Which number line correctly shows 2 2/5, 2 4/5, and 11/5?

Is it true that the planes x + 2y − 2z = 7 and x + 2y − 2z = −5 are two units away from the plane x + 2y − 2z = 1?

zhuklara [117]

Lets Find It Out..

First we'll find the equation of ALL planes parallel to the original one.

As a model consider this lesson:

Equation of a plane parallel to other

The normal vector is:
→n=<1,2−2>

The equation of the plane parallel to the original one passing through P(x0,y0,z0)is:

→n⋅< x−x0,y−y0,z−z0>=0
<1,2,−2>⋅<x−x0,y−y0,z−z0>=0
x−x0+2y−2y0−2z+2z0=0
x+2y−2z−x0−2y0+2z0=0

Or

x+2y−2z+d=0 [1]
where a=1, b=2, c=−2 and d=−x0−2y0+2z0

Now we'll find planes that obey the previous formula and at a distance of 2 units from a point in the original plane. (We should expect 2 results, one for each half-space delimited by the original plane.)
As a model consider this lesson:

Distance between 2 parallel planes

In the original plane let's choose a point.
For instance, when x=0 and y=0:
x+2y−2z=1 => 0+2⋅0−2z=1 => z=−12
→P1(0,0,−12)

In the formula of the distance between a point and a plane (not any plane but a plane parallel to the original one, equation [1] ), keeping D=2, and d as d itself, we get:

D=|ax1+by1+cz1+d|√a2+b2+c2
2=∣∣1⋅0+2⋅0+(−2)⋅(−12)+d∣∣√1+4+4
|d+1|=2⋅3 => |d+1|=6First solution:
d+1=6 => d=5
→x+2y−2z+5=0Second solution:
d+1=−6 => d=−7
→x+2y−2z−7=0

8 0

2 years ago

When Alice spends the day with the babysitter, there is a 0.6 probability that she turns on the TV and watches a show. Her littl

slava [35]

Answer:

a) There is a 48% probability that both Alice and Betty watch TV tomorrow.

b) There is a 48% probability that Betty watches TV tomorrow.

c) There is a 12% probability that only Alice watches TV tomorrow.

Step-by-step explanation:

We have these following probabilities:

A 60% probability that Alice watches TV.

If Alice watches TV, an 80% probability Betty watches TV.

If Alice does not watch TV, a 0% probability that Betty watches TV, since she cannot turn the TV on by herself.

a) What is the probability that both Alice and Betty watch TV tomorrow?

Alice watches 60% of the time. Betty watches in 80% of the time Alice watches. So:

$P = 0.6*0.8 = 0.48$

There is a 48% probability that both Alice and Betty watch TV tomorrow.

b) What is the probability that Betty watches TV tomorrow?

Since Betty only watches when Alice watches(80% of the time), this probability is the same as the probability of both of them watching. So

$P = 0.6*0.8 = 0.48$

There is a 48% probability that Betty watches TV tomorrow.

c) What is the probability that only Alice watches TV tomorrow?

There is a 60% probability that Alice watches TV tomorrow. If she watches, there is an 80% probability that Betty watches and a 20% probability she does not watch.

So

$P = 0.6*0.2 = 0.12$

There is a 12% probability that only Alice watches TV tomorrow.

7 0

3 years ago

Add and Simplify 9/12+1/2

lesya [120]

1 and 1/4..................................

4 0

3 years ago

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You have 90.43 in your bank account and you make a deposite. Your account will:

quester [9]

Answer:

be adding more money

Step-by-step explanation:

deposit means to add withdraw means to take out

8 0

2 years ago

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Which table of values can be represented by the function y = 3x + 2 ?

mezya [45]

Answer:

Graph A.

Step-by-step explanation:

When x is equal to 0, why has to be equal to 2. The slope also has to be 3. To find this out, we do y2-y1/x2-x1. For A, the slope is -7--4/-3--2. This is equal to -3/-1. This is equal to 3. Because y=2 when x=0. option A is correct. For option D, when x=0, y=32. Therefore, this option is not correct. For option B, when x=0, y=2 so this could be correct. Plug it into y2-y1/x2-x1. This is equal to -1-0/-1-2. This is equal to -1/-3. 1/3 is not equal 3 so this option is not correct either. When x=0, y=32 for option C. Therefore, this option is not correct. Therefore, the answer is option A.

If this helps please mark as brainliest

6 0

2 years ago

Read 2 more answers