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OlgaM077 [116]
3 years ago
12

Which figure shows a reflection of pre-image DEFG over the x-axis?

Mathematics
1 answer:
Sergio [31]3 years ago
3 0
The image that shows the reflection of DFEG over the x-axis is the FIRST option. The x-axis is the mirror line. The distance from the mirror line to the reflected shape equals to the distance from the original image to the mirror line.
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Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)? y squared over 40 minus x square
N76 [4]

The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is \frac{x^2}{10} + \frac{y^2}{15} = 1

<h3>How to determine the equation of the hyperbola?</h3>

The given parameters are:

  • Directrices at x = ±2
  • Foci at (5, 0) and (−5, 0)

The foci of a hyperbola are represented as:

Foci = (k ± c, h)

The center is:

Center = (h,k)

And the directrix is:

Directrix, x = h ± a²/c

By comparison, we have:

k ± c = ±5

h = 0

h ± a²/c = ±2

Substitute h = 0 in h ± a²/c = ±2

0 ± a²/c = ±2

This gives

a²/c = 2

Multiply both sides by c

a² = 2c

k ± c = ±5 means that:

k ± c = 0 ± 5

By comparison, we have:

k = 0 and c = 5

Substitute c = 5 in a² = 2c

a² = 2 * 5

a² = 10

Next, we calculate b using:

b² = c² - a²

This gives

b² = 5² - 10

Evaluate

b² = 15

The hyperbola is represented as:

\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1

So, we have:

\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1

Evaluate

\frac{x^2}{10} + \frac{y^2}{15} = 1

Hence, the equation of the hyperbola is \frac{x^2}{10} + \frac{y^2}{15} = 1

Read more about hyperbola at:

brainly.com/question/3405939

#SPJ1

6 0
2 years ago
Help me im tired of posting
yaroslaw [1]

Stop posting this. It's very rude to continue posting this. One post was enough.

8 0
2 years ago
Read 2 more answers
How can you tell that the inequality 3t+1&gt; 3t + 2
lutik1710 [3]

Answer:

see below

Step-by-step explanation:

3t+1> 3t + 2

Subtract 3t from each side

1>2

This is never true so there is no solution

Since the variable terms are the same, we only have to look at the constants

6 0
3 years ago
A pool is being drained at a rate of 120 gallons per minute.What is this rate in quarts per hour?
zysi [14]
There are 4 quarts in 1 gallon, so a rate of 120 gallons per minute converts to 4 x 120 = 480 quarts per minute. To find the per hour rate, we simply multiply our per minute rate by 60, obtaining 480 x 60 = 28800 quarts per hour.
7 0
2 years ago
Mrs. Smith's class is working on a variety of science experiments. Each
SVETLANKA909090 [29]

Answer:

66

Step-by-step explanation:

If there are  <em>n</em>  students, then the number of pairs is \frac{n(n-1)}{2}.

With 12 students, \frac{12(12-1)}{2} = \frac{132}{2}=66 pairs can be formed.

The reason the formula works is this:  Each of the 12 students can be paired with 11 other students (no student is paired with him/her self).  But counting 12 x 11 = 132  counts each pair <u>twice</u>.  Example: student A can be paired with student B,..., student B can be paired with student A.  The pair was counted two times.

See the attached image that shows pairings of 5 students.  There are

5(5 - 1)/2 = 5(4)/2 = 10 pairs.

8 0
3 years ago
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