Answer:
$4.29
Step-by-step explanation:
An easy way to do this is to move the decimal point to the left one space.
So 42.87 would become 4.287
But since we are talking about currency, we only want two numbers to the right of the decimal point: 4.28.
And since we are rounding to the nearest cent, the 7 on the end means we round up by 1, making the final answer 4.29!
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](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B10%7D%20%2B%20%5Cfrac%7By%5E2%7D%7B15%7D%20%3D%201)
<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](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%20-%20k%29%5E2%7D%7Ba%5E2%7D%20%2B%20%5Cfrac%7B%28y%20-%20h%29%5E2%7D%7Bb%5E2%7D%20%3D%201)
So, we have:
![\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%20-%200%29%5E2%7D%7B10%7D%20%2B%20%5Cfrac%7B%28y%20-%200%29%5E2%7D%7B15%7D%20%3D%201)
Evaluate
![\frac{x^2}{10} + \frac{y^2}{15} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B10%7D%20%2B%20%5Cfrac%7By%5E2%7D%7B15%7D%20%3D%201)
Hence, the equation of the hyperbola is ![\frac{x^2}{10} + \frac{y^2}{15} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B10%7D%20%2B%20%5Cfrac%7By%5E2%7D%7B15%7D%20%3D%201)
Read more about hyperbola at:
brainly.com/question/3405939
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Answer:
The answer should be -124.
Answer:
Step-by-step explanation:
The parent function for a square root graph is
![y=\sqrt{x}](https://tex.z-dn.net/?f=y%3D%5Csqrt%7Bx%7D)
The standard form for this type of function is
where h is indicative of side to side movement and k is indicative of up and down movement. If we are translating the parent function 6 units right, the sign on the 6 is positive, so the function becomes:
and we can remove the parenthesis and write it simply as