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:
which is the first option in the list of possible answers.
Step-by-step explanation:
Recall that the minimum of a parabola generated by a quadratic expression is at the vertex of the parabola, and the formula for the vertex of a quadratic of the general form:
is at 
For our case, where 
we have:
And when x = 1, the value of "y" is:
Recall now that we can write the quadratic in what is called: "vertex form" using the coordinates 
of the vertex as follows:
Then, for our case:
Then, for the quadratic equal to zero as requested in the problem, we have:
Let the number of tie-dyed T-shirts = x
The man sold 4 times as many tie-dyed T-shirts as silk-screened shirts.
So, the number of silk-screened shirts = 4x
He sold 180 shirts altogether
So,
So, the number of tie-dyed shirts = 36
Answer:
the answer is 72 square feet
Step-by-step explanation:
(5×4)+(5×5)+(5×3)+(12)=72
