of similar triangles is constant, so
.
3. Knowing lengths you could state that
.
4. This ratio is equivalent to
.
5.
, then
and triangles BDC and BCA are similar by AAA theorem.
6. The ratio of the corresponding sides of similar triangles is constant, so
.
7. Knowing lengths you could state that
.
8. This ratio is equivalent to
.
9. Now add results of parts 4 and 8:
.
10. c is common factor, then:
.
11. Since
you have
.
x - 5y = -5, -5x - 25y = 25
First, you'll need to get the x variable by itself.
x - 5y = -5<u>
</u><u> +5 +5</u><u>
</u> x = 0
So x is plotted on the 0.
For the second part of the first equation, you'll be looking for what the y variable represents.
x - 5y = -5
<u>-x -x</u><u>
</u> <u>-5y</u> = <u>-5</u><u>
</u><u> 5 5</u><u>
</u> y = 1
So y is plotted on the 1 on the vertical line above the 0.
For the first part of the second equation, you'll do the same thing as in the first equation.
-5x - 25y = 25
<u> +25 +25</u><u>
</u> <u>-5x</u> = <u>50</u><u>
</u> 5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.
For the second part of the second equation, you will do the same thing as in the first equation.
-5x - 25y = 25
<u>+5 +5</u><u>
</u> <u>-25y</u> = <u>30</u><u>
</u> 25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.
<h2>
Answer: B) Perpendicular</h2>
Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.
Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.
Intersecting means the lines may or may not be of equal length but will touch each other.
Answer:
4,000,000
Step-by-step explanation:
ANSWER

EXPLANATION
Since the directrix is

the axis of symmetry of the parabola is parallel to the y-axis.
Again, the focus being,

also means that the parabola will open upwards.
The equation of parabola with such properties is given by,

where

is the vertex of the parabola.
The directrix and the axis of symmetry of the parabola will intersect at

The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.
This implies that,

and

The equation of the parabola now becomes,


Thus, the distance between the vertex and the directrix.
This means that,

Since the parabola opens up, we choose

Our equation now becomes,

This simplifies to

or

This is the same as,

The correct answer is D .
Answer:
The answer to your question is
Step-by-step explanation:
Data
Foci (-2, 2) (4, 2)
Major axis = 10
Process
1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.
From the graph we conclude that it is a horizontal ellipse.
2.- Determine the foci axis (distance between the foci)
2c = 6
c = 6/2
c = 3
3.- Determine a
2a = 10
a = 10/2
a = 5
4.- Determine b using the Pythagorean theorem
a² = b² + c²
-Solve for b
b² = a² - c²
b² = 5² - 3²
b² = 25 - 9
b² = 16
b = 4
5.- Find the center (1, 2) From the graph, it is in the middle of the foci
6.- Find the equation of the ellipse
