In a hotel, Elevator 1 stops at the third floor at an elevation of 40ft. Elevator 2 stops at the parking level at an elevation of -25ft.

How far apart, in feet, are the two elevators? Show or explain your work.

PLEASEEE ANSWER!!!

Answer:

Equation of Sphere =  [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

[tex](PA)^{2} = (2PB)^{2}[/tex]

[tex](PA)^{2} = 4 (PB)^{2}[/tex]

[tex](x - (-3))^{2}[/tex] + [tex](y - 6)^{2}[/tex] + [tex](z-3)^{2}[/tex] = 4 x [tex](x-6)^{2}[/tex] + [tex](y-2)^{2}[/tex] + [tex](z-(-3))^{2}[/tex]

Solving the above equation:

[tex](x + 3))^{2}[/tex] + [tex](y - 6)^{2}[/tex] + [tex](z-3)^{2}[/tex] = 4 x {[tex](x-6)^{2}[/tex] + [tex](y-2)^{2}[/tex] + [tex](z + 3))^{2}[/tex]}

[tex]x^{2}[/tex] + 9 + 6x + [tex]y^{2}[/tex] + 36 - 12y + [tex]z^{2}[/tex] + 9 - 6z = 4 { [tex]x^{2}[/tex] + 36 - 12x + [tex]y^{2}[/tex] + 4 - 4y + [tex]z^{2}[/tex] + 9 + 6z}

[tex]x^{2}[/tex] + 9 + 6x + [tex]y^{2}[/tex] + 36 - 12y + [tex]z^{2}[/tex] + 9 - 6z = 4[tex]x^{2}[/tex] + 144 - 48x +4[tex]y^{2}[/tex] + 16 - 16y + 4[tex]z^{2}[/tex] + 36 + 24z

Putting the right hand side = 0 and solving the equation:

[tex]x^{2}[/tex] - 4[tex]x^{2}[/tex] + [tex]y^{2}[/tex] - 4[tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 4[tex]z^{2}[/tex] + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3[tex]x^{2}[/tex] - 3[tex]y^{2}[/tex]  -3[tex]z^{2}[/tex]  + 54x + 4y -30z -142  = 0

Taking (-) common

- ( 3[tex]x^{2}[/tex] + 3[tex]y^{2}[/tex] + 3[tex]z^{2}[/tex]  - 54x - 4y +30z + 142) = 0

3[tex]x^{2}[/tex] + 3[tex]y^{2}[/tex] + 3[tex]z^{2}[/tex]  - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

[tex]x^{2}[/tex] + [tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 54/3x - 4/3y +30/3z + 142/3 = 0

[tex]x^{2}[/tex] + [tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 54/3x - 4/3y +30/3z + 142/3 = 0

[tex]x^{2}[/tex] + [tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 18x - 4/3y +10z + 142/3 = 0

The equation of the sphere for all surface point P such that [tex]AP = 2\cdot BP[/tex] is [tex]x^{2}+y^{2}+z^{2}-18\cdot x -\frac{4}{3}\cdot y + 10\cdot z +\frac{142}{3} = 0[/tex].

Mathematically speaking, we have the following geometric locus:

[tex]AP = 2\cdot BP[/tex] (1)

Then, we expand the expression presented above by Pythagorean theorem, used to determine the length of a line segment in the field of analytical geometry:

[tex]\sqrt{(x +3)^{2} + (y-6)^{2} + (z-3)^{2}} = 2\cdot \sqrt{(x-6)^{2}+(y-2)^{2}+(z+3)^{2}}[/tex]

[tex](x+3)^{2}+(y-6)^{2}+(z-3)^{2} = 4\cdot (x-6)^{2}+4\cdot (y-2)^{2}+4\cdot (z+3)^{2}[/tex]

Now we expand and simplify the resulting expression:

[tex]x^{2}+6\cdot x + 9 + y^{2}-12\cdot y + 36 + z^{2}-6\cdot z + 9 = 4\cdot (x^{2}-12\cdot x +36) + 4\cdot (y^{2}-4\cdot y +4) + 4\cdot (z^{2}+6\cdot z + 9)[/tex]

