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: See explanation
Step-by-step explanation:
a. how old is Cheryl?
Cheryl's age = d + 5
b. how old is Brandon?
d + 5 + 2
= d + 7
c. what was the difference in their ages 5 years ago?
Cheryl age five years ago = d
Brandon's age five years ago = d + 2
Difference = d + 2 - d = 2 years
d. what is the sum of their ages now?
Cheryl's age = d + 5
Brandon age = d + 7
Sum = d + 5 + d + 7
= 2d + 12
e. what will the sum of their ages be two years from now?
Two years from now,
Cheryl's age = d + 5 + 2 = d + 7
Brandon age = d + 7 + 2 = d + 9
Sum = d + 7 + d + 9
= 2d + 16
f. what will the difference of their ages be two years from now
Two years from now,
Cheryl's age = d + 5 + 2 = d + 7
Brandon age = d + 7 + 2 = d + 9
Difference = Brandon age - Cheryl age
= (d + 9) - (d + 7)
= 2 years.
Answer:
1) y = 0.3x + 1000
2) slope = 0.3
The slope is the fraction of the monthly sales that is added to your salary.
3) y-intercept = 1000
The y-intercept is the fixed part of the salary, $1000.
4) The salary is $2500
Step-by-step explanation:
1)
monthly salary = fixed part + variable part
The fixed part is $1000. Every month you receive $1000 no matter the amount of sales.
The variable part varies according to the amount of sales. You get 30% of the of the monthly sales. Let the monthly sales be x. The variable part is 0.3x
Let the monthly salary = y.
y = 1000 + 0.3x
y = 0.3x + 1000
2)
slope = 0.3
The slope is the fraction of the monthly sales that is added to your salary.
3)
y-intercept = 1000
The y-intercept is the fixed part of the salary, $1000.
4)
In this case, x = 5000
y = 0.3x + 1000
y = 0.3(5000) + 1000
y = 1500 + 1000
y = 2500
The salary is $2500.
Answer:
5
Step-by-step explanation:
She received $75
1 CD cost $14.95
Therefore the number of CDs that can be bought are $75/$14.95 is
5.016
Answer:
$120
Step-by-step explanation:
$1,440/12= $120
Hope this helps :)
