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n = 7

box = 8

(3x+2)(12x-8) =

36x^2 +24x -24x - 16

36x^2 -16     is the binomial

why are you having difficulty with such a simple question. As Melody suggests:

Top row =(n+1) + 1 + (n - 1)=Diagonal from top left-hand corner=(n+1) + (2n-9) + 2

(n+1) + 1 + (n - 1)=(n+1) + (2n-9) + 2

2n + 1 =3n - 6

3n - 2n =6 + 1

n == 7

I got 5n-9n is that correct?

I have given you help and I have asked you to respond. (Which you have not done, complaining does not count)

Add up the middle row, what do you get?

I tried my best and got no luck which is why I asked you guys for help

The top row adds to 2n+1

Find a row or column or diagonal that equals something different from that.

Put them equal to each other and solve.

Show us what you try. and tell us the answer if you get one.

AAA BBBB CC  in a row

9! / (3!*4!*2!)

\(|2n^2+23n+11|=|(n+11)(2n+1)|\)

If this is to be prime then one of the factors must be +/-1 and the other must be  +/- a prime number.

so either

\(n+11=\pm1\qquad and \qquad |2n+1|\;\;is \;\;prime\\ or\\ 2n+1=\pm1 \qquad and \qquad |n+11|\;\;is \;\;prime\\\)

solve and you will have your answer,

\(x=\frac{21}{31} \)

LCM or Least Common Multiplier of 3&7 = 21

\(\frac{x}{7}\cdot \:21+\frac{x}{3}\cdot \:21=1\cdot \:21-x\cdot \:21\)

Simplify:

\(3x+7x=21-21x \)

\(10x=21-21x\)

Add 21x to both sides:

\(10x+21x=21-21x+21x \)

\(31x=21\)

Divide:

\(\frac{31x}{31}=\frac{21}{31}\)

\(x=\frac{21}{31}\)

Hope it helps! :)

3x - ( 1 - x)  = 5

3x  - 1 +  x   = 5

4x  - 1   =  5

4x  = 5 + 1

4x =  6

x  = 6/4  =  3/2

C)   rounded to the nearest hundredth =  65.13

We have  7  ways  to fill  the hundreds place  [  7, 9 and  0 cannot be used ]

Then , we  have 8 ways to fill the  tens  digit  [ 7 and  9 can't be used]

Finally we have  5 ways to fill  the  units digit (0, 2,4,6,8 )

So

7 *  8  *  5    =      280  such numbers

If tan (theta)  =1/2....then    y = 1  and  x  = 2

So  r  = sqrt (1^2 + 2^2 )  = sqrt (5)

So.....sin (theta)  = 1/sqrt (5)

Area of triangle =   (1/2) (40)(60) * sin (theta)   =  (1/2) (2400) / sqrt (5)  =

1200 /sqrt (5)   =   1200sqrt (5)  / 5    =    240 sqrt (5)  units

n√n=2√4

\(n\sqrt n=2\sqrt 4\\ \sqrt {n*n^2}=\sqrt {4*4}\\ n^3=16\\ n=\sqrt[3]{16} \)

Call the length of  the  top side of one of the quadrilaterals, 2a

The length of the right side of this quadilateral   (a - a/3) =  (2/3)a  =  (2a)/3

The length of the  bottom of the quadrilateral   =  sqrt [ ( a - -  a)^2  + (a/3 - - a/3)^2 ] =

sqrt [ 4a^2  + (4/9)a^2  ]  =   a sqrt  [ 36 + 4]/3  =  (a/3)sqrt (40)

The left side of the quadrilateral =  (a - - a/3) =  (4a)/3 

Perimeter of quadrilateral =   

a [ 2 + 2/3 + sqrt (40)/3  + 4/3 ]  =   a   [ 4 + sqrt (40)/3 ]  = a [ 12  + 2sqrt (10) ] / 3

Dividing this  by  a  =      [ 12 + 2sqrt (10)] / 3    =    4 + (2/3)sqrt (10)

 what is another name for line QR 

<—>

SQ                  <—> 

                          QT

                                                          <—>

                                                            RT

      <—> 

          TS

4x^2  +  7x  +  k

By Vieta's Theorem :

Product of the  roots  = k/4   ....so....

(-7 + i sqrt (79) )           (-7 - i sqrt (79) )

_____________   *   ______________   =

           8                               8

49 - 79i^2

________   =

      64

49 - 79 (-1)

__________  =

       64

49  +  79

________  =

      64

128

____  =    2

 64

And this =   k/4

So.....

k =  8

...and 4^2/3 = \(\sqrt[3]{16}\)

x(3 + 4)  = 4(x + 3)              4x + 5  = 3(x + 2)                    (x + 2)  + 5(x - 1)  =  3(x + 3)

7x  = 4x + 12                        4x + 5 =  3x + 6                       x + 2 + 5x - 5  = 3x + 9

7 - 4x  =12                            4x - 3x  =  6 - 5                           6x - 3 =  3x + 9

3x  = 12                                       x  =  1                                    6x - 3x  = 9 + 3

x  = 4                                                                                              3x  = 12

                                                                                                         x  = 4

Sorry....it is soooo similar to the other Q that you should have been able to figure this one out

n^3/2 = 2^5/2

n = 2 ^{5/2 * 2/3} = 2 ^10/6 = 2 ^5/3  = 2 cubrt 4

The shelves can hold  3 * 40   = 120  video games

He can put   120 - 85  =  35 more games on the  shelves

a) This triangle is isosceles   ....let  GI  be the  base  and  GH  and HI  be the equal sides

Draw  altitude  HJ......

This will form a Pythagorean  Triple triangle  HIJ   where  HJ = 15, JI = 20  and HI  =  25 

sin GIH  = HJ / HI  =  15/ 25  =  3/5

b)  sin GHI  =  sin (2 * JHI)  =  2 *sin JHI * cos JHI  =  2 * 20/25 * 15