[tex]x^{2} + y^{2} + z^{2} + 6\cdot x -12\cdot y - 6\cdot z +54 = 4\cdot x^{2} +4\cdot y^{2} + 4\cdot z^{2} -48\cdot x -16\cdot y +24\cdot z +196[/tex]

[tex]3\cdot x^{2} + 3\cdot y^{2} + 3\cdot z^{2} -54\cdot x -4\cdot y + 30\cdot z + 142 = 0[/tex]

[tex]x^{2}+y^{2}+z^{2}-18\cdot x -\frac{4}{3}\cdot y + 10\cdot z +\frac{142}{3} = 0[/tex] (2)

This expression corresponds to the general form of the equation of the sphere for all surface point P such that [tex]AP = 2\cdot BP[/tex]. [tex]\blacksquare[/tex]

To learn more on geometric loci, we kindly invite to check this verified question: https://brainly.com/question/521553

Answer:

3x-5+2y

Step-by-step explanation:

Wasnt much detail to the question so i created a random algebra expression you cannot have an equal sign for an expression because that would change it from an expression to an equation.

Answer:

6^5

Step-by-step explanation:

You too, btw!

Answer:

6 with a small 5 on the side so press the button with the a and the small be then put 6 and 5 as the small number

exponents are just 6 x 6 x 6 x 6 x 6 just count the number of 6's and put it as the little number if that names sense

Step-by-step explanation:

Answer:

-28

Step-by-step explanation:

=5(2)²+16(-3)

=5(4)+(-48)

=20-48

=-28

Answer:

-28

Step-by-step explanation:

Expression: 5x²+16y

x=2 and y=-3

We'll substitute x as 2 and y as -3

5(2)²+16(-3)

Following Order of Operations, do the exponent part first

5(4)+16(-3)

Multiply

20-48

subtract

-28

Hope this helps

Answer:

9/2

5/3

13/4

3/2

Step-by-step explanation:

The required number of students in the class is given as 32, as per the given condition.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Let the number of students in the class be x,
according to the question,
50% of x = 16
x = 16/50%

x = 16/0.5

x = 160/5
x = 32

Thus, the required number of students in the class is given as 32, as per the given condition.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ1

Answer:

75 dollars

Step-by-step explanation:

Answer:

its 0.001

Step-by-step explanation:

Hope this helps :)

Answer:

0.001

Step-by-step explanation:

10^-3 = 0.001

You don't multiply since it's a negative power.

Ace

Answer:

A. 2(5x + 2) = 3x + 32

F. ½(3x + 32) = 5x + 2

Step-by-step explanation:

GH = 5x + 2

KL = 3x + 32

Based on the midsegment theorem,

½(KL) = GH

That is:

½(3x + 32) = 5x + 2

Or

2(GH) = KL

That is:

2(5x + 2) = 3x + 32

Answer:

The rate of the jet in still air is 738 mph and the rate of the wind is 90 mph

Step-by-step explanation:

Check: (738+90)*6 = 648*6 = 3888 mike's against the wind

(738-90)*6 = 828*6 = 4968 miles with the wind

Answer:

The measure of Angle S is 75 (degrees).

Step-by-step explanation:

Key skills needed to solve this are: Sums of a triangle, one variable equation, operations

1) All the angles in a triangle add up to equal 180 degrees.

2) We can use this to say that Angle S + Angle R + Angle T is 180 degrees.

3) Subsitute in the expression for each angle: 7x+40+8x+25+5x+15 = 180

4) Combine like terms

7x + 8x + 5x is 20x & 40 + 25 + 15 is 80

This means that 20x + 80 = 180

5) Move 80 to the right side: 20x = 100

6) Divide by 20 andbget x equal to 5

7) To find Angle S, you need to plug in 5 into the expression.

7x + 40 = 7(5) + 40 = 35 + 40 = 75 degrees

The measure of Angle S is 75

Answer:

it's 5000

Step-by-step explanation:

50*100=5000

hope it helps:p

Answer:

x=-3

Step-by-step explanation:

First you must distribute -5 to 2x and -7

so you get

-10x+35+24=89

then you will subtract 35 from both sides and get

-10x+24=54 then you will subtract 24 from each side and get

-10x=30 then you will divide -10 and get

x=-3

Answer:

$24,166.67

Step-by-step explanation:

Let carry out the breakdown:

So Norman Jean makes a flat rate of $25 per hour, also she works 35 hours per week.

