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3 years ago

Write an equation in slop-intercept form for the line that passes through (5, 4) and is parallel to the line y = 2x + 1.

Mathematics

1 answer:

Vladimir79 [104]3 years ago

8 0

Answer:

y = 2x - 6

Step-by-step explanation:

The slopes of parallel lines have the same slope, so the other line must also have a slope of 2.

First, we know that an equation in point-slope form is y-y1 = m(x-x1). We can plug in the values here (5, 4) into the equation:

y - 4 = 2(x-5)

Simplify:

y - 4 = 2x - 10

Therefore, the equation is:

y = 2x - 6

You might be interested in

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of

diamong [38]

Answer:

The point estimate for the true difference between the population means is 0.13.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

Step-by-step explanation:

To solve this question, before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When we subtract two normal variables, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 263 cars owned by students had an average age of 7.25 years. The population standard deviation for cars owned by students is 3.77 years.

This means that:

$\mu_s = 7.25, \sigma_s = 3.77, n = 263, s_s = \frac{3.77}{\sqrt{263}} = 0.2325$

A sample of 291 cars owned by faculty had an average age of 7.12 years. The population standard deviation for cars owned by faculty is 2.99 years.

This means that:

$\mu_f = 7.12, \sigma_f = 2.99, n = 291, s_f = \frac{2.99}{\sqrt{291}} = 0.1753$

Difference between the true mean ages for cars owned by students and faculty.

Distribution s - f. So

$\mu = \mu_s - \mu_f = 7.25 - 7.12 = 0.13$

This is also the point estimate for the true difference between the population means.

$s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2325^2+0.1753^2} = 0.2912$

90% confidence interval for the difference:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = zs = 1.645*0.2912 = 0.48$

The lower end of the interval is the sample mean subtracted by M. So it is 0.13 - 0.48 = -0.35 years

The upper end of the interval is the sample mean added to M. So it is 0.13 + 0.48 = 0.61 years.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

5 0

3 years ago

6.) *

labwork [276]

Answer:

the common difference is 5.4 and yes, this is an arithmetic sequence

Step-by-step explanation:

Each new term is derived by adding 5.4 to the previous term:

2.1 + 5.4 = 7.5,

7.5 + 5.4 = 12.9,

and so on,

so the common difference is 5.4 and yes, this is an arithmetic sequence.

8 0

3 years ago

Add (2+3i) + (4-6i) I need help I have to show all work

prisoha [69]

Explanation: Just add like terms, picture is attactched

4 0

3 years ago

Read 2 more answers

The answers are 2x1/3 , 3x1/3, 5x1/3or 4x1/3

Oxana [17]

Answer:

what is the question? Please ask a question.

6 0

3 years ago

A large rectangle is divided into four smaller rectangles.

melomori [17]

Answer:

a) A = 3x, B = 21, C = x^2, and D = 7x

b) x^2 + 10x + 21

c) See below!

Step-by-step explanation:

What you want to do here is use the formula you know for the area of a rectangle, length * width. Start with rectangle A. The length of this one is x, the width is 3, so the area must be 3x. For B, the area must be 7*3, or 21. For C, the area must be x*x, or x^2. For D, the area is 7*x, or 7x. If it helps, cover everything besides the rectangle you're focusing on so you don't get distracted by the unnecessary numbers.

So, from all that, you have

A = 3x, B = 21, C = x^2, and D = 7x.

Next, you want to use these to write a polynomial for the area of the large rectangle. Well, we just found the area for all the rectangles inside this big rectangle, so all you have to do now is add up those smaller areas to get the overall Area = x^2 + 7x + 3x + 21 = x^2 + 10x + 21. (A "simplified" polynomial just means one that's arranged from highest degree/exponent to lowest degree/exponent. x^2 goes first.)

Now, instead of breaking it into smaller rectangles, you could just cover everything in the middle and look at those 4 values on the outside. How would you use those to find the area? Again, your area formula is length*width. For the top side, part of it is x, and the other part is 7. Therefore, that side has a length of x + 7. For the left side, part of it is 3, and the other part is x, so it has a width of x + 3. Remember length * width. So now all you do is take those two lengths like this:

Area = length*width = (x + 3)(x + 7)

And multiply that out, if you're familiar with the FOIL method, and you should get x^2 + 10x + 21, which is identical to our answer to part b.

4 0

4 years ago