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3 years ago

Points Pand Q lie in plane A. How many lines contain P

Mathematics

1 answer:

jeka943 years ago

8 0

Answer:

The correct answer is :

1. Line PQ (One line PQ).

Step-by-step explanation:

The first step to solve this question is to draw the plane A with the points P and Q lying on it.

We know that given two different points there is only one line that contains this two different points.

Let's analyze each option.

''2. Lines PQ and QP''

This option is wrong because there aren't two different lines. In fact it is only one line that can be named line PQ or line QP.

''3. The 2 lines PQ and QP plus another line that does not lie in plane A.''

This option is assuming that exist three lines that contain P and Q. This option is also wrong.

''1. Line PQ''

This option is correct. It will be clarify with the drawing I will attach.

''We can't name them all!''

This option is assuming that exist infinite lines that contain P and Q. This option is wrong.

In the drawing I call the line that contains P and Q as line L.

Given that P and Q lie in plane A necessarily the line L must lie on the plane A.

You might be interested in

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

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

$df=n-1=25-1=24$

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: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$

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

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

7 0

3 years ago

Miss Jones attended a a southern living home party she purchased a vase which cost $34.99The shipping charge was three dollars a

jenyasd209 [6]

The answer is $41.12
(Work is below)

First add the total of the vase and shipping-
Vase: $34.99
Shipping: $ 3.00
+__________
$37.99

Then calculate sales tax by multiplying $37.99 x 0.0825 -
Above Total: $37.99
Sales Tax Rate: $ 0.0825
x__________
$ 3.1341
You round down because ^ less than five (five or above you would round up)

Sales Tax: $3.13

Then you add the sales tax to the above total

Vase: $37.99
Shipping: $ 3.13
+__________
$41.12

8 0

2 years ago

3.27x+1.28y+1.83x−2.77y

Firdavs [7]

Answer:

5.1x - 1.49y

Step-by-step explanation:

We need to add or substract like terms.

like terms are the terms that have the same variable, in this case:

3.27x and 1.83x are like terms, and adding them we get:

3.27x + 1.83x = 5.1x (you add only the coefficients and the x stays the same)

we do the same for the terms with 'y':

1.28y and −2.77y are like terms, but in this case we must substract because of the − sign:

1.28y −2.77y = -1.49y

the final answer is the conjunction of the two results that we obtained:

5.1x - 1.49y

8 0

2 years ago

Help me for 8 and 9?????

Digiron [165]

8. In A, because those trees are in the deciduous.
9. All of these forests contains life and lot and lots of trees.

Hope this helps!

3 0

3 years ago

PLEASE PLEASE PLEASE HELP!!

Marta_Voda [28]

Okay I'll try to show it step by step

Step 1. So first you need to recognise that the diagram is a right angled triangle, with the right angle being at the bottom. This means we can do Pythagoras' Theorem.

Step 2. Now that you know you can use Pythagoras' Theorem, you can apply it. If you don't know, the theorem is a² + b² = c², with, in this case, a being 5 and b being 8. This means we can do 5² + 8² = 25 + 64 = 89.

Step 3. From the previous step, we now know that the length of the side including x is √89, and because we know that part of this side is 3, if we subtract 3 from √89 we get the value of x, so: √89 - 3 = 9.434 - 3 = 6.434, which is your answer.

I hope this helps!

5 0

3 years ago