Which sum or difference is modeled by the algebra tiles?

The focal points of an ellipse are (12, 0) and (−12, 0), and the point (12, 7) is on the ellipse. Find the points where this cur

natulia [17]

Answer:

x - ( 16 , 0 ) , ( -16 , 0 )

y - ( 0 , 4√7 ) , ( 0 , -4√7)

Step-by-step explanation:

Solution:

- The sum of the distances from a point on the ellipse to its foci is constant. You have both foci and a point, so you can find the sum of the distances.

-Then you can find the vertices since they are points on the ellipse on the x-axis whose sum of distances to the foci are that value.

- The 7 in y coordinate of (12,7) is the length of semi-latus rectum. Also c is 12:

c^2 = a^2 + b^2

Where, a: x-intercept

b: y-intercept

- The length of semi-latus rectum is given by:

b^2 = 7*a

- Substitute latus rectum expression in the first one we get:

c^2 = a^2 + 7a

a^2 + 7a - 144 = 0

( a - 16 ) * ( a - 9 ) = 0

a = +/- ( 16 )

- The y-intercept we will use latus rectum expression again:

b = +/- √(7*16)

b = +/- 4√7

- The intercepts are:

x - ( 16 , 0 ) , ( -16 , 0 )

y - ( 0 , 4√7 ) , ( 0 , -4√7)

6 0

3 years ago

The vertices of ΔABC are A(−3,4), B(−2,4), and C(−5,2). If ΔABC is reflected across the line y=−2 to produce the image ΔA'B'C

Mumz [18]

The coordinates of vertex B' is $P'(x,y) = (-2, -8)$ .

<h3>How to calculate the coordinate of point by reflection</h3>

A point if reflected across the line $y = -2$ by means of the following formula:

$P'(x,y) = P(x,y)+2\cdot [(x_{P}, -2)-P(x,y)]$ (1)

Where:

$P(x,y)$ - Original point
$x_{P}$ - x-Coordinate of point P
$P'(x,y)$ - Resulting point

If we know that $P(x,y) = (-2,4)$ and $x_{P} = -2$ , then the coordinates of the vertex is:

$P'(x,y) = (-2, 4) + 2\cdot [(-2,-2)-(-2,4)]$

$P'(x,y) = (-2, 4) +2\cdot (0, -6)$

$P'(x,y) = (-2, 4) + (0,-12)$

$P'(x,y) = (-2, -8)$

The coordinates of vertex B' is $P'(x,y) = (-2, -8)$ . $\blacksquare$

To learn more on reflections, we kindly invite to check this verified question: brainly.com/question/1878272

3 0

3 years ago

On a map, Maya uses a ruler to find the approximate distance between her town and Los Angeles. The distance on the map is 25 cm.

zlopas [31]

Answer:

Scale of the Map = 1 cm to 82 Km

Step-by-step explanation:

25cm is equivalent to 2050Km

Hence 1cm will be equivalent to 2050/25 = 82Km

7 0

3 years ago

Read 2 more answers

What is the measure of Zc<br>

maks197457 [2]

Answer: 56 degrees

Step-by-step explanation:

We know that angle between b and c is 90 degrees. Because there is a line dividing angles a and b from 124 and c, we also know that each side is 180 degrees (a and b add to 180, and 124 and c add to 180).

124 and c are supplementary angles. We can represent this in an equation to solve for c:

$124 + c = 180\\\\c = 56$

3 0

3 years ago

A group of friends has gotten very competitive with their board game nights. They have found that overall, they each have won an

Sati [7]

The standard deviation is 4 games

A standard deviation (or σ) is a measure of how dispersed the facts are in relation to the mean. Low general deviation method statistics are clustered around the imply, and excessive trendy deviation indicates facts are more unfold.

Don't forget the statistics set: 2, 1, 3, 2, four. The mean and the sum of squares of deviations of the observations from the mean will be 2. 4 and 5.2, respectively. as a consequence, the same standard deviation could be √(5.2/5) = 1.01.

In data, the same old deviation is a degree of the quantity of variant or dispersion of a set of values. A low preferred deviation indicates that the values tend to be close to the mean of the set, while a high general deviation shows that the values unfold out over a much broader variety.

Given that,

mean = μ = 18

standard deviation = Σ = 6

n = 2

μ x = μ = 18 games

√ x = Σ / √ = 6

√2 = 4 games

Learn more about standard deviation here brainly.com/question/12402189

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6 0

2 years ago