All categories

3 years ago

Find the equation of a line that is parallel to the line -3x+2y=10 and goes through the point (0,7).

Mathematics

1 answer:

Delvig [45]3 years ago

6 0

Answer:

3x -2y = -14

Step-by-step explanation:

The parallel line will have a new constant that can be found by substituting the given point for x and y.

-3x +2y = -3(0) +2(7) = 14

An equation for the parallel line is ...

-3x +2y = 14

In standard form, the leading coefficient is positive, so the standard form equation is ...

3x -2y = -14

You might be interested in

Nine more than the quotient of 2 and a number of x

Naddika [18.5K]

Answer: 9 + 2/x - x = -19

4 0

3 years ago

Don't understand this at all

Sergeu [11.5K]

3 quarts, because 12 is how many cups you have, and there are 4 cups in a quart. 12/4 is 3, so 3 quarts.

7 0

3 years ago

5y + (86 - y) = 86 + 4y

Viefleur [7K]

Answer:

All real values, (-∞, ∞)

Step-by-step explanation:

Step 1: Distribute

5y + (86 - y) = 86 + 4y

5y + 86 - y = 86 + 4y

Step 2: Combine like terms

5y + 86 - y = 86 + 4y

4y + 86 = 86 + 4y

Step 3: Subtract 4y from both sides

4y + 86 - 4y = 86 + 4y - 4y

86 = 86

Step 4: Subtract 86 from both sides

0 = 0

Answer: All real values, (-∞, ∞)

8 0

3 years ago

Read 2 more answers

What is the GFC of 40 and 60

Svetradugi [14.3K]

Answer:

GCF: 20

Step-by-step explanation:

The thing you want to do is factor both numbers down to their lowest primes.

40:2 * 2 * 2 * 5

60:2 * 2 * 5 * 3

Now underline what is in both sets of primes. I'll bold them. The number that is bolded comes from 2 * 2 * 5 which is 20

The highest common factor is 20

3 0

3 years ago

A sample of eight workers in a clothing manufacturing company gave the following figures for the amount of time(in minutes) need

lilavasa [31]

Answer:

$10.108 < \mu < 13.892$

Step-by-step explanation:

1) 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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

We have the following distribution for the random variable:

$X \sim N(\mu , \sigma=0.45)$

And by the central theorem we know that the distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

2) Confidence interval

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12$

The sample deviation calculated $s=2.268$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=8-1=7$

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 tabel to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.36$

Now we have everything in order to replace into formula (1):

$12-2.36\frac{2.268}{\sqrt{8}}=10.108$

$12+2.36\frac{2.268}{\sqrt{8}}=13.892$

So on this case the 95% confidence interval would be given by (10.108;13.892)

$10.108 < \mu < 13.892$

7 0

3 years ago