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3 years ago

Given the lines AB and CD, what conclusion can be made about the relationship of the lines? Be sure to include, in

Mathematics

1 answer:

Ahat [919]3 years ago

7 0

Answer: They are perpendicular lines, because their slopes are negative reciprocals ( $AB\perp CD$ )

Step-by-step explanation:

The missing graph is attached.

You need to remember that the slope of a line can be found with the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

First, find the slope of the line AB. The steps are:

- Choose two points on the line. These can be:

$(0,-1)\\(5,3)$

You can say that:

$y_2=-1\\y_1=3\\\\x_2=0\\x_1=5$

Substituting values into the formula and evaluating, you get that the slope of this line is:

$m_{AB}=\frac{-1-3}{0-5}=\frac{4}{5}$

Now you must find the slope of the line CD. The steps are shown below:

- Choose two points on the line. These can be:

$(2,3)\\(6,-2)$

- You can say that:

$y_2=-2\\y_1=3\\\\x_2=6\\x_1=2$

- Now you must substitute values into the formula and evaluate, in order to find the slope. This is:

$m_{CD}=\frac{-2-3}{6-2}=-\frac{5}{4}$

By definition, the slopes of perpendicular lines are negative reciprocals.

Therefore, since the slopes of the lines AB and CD are negative reciprocals, you can conclude that they are perpendicular.

You might be interested in

On a trip, you had to change your money from dollars to euros. You got 450 euros for 600 dollars. Which is a unit rate that desc

chubhunter [2.5K]

The number of Euros received against 600 dollars = 450
Then
For 1 dollar, the number of euros = (450/600) euros
   = (45/60) euros
   = ( 3/4) euros
   = 0.75 euros
So the unit rate that describes the exchange rate is 0.75 euros per dollar. So the correct option among all the options given in the question is option "A". I hope the procedure for getting to the correct result is clear enough for you to understand. In future you can use this procedure for solving similar problems.

7 0

3 years ago

Question 1: The Millers have hired an interior designer to decorate their family room. they want to have a 22" by 30" oil painti

____ [38]

Answer: Total molding cost is $197.20.

Step-by-step explanation:

Since we have given that

Length of oil painting frame = 22 inch

Width of oil painting frame = 30 inch

Width for molding = 4 inches

So, Length after molding would be

4+22+4 = 30 inches

Width after molding would be

4+30+4 = 38 inches

So, Perimeter of molding would be

$2(L+B)\\\\=2(30+38)\\\\=2\times 68\\\\=136\ inches$

Cost per inch = $1.45

So, Total molding cost would be

$1.45\times 136\\\\=\$197.20$

Hence, Total molding cost is $197.20.

6 0

3 years ago

Write the equation of the line that passes through the points (4,-3) and (3,2). Put your answer in fully reduced point-slope for

shtirl [24]

Answer:

y=−5x+17

Step-by-step explanation:

use the formula given in reference chart.

6 0

3 years ago

Find the solution of this system of equations.

Brrunno [24]

Answer:

x=-11, y=0. (-11, 0).

Step-by-step explanation:

x-12y=-11

x-y=-11

-------------

x=y+(-11)

x=y-11

y-11-12y=-11

-11y=-11+11

-11y=0

y=0/-11=0

x-0=-11

x=-11+0=-11

8 0

3 years ago

The General Social Survey asked the question: "For how many days during the past30 days was your mental health, which includes s

serg [7]

Answer:

a) For this case we can conclude that we are 95% confident that the true mean for the variable of interest is between 3.4 and 4.24 days in the US population.

b) The 95% confident means that if we select 100 different samples and calculate the 95% confidence interval for each sample selected, then we will have approximately 95 out of 100 confidence intervals will contain the true mean for the parameter of interest.

c) If we have the same info but we want more confidence that implies that the confidence interval would be wider, since the margin of error increase with more confidence.

d) Assuming that we have the same confidence level and the value for the deviation not changes. If we see if we decrease the sample size, then the margin of error would be lower since the original sample size was 1151. So then if we use 500 Americans we would have a lower value for the margin of error for this new interval. And then our confidence interval would smaller than the original.

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".

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

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The confidence interval after apply the formulas was (3.40 ,4.24)

Part a

For this case we can conclude that we are 95% confident that the true mean for the variable of interest is between 3.4 and 4.24 days in the US population.

Part b

The 95% confident means that if we select 100 different samples and calculate the 95% confidence interval for each sample selected, then we will have approximately 95 out of 100 confidence intervals will contain the true mean for the parameter of interest.

Part c

If we have the same info but we want more confidence that implies that the confidence interval would be wider, since the margin of erroe increase with more confidence, because the critical value increase.

Part d

We need to take in count that the margin of error is given by:

$ME=t_{\alpha/2}\frac{s}{\sqrt{n}}$

Assuming that we have the same confidence level and the value for the deviation s not changes. If we see if we decrease the sample size, then the margin of error would be lower since the original sample size was 1151. So then if we use 500 Americans we would have a lower value for the margin of error for this new interval. And then our confidence interval would smaller than the original.

4 0

3 years ago