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Find length of the diameter with distance equation..... then area =  pi r²     whre r= 1/2 d

Distance = sqrt (  (3-7)² + (5-10)²  )

               = sqrt (16 + 25)

             diameter = 7 units          

                            r = 3.5 units           area = pi (3.5)²    units²

thx man

Let  the  x coordinates  of the vertices be    a,  b  and  c

Midpoint  x value  of  a,b coordinates =   (a + b)/2

Midpoint  x  value  of  b,c coordinates  = (b + c)/2

Midpoint x value of a,c coordinates =  (a + c) / 2

The sum of the midpoint x values is

[  2a  + 2b + 2c  ]   / 2   =    a  + b + c   = 10

Look at this answer here  :

https://web2.0calc.com/questions/a-teacher-gave-tom-the-following-problem-license

Factors  of 18 =  1,2,3,6,9,18

Factors of 2   = 1, 2

All possible rational roots  =

 ± [ 1,2,3,4,6,9,18 , 3/2 , 9/2  ]

9852  + 9706  =  19558 mL

Nearest  10mL  rounds to     19560mL

The area of  one of the  right triangular white regions in the smaller square is

(4^2 - 88/15)/2  =  76/15

So......the other leg , L,  of  one of these right triangles can be found as

76/15 =  (1/2) 4 *  L

76/30  = L  =  38/15

So   the top side of the red region  has the length  =   4 - 38/15 =   [60 -38]/15 = 22/15

And using similar triangles  the difference, D, in height between the larger square and the smaller square is

4/(38/15)  =  D/ ( 22/15)

4/38 =  D/22

88 = 38D

88/38 = D

44/19 =   D

a  =  4  + 44/19  =    [76 + 44 ]  /19  =  120/19

Wow..ty! OUr teacher expects us to know this lol ty again! Ur a life saver 

(1/3)^3  =  (1/3)(1/3( (1/3)   =  1/27

One  root is 3greater than the  x coordinate of the  vertex  =8

Because of symmetry...the other root will be  3 less than the  x  coordinate  of the  vertex  =  5 - 3  =  2

a)   Tom chose  any   4 of 6  places for the A's  and  for each of these, he  chose  any of 26 letters for the final two places

b )  Tom's   answer is wrong  because he  forgot to break the  problem down into cases.....the answer should  be smaller  (we will prove this in a sec ).....his answer  = 10140  plates 

c )   At least 4 As  means 4As, 5As or 6As

4As   =   C(6,4) (25)^2        choose any 4 positions for the  As   and choose any of 25 letters for the other two positions

5As =  C(6,5) ( 25)             Choose any 5 of  6 positions for the As and we can use any of twenty five letters in the  remaining position

6As  =   obviously only one way  for this to  occur

C(6,4)(25)^2  + C(6,5)(25)  +   1   =

9526 plates

A region is bounded by semicircular arcs constructed on the side of a square whose sides measure 2 / pi, as shown. What is the perimeter of this region?

Perimeter      P = 2[ pi(2 / pi)] = 4

The conjugates of these are also roots

( x - (1 - sqrt (2)) ( x - (1 + sqrt (2) ) = 

x^2  -x( 1-sqrt (2))  - x ( 1 + sqrt (2)  + ( 1-sqrt (2))(1 +sqrt (2))

x^2  -2 x +  1 -2 =

(x^2 -2x -1)

And

(x - (3 + sqrt (3))  ( x - (3 + sqrt (3))  =

x^2 -x ( 3 + sqrt (3)) - x (3 -sqrt(3))  +  (3 -sqrt (3)) (3 + sqrt (3))

x^2  - 6x  + 9 - 3  =

(x^2 - 6x + 6)

So

(x^2 - 2x  - 1) (x^2  - 6x + 6)  =

x^4 - 6x^3 + 6x^2

      -2x^3  + 12x^2   - 12x

                     -x^2     +6x   - 6

_________________________

x^4  - 8x^3 + 17x^2 -  6x  - 6   

I assume  that the missing vertex  is  (5,-2)

See the gtaph here : 

This is just the area of a quarter circle with a  radius of  3......the area  is

pi (3)^2/4  =  (9/4) pi  units^2

It's  called childish gibberish, Dunce.

2x - y + 5z = 28     (1)

2x - 10y - 5z = 6   (2)

x + 5y - 4z = -23     (3)

Multiply first equation by -10

-20x + 10y - 50z  = -280

Add this to  (2)  and we  get

-18x - 55z  = -274   (4)

Multiply the last equation  by 2

2x  + 10y - 8z  = -46 (5)

Add this to(2)  and we get

4x -13z = -40  (5)

Using (4)  and (5)

-18x - 55z  = -274                 multiply  by 4

4x - 13z  =  -40                     multiply by 18

-72x - 220z = -1096

72x -234 z  = -720         add these

- 454z =  1816    divide both sides  by  -454

z  = 4

And

4x - 13(4)  = -40

4x -52  =  -40

4x = 52-40

4x = 12

x  = 3

And

2(3) - y  + 5(4)  = 28

12-y + 20 =  28

32 - y = 28

y  = 4

{ x, y, z}  = { 3, 4, 4}

Let P  be  the number of people who got coach tickets  and  16 - P  be  the number of people who got  first class tickets

So  we have

Price of  coach * people in coach + Price of  first  class * people in  first  class  =  Total cost

So

250P  +  1030 (16 - P)   =  11020

250 P  + 16480  - 1030P   =  11020

Rearrange

16480 - 11020  = 1030 P  -  250 P

5460 =  780P     divide  both sides by  780

7 =  P   = coach  tickets

3^(x +y)   = 81

81^(x - y)  =  9

Write everything in terms of base 3

3^(x +y)  = 3^(4)

3^[4(x -y)]  = 3^(2)

Equate  the exponents  ......we have  these  equations

x + y  = 4

4 [ x - y] =  2   →   2x - 2y  = 1  →  x - y  =1/2

x + y =  4

x - y  =1/2           add these equations

2x  = 9/2

x = 9/4

And

x + y =  4

9/4 + y  =16/4

y = 7/4

xy  =  (9/4)(7/4)   =   63/16

5/1.75  = x / 1       cross--multiply

5   = 1.75x           divide both sides  by 1.75

x ≈ 2.8 apples for $1

Cost per apple =   1.75 / 5  =    35 cents

Possible rational roots

All  Factors of 15 /  All Factors  of 9

Factors of 15  =   1,3,5,15

Factors of 9 =  1,3, 9

So....

 ±  [ 1, 1/3 , 1/9 , 3 , 5 , 5/3 , 5/9, 15  ]

The  base  10 representation of these  numbers =  a(5)ⁿ  + b(5)^{n -1}  +  c(5)^n-2  +  . .. +  ...2

The units digit of their product   = 4  when expressed in base 5

1x^3  + a2x^2  + a1x   - 11  =   0 

q                                    p

The possible integer roots =     p/q

All factors  of  - 11  /  All factors of  1

So we  have   -11, 11, -1, 1

Hint: the denominator is (k-1)(k)(k+1). Can you solve from here?