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In the word MISSISSIPPI, what is the ratio of the number of S'sto the total number of letters? (Write your answer as a fraction in simplest form.)

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:

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:

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:

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: 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.

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:

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:

45

Step-by-step explanation:

detrain of the value they was given

Answer:

Length = 37 feet

width = 11 feet

Step-by-step explanation:

First, let us find the value of x.

They've already given that the perimeter of this rectangle is 96 feet.

So,

4x - 7 + 4x - 7 + x + x = 96

10x - 14 = 96

10x = 96 + 14

10x = 110

Divide both sides by x.

x = 11 feet

And now we can find the value of the width and length.

Given that,

Length = ( 4x - 7 ) ⇒ ( 4 × 11 - 7 )

                                  44 - 7

                                    37 feet

Width = x ⇒ 11 feet

Let me know if you have any other questions :-)

9514 1404 393

Answer:

  w = 2.3

Step-by-step explanation:

It looks like you have ...

  4.6/6 = w/3

To solve this, you need to clear the 3 from the denominator of the w term. Do that by multiplying both sides of the equation by 3.

  3(4.6/6) = 3(w/3)

  4.6(3/6) = w . . . . simplify (rearrange the product to make mental arithmetic easier: 3/6 = 1/2)

  w = 2.3 . . . . . . . . do the arithmetic

Answer:

2.3

Step-by-step explanation:

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

Answer:

75 dollars

Step-by-step explanation:

Answer:

10x²

Step-by-step explanation:

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

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!!! ^^

Answer:

it's 5000

Step-by-step explanation:

50*100=5000

hope it helps:p

Answer:

Answer: Choice G.

Step-by-step explanation:

Dilations

Suppose a point P(x,y) is dilated across the origin, that is, the origin is the center of dilation, by a scale factor k.

The image of P is P' whose coordinates are P'(kx,ky).

If an image is formed by several points and each one is dilated by the same factor, then:

If |k| > 1, the image maps to a stretched or larger image.

If |k| < 1, the image maps to a shrunk or shorter image.

We have a hexagon graphed on a coordinate grid. The hexagon is dilated to create a larger hexagon. This means k must be greater than 1 and it should multiply each original coordinate (x,y).

Options F and H don't multiply by the coordinates but add to them, thus they are not valid answers.

Option J actually multiplies by the factor 0.2 but since it's less than 1, it does not correspond to an enlargement.

Only option G multiplies by a factor 4/3=1.3 greater than 1.

Answer: Choice G.

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:

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:

B , C, and D

Step-by-step explanation:

x + y and x+ z both make a straight line which is 180 degrees, and Z and Y are congruent angles.

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:

-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:

we need a picture

Step-by-step explanation:

Answer:

9/2

5/3

13/4

3/2

Step-by-step explanation:

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

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

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:

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:

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