Answer:
![\frac{x^2}{16}-\frac{b^2}{4}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B16%7D-%5Cfrac%7Bb%5E2%7D%7B4%7D%3D1)
Step-by-step explanation:
A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.
The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:
![\frac{x^2}{a^2}-\frac{y^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Ba%5E2%7D-%5Cfrac%7By%5E2%7D%7Bb%5E2%7D%3D1)
The coordinates of the foci is at (±c, 0), where c² = a² + b²
Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:
![\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Ba%5E2%7D-%5Cfrac%7By%5E2%7D%7Bb%5E2%7D%3D1%5C%5C%5Cfrac%7B4%5E2%7D%7Ba%5E2%7D-%5Cfrac%7B0%7D%7Bb%5E2%7D%20%3D1%5C%5C%5Cfrac%7B4%5E2%7D%7Ba%5E2%7D%3D1%5C%5C%20a%5E2%3D16%5C%5Ca%3D%5Csqrt%7B16%7D%3D4%5C%5C%20a%3D4)
The foci c is at +/-2√5, using c² = a² + b²:
![c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2%5C%5C%282%5Csqrt%7B5%7D%20%29%5E2%3D4%5E2%2Bb%5E2%5C%5C20%20%3D%2016%20%2B%20b%5E2%5C%5Cb%5E2%3D20-16%5C%5Cb%5E2%3D4%5C%5Cb%3D%5Csqrt%7B4%7D%3D2%5C%5C%20b%3D2)
Substituting the value of a and b to get the equation of the hyperbola:
![\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7Ba%5E2%7D-%5Cfrac%7By%5E2%7D%7Bb%5E2%7D%3D1%5C%5C%5C%5C%5Cfrac%7Bx%5E2%7D%7B16%7D-%5Cfrac%7Bb%5E2%7D%7B4%7D%3D1)
I think that the first part is true but the second is wrong because a number and its opposite will have the same absolute value. For example, the 5 is the absolute value of 5 and -5. This works with all numbers and their opposites. Since the number 0 doesn't have an opposite value, I think that 0, as an absolute value, only represents 0.
Hope this helps :P
Answer:
x = -20
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
2x - 12 = -52
<u>Step 2: Solve for </u><em><u>x</u></em>
- Add 12 on both sides: 2x = -40
- Divide 2 on both sides: x = -20
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 2(-20) - 12 = -52
- Multiply: -40 - 12 = -52
- Subtract: -52 = -52
Here we see that -52 does indeed equal -52.
∴ x = -20 is the solution to the equation.
I really don’t know but ima just be putting this
Answer:
C
Step-by-step explanation:
The x's can not completely cancel each other out so they are still included but you have to divide the numbers, exponents and whole numbers.