The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is 
<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:
So, we have:
Evaluate
Hence, the equation of the hyperbola is
Read more about hyperbola at:
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Answer: 27.4 hours
Step-by-step explanation:
According to the given statement "A survey of 45 teens found that they spent an average of 25.6 hours per week in front of a screen (television, computer, tablet, phone, etc.)."
Since the word average is synonym of word mean.
Therefore, the sample mean must have the nearest value to the given average.
From the given options 27.4 is the nearest value to the average of 258.6.
Hence, the population mean = 27.4 hours.
Answer:
The answer is about 32,000.
Step-by-step explanation:
If you multiply 3.2 by 10, for 10 years, you get 32 percent. From there, if you multiply 25,000 by 0.32, you get 8000. If you add 25,000 to 8000, you get about 32,000.
Your slope is wrong! Your slope is going to be 3/2, or C for the first problem. Your y intercept is wrong! Your Y- intercept is actually (0, -1.3) or B for the second problem.
Your equation is going to be
y= 3/2x-1.3
