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By Vieta.....in the last quadratic.....call the roots  m ,n

Sum of the  roots  =  m + n =  5/3  

Product  of the  roots  = mn = -7/3   

And in the first quadratic, 

Product of  the roots  = c

(m+ 2) ( n + 2)   =  c

mn + 2m + 2n+ 4    =  c

-7/3 + 2 ( m + n)  + 4  = c

-7/3 + 2 ( 5/3)  + 4   =c

-7/3  + 10/3 + 4   = c

1 + 4   =  c

5    = c

CORRECTED   !!!

We have  that

x + 6y  =  372    ⇒   x = 372  - 6y    (1)

4x + 12y =  780     (2)

Sub (1)  into (2)

4 ( 372 - 6y) + 12y   =  780

1488  - 24y + 12y   =  780

1488   -12y  =  780

1488 - 780   =  12y

708  = 12y

708 / 12   = y   =  59  students to a bus

And using (1)

372 - 6(59)  =  x  =  18  students to a van

You just have to add 3.1 + 3.1 + 2.2 + 2.2 = 10.6 and then do 4.4 + 4.4 + 4.1 + 4.1 = 17 and then add 10.6 + 17 = 27.6!

27.6 is your answer! 🙂

Hope this Helps! 

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There are: 7 nCr 2 = 21 differences as follows:

(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6)>>Total = 21

Simply count all the numbers from 3 and up and divide the total by 21, and that would be the probability.

Easy.....since  the line we  seek is parallel  to  x  = 0.......this will be a  vertical line through  4

The equation is    x   = 4

x^2  + y^2  = 6(x + y)

x^2 + y^2  = 6x + 6y

x^2   - 6x  + y^2 - 6y   = 0       complete the  square  on x,y

x^2  -6x + 9  + y^2  - 6y + 9   =  9 + (

(x -3)^2  + (y - 3)^2   = 18

This is a circle with a center of  (3,3)   and a  radius of  sqrt (18)

The max value of  y   is     3 + sqrt (18)    =    3 + 3sqrt (2)

Since J is the midpoint.....it must be that   HJ   = JK

So

9x - 2   =  4x  + 13

9x - 4x  = 13  + 2

5x   =  15

x =  3

So   HJ =  9(3) - 2  =  25

And if we did everything right....JK  =4(3) + 13   = 25

And HK   must  = HJ + JK = 25 + 25    = 50

Reflection  of a vector across the xy plane  just reverses the vector components

The reflection matrix, R,  is

[  0    1

   1    0 ]

Proof

⟨a,b⟩   [  0  1      =     ⟨ a* 0  + b * 1,  a*1  + b*0 ⟩  =  ⟨b,a⟩

            1   0 ]

Put these in order from least to greatest

9.9 , 10.8, 11.5, 12.3, 12.8,13.1, 34.5

a) 

Median =  in an odd number of values, the  median is the middle  value =   12.3

Mean    .add the values and  divide  by 7......this gives us  ≈  14.99

b)  The median  is  better because  the  value of  34.5  tends  to raise  the  average score

c)   Outliers  -  34.5  appears to be the outlier......this should be removed from the data set....it  tends to exaggerate the mean

d)  Without  the outlier

Median  =  ( 11.5  + 12.3)/2  = 11.9

Mean  ≈  11.73

Note that the median isn't affected much, but the mean drops by more than 3

The median is 12.3 and the avarage is 12498682.1052 so the answer is 153733789.894

(3 + x) mod 3^3 = 2^2
(5 + x) mod 5^3 = 3^2
(7 + x) mod 7^3 = 5^2, solve for x

Using CRT + MMI, we have:

x = 1157625 n + 506629, where n =0, 1, 2, 3........etc.

The smallest x = 506629

506629 mod 105 == 4

Assuming the number of cookies goes up the same ammount each year:

5600 - 4200 = 1400  increase  in 5 years   

                              1400/5 = 280 increase  per year

y = 4200 + 280 x     where x = number of years after 2010

The answer is 700 N/m².

7560 = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 54, 56, 60, 63, 70, 72, 84, 90, 105, 108, 120, 126, 135, 140, 168, 180, 189, 210, 216, 252, 270, 280, 315, 360, 378, 420, 504, 540, 630, 756, 840, 945, 1080, 1260, 1512, 1890, 2520, 3780, 7560)>>Total = 64

8400 = (1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400)>>Total = 60

Note: Simply count the divisors they have in common.

I suppose you are looking for the angle that has a tan of 1.1

you need   arc tan (1.1)   sometimes written as tan^-1 (1.1)    also written as  atan (1.1)

atan(1.1) = 47.726310993906 ^o

Each garden has 4 sides    the first one has two sides that are 3.1 and two sides that are 2.2 m

  the amount of fence she needs for this garden is    3.1 + 3.1 + 2.2 + 2.2 = 10.6 m

now do the same for the second garden....then add the two fences together for the total fencing needed.....

There are only 4! = 24 permutations, which are listed here. Simply count the ones that meet your conditions and divide that number by the total of 24:

12,34,56,78
12,34,78,56
12,56,34,78
12,56,78,34
12,78,34,56
12,78,56,34
34,12,56,78
34,12,78,56
34,56,12,78
34,56,78,12
34,78,12,56
34,78,56,12
56,12,34,78
56,12,78,34
56,34,12,78
56,34,78,12
56,78,12,34
56,78,34,12
78,12,34,56
78,12,56,34
78,34,12,56
78,34,56,12
78,56,12,34
78,56,34,12
#N : 24

Sure! Give me a second to draw up an image.

Ok, it's a bd image.

Basically, your image (D) is basically rotated 180 degrees- it's a reflection, so as you can see it's now symmetrical

Then, we reflect again(now as you can see it's still symmetrical but this time across line m)

...sorry   -3x+6    should equal  -3 (x-2)

Something else is amiss

1^2 = 1   right

soooo

1 - (3x-5) = 1 -3x +5  =   -3x + 6  =  -3(x+2)   

-209 ft / -19 ft/sec = 11 seconds

= 2 + 6   - 442/7   x 5   =   -275.71

-12.8571429