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2 years ago

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Mathematics

1 answer:

ioda2 years ago

7 0

Answer:

1. 4(x - 3) = 32

4x - 12 = 32

4x = 44

x = 11

2. 12(2x + 4) = 24

24x + 48 = 24

24x = -24

x = -1

3. 3(3s + 4) = 21

9s + 12 = 21

9s = 9

s = 1

4. 3(c - 2) = 2(c + 3)

3c - 6 = 2c + 6

c - 6 = 6

c = 12

5. 12(r - 3) = 6(r + 3)

12r - 36 = 6r + 18

6r - 36 = 18

6r = 54

r = 9

6. 2(x+5) = 30

2x + 10 = 30

2x = 20

x = 10

7. 3(b+2) = 6(b-2)

3b + 6 = 6b - 12

6 = 3b - 12

18 = 3b

6 = b

8. 4(c-2) = 16

4c - 8 = 16

4c = 24

c = 6

9. 7(y+2) = 28

7y + 14 = 28

7y = 14

y = 2

10. 4(d-2) = 2(d+3)

4d - 8 = 2d + 6

2d - 8 = 6

2d = 14

d = 7

11. 5(L+5) = 35

5L + 25 = 35

5L = 10

L = 2

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An equation of a hyperbola is given.

siniylev [52]

Answer:

The vertices are $\left(3,\:0\right),\:\left(-3,\:0\right)$ .

The foci are $\left(3\sqrt{5},\:0\right),\:\left(-3\sqrt{5},\:0\right)$ .

The asymptotes are $y=2x,\:y=-2x$ .

b) The length of the transverse axis is 6.

c) See below.

Step-by-step explanation:

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$ is the standard equation for a right-left facing hyperbola with center $\left(h,\:k\right)$ .

The vertices $\:\left(h+a,\:k\right),\:\left(h-a,\:k\right)$ are the two bending points of the hyperbola with center $\:\left(h,\:k\right)$ and semi-axis a, b.

Therefore,

$\frac{x^2}{9}-\frac{y^2}{36}=1$ , is a right-left Hyperbola with $\:\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6$ and vertices $\left(3,\:0\right),\:\left(-3,\:0\right)$ .

For a right-left facing hyperbola, the Foci (focus points) are defined as $\left(h+c,\:k\right),\:\left(h-c,\:k\right)$ where $c=\sqrt{a^2+b^2}$ is the distance from the center $\left(h,\:k\right)$ to a focus.

Therefore,

$\frac{x^2}{9}-\frac{y^2}{36}=1$ , is a right-left Hyperbola with $\:\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6$ $c=\sqrt{3^2+6^2}= 3\sqrt{5}$ and foci $\left(3\sqrt{5},\:0\right),\:\left(-3\sqrt{5},\:0\right)$

The asymptotes are the lines the hyperbola tends to at $\pm \infty$ . For right-left hyperbola the asymptotes are: $y=\pm \frac{b}{a}\left(x-h\right)+k$