From the above statement Jean will make => 25 × 35 = $875 in a single week without commission.

For Jean to make $4500 in a week, we derive an equation for this:

875 + x = 4500;

x is the amount of commission Jean has to get in a week to make up to $4500 in that week => x = 4500-875; x = $3625.

Let y be the amount of sales Jean has to make to get a commission of x, we derive the following equation: 0.15 × y = x.

y = x ÷ 0.15 => 3625 ÷ 0.15

y = 24166.67.

So for Jean to meet her target of $4500 in a single week, Jean needs to make a sale worth $24,166.67.

Answer:

10x²

Step-by-step explanation:

all have the same exponential value so you can add them directly

Answer:

Expression 1

Step-by-step explanation:

14x + 35 - 21y

[tex]14x + 35 - 21y \\ \frac{14x}{7} + \frac{35}{7} - \frac{21y}{7} \\ 2x + 5 - 3y[/tex]

Answer:

Its Expression 2: 7(2x + 5 - 3y)

Step-by-step explanation:

just got it right

Well we need what reasons they could be similar. Is that all you are given or are there options?

Answer:

The answer is 50

Step-by-step explanation:

Got it right on edge

Answer:

50 the guy under me got it right on edge 2021

Step-by-step explanation:

Hopes this helps!!! ^^

Missing addend: 1/2 + 1/4

Missing Sums: 5/8 and 3/4

Step-by-step explanation:

The pattern of the addend is that the first term increases by 1/8 and the second term is always 1/4. If only the first term increases by 1/8, that means the total sum will increase by 1/8 each time also.

Answer:

A- 4.50

B- unit price is 2 dollar per a hat. Price would be 24 dollars

C- unit price is .40

D- 69

Step-by-step explanation:

Answer:

3 1/4*1 1/3 = 4 1/3

Step-by-step explanation:

I have a confusion is it 3 1/4 *1 1/3 does 3 and 1 have space or 31/4 *11/3 fully joined!?

Answer:

6/7

Step-by-step explanation:

1 x 7/6 x 6/7 = 1

A scale factor of 6/7 would shrink the dilated figure back to its original size.

To return the dilated figure back to its original size, you would need to use a scale factor that is the reciprocal of the original dilation scale factor. The reciprocal of a fraction is obtained by flipping the numerator and denominator.

Given the original dilation scale factor of 7/6, the scale factor that would shrink the dilated figure back to the original size is:

Reciprocal of 7/6 = (6/7)

So, using a scale factor of 6/7 would shrink the dilated figure back to its original size.

To know more about scale factor

https://brainly.com/question/29967135

#SPJ2

Answer:

C. 19,306 and 21,694

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Central Limit Theorem

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

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

In this question, for samples of 30:

Mean: 20,500

Standard deviation: [tex]s = \frac{2180}{\sqrt{30}} = 398[/tex]

99.7% of the sample means fall within 3 standard deviations of the mean, by the Empircal Rule with the Central Limit Theorem:

Lower bound: 20500 - 3*398 = 19,306

Upper bound: 20500 + 3*398 = 21,694

So the correct answer is option C.

Answer: The triangles can be proven congruent using SSS.

HOPE THIS HELPS

CAN YOU PLEASE GIVE ME BRAINLIEST

Answer:

The triangles can be proven congruent using SSS.

Step-by-step explanation:

The four-sided geometric figure pictured is called a parallelogram. One feature of parallelograms is that opposite sides have equal lengths.

A parallelogram is shown. It is folded from one point to another to form 2 triangles.

The dotted line splits the parallelogram into two triangles. What is true about the congruency of the two triangles?  

More information is needed.

The triangles can be proven congruent using SSS.

The triangles can be proven congruent using HL.

The triangles are not congruent.

Answer:

4 math problems per minute

Step-by-step explanation:

68 ÷ 17 = 4

4 math problem per minute

Answer:

9.71428571429 or 9.7

Step-by- step explanation:

ok so for this we need to divide 68 into 17 , we get the large number above.

Answer:

well hunny child whats the equation y'all use?

Step-by-step explanation:

Answer:

i wish i could help but what ik bout this is dat every  triangle is 180* if dat help :(

but hey keep trying u can do dis :) <3