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3 years ago

Is y=4x-1 and 12x=3y+7 parallel, perpendicular, or neither

2 answers:

5 0

First, you simplify 12x=3y+7. Subrtact 7 from both side, get 12x-7=3y. Divide 3 from both sides, get y=4x-(7/3). Your 2 equations are y=4x-1 and y=4x-7/3. The 2 lines are parallel, since they have the same slope but different b's.

icang [17]3 years ago

3 0

Answer:

Neither is the answer.

Step-by-step explanation:

If a line y = m₁x + c₁ and y = m₂x + c₂ are perpendicular to each other then m₁ × m₂ = -1

If both the lines are parallel to each other then m₁ = m₂

Now two lines have been given as

y = 4x - 1 ----------(1)

12x = 3y + 7

3y = -12x + 7

y = -4x + $\frac{7}{3}$ ------(2)

Now from equation (1) and equation (2),

m₁ = 4 and m₂ = -4

Since m₁ ≠ m₂

Therefore, these lines are not parallel

m₁ × m₂ = 4 × (-4) = -16

Therefore, both the lines are neither parallel nor perpendicular.

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=320128$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=50324$ represent the population standard deviation

n=529 represent the sample size

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$