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Evgen [1.6K]
3 years ago
14

Untitled Question *

Mathematics
1 answer:
klasskru [66]3 years ago
6 0
Answer:
c
hope it helps
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This hyperbola is centered at theorigin. Find its equation.Foci: (-2,0) and (2,0)Vertices: (-1,0) and (1,0)
beks73 [17]

SOLUTION

From the question, the center of the hyperbola is

\begin{gathered} (h,k),\text{ which is } \\ (0,0) \end{gathered}

a is the distance between the center to vertex, which is -1 or 1, and

c is the distance between the center to foci, which is -2 or 2.

b is given as

\begin{gathered} b^2=c^2-a^2 \\ b^2=2^2-1^2 \\ b=\sqrt[]{3} \end{gathered}

But equation of a hyperbola is given as

\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1

Substituting the values of a, b, h and k, we have

\begin{gathered} \frac{(x-0)^2}{1^2}-\frac{(y-0)^2}{\sqrt[]{3}^2}=1 \\ \frac{x^2}{1}-\frac{y^2}{3}=1 \end{gathered}

Hence the answer is

\frac{x^2}{1}-\frac{y^2}{3}=1

5 0
1 year ago
Solve: -7 < 2x+5 < 7
kondor19780726 [428]

Answer:

- 6 < x < 1

Step-by-step explanation:

first things first:

- 7 < 2x  + 5 \\  - 7 - 5 < 2x  + 5 - 5 \\  - 12 < 2x \\  - 6 < x

now:

2x + 5 < 7 \\ 2x + 5 - 5 < 7 - 5 \\ 2x < 2 \\ x < 1

now the intersection is:

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(a) Without solving the equation we can't determine whether its true or false.

(b) If x = 3

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No, if x = 3, the equation will not be true.

(c) 4x + 1 = 2x + 5

4x - 2x = 5 - 1

2x = 4

x = 4/2

x = 2

This shows that x = 2 makes the equation true.

8 0
3 years ago
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