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avanturin [10]
4 years ago
11

Which equations represent the asymptotes of the hyperbola?

Mathematics
1 answer:
makvit [3.9K]4 years ago
4 0

Answer:

  see below

Step-by-step explanation:

The equation of the hyperbola can be written as ...

  ((x -h)/a)² -((y -k)/b)² = 1

This has asymptotes ...

  (x -h)/a ± (y -k)/b = 0

Solving for y, we have ...

  y = ±(b/a)(x -h) +k

Filling in the given values a=6, b=8, h=1, k=2, we have ...

  y = ±8/6(x -1) +2

  y=\dfrac{\pm4x\mp4+6}{3}\\\\\boxed{y=\dfrac{4x+2}{3}\ \text{and }y=\dfrac{10-4x}{3}}

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Each Saturday the gym holds 45 minute yoga classes. The weekday yoga classes last 30 minutes. The number of weekday classes vari
yanalaym [24]

For this case we have that the total minutes spent in yoga classes last week was 165.

Subtracting the 45 minutes of the Saturday day we have:

165-45 = 120

Those 120 minutes were distributed in the weekly yoga classes

where each lasted 30 minutes.

\frac {120} {30} = 4

So, 4 week yoga classes were held

ANswer:

4 week yoga classes were held

6 0
3 years ago
Is a rational number divided by a rational number always rational?
miss Akunina [59]

Answer:

Yes

Step-by-step explanation:

When two rational numbers are divided, the outcome will always come out rational.

3 0
4 years ago
Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A drug is used to help prevent blood c
Alla [95]

Answer:

a) \hat p=\frac{148}{4167}=0.036

b) 0.0355 - 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.030

0.0355 + 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.041

Step-by-step explanation:

The sample proportion have the following distribution

\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Part a

The estimated proportion for this case can be calculated like this:

\hat p=\frac{148}{4167}=0.036

Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Replacing we got:

0.0355 - 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.030

0.0355 + 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.041

8 0
4 years ago
How many meters are in 9.3 centimeters ​
Schach [20]

Answer:

0.093 meter?

Step-by-step explanation:

hope this helps

3 0
3 years ago
Which equation shows 4n = 2(+ - 3) solved for T?
Ghella [55]

Answer:

C. T = 4n+6/2

Step-by-step explanation:

4n = 2(T-3)

or, 4n = 2T-6

or, 4n + 6 = 2T

or, 4n + 6 / 2 = T

or, T = 4n + 6 / 2

5 0
2 years ago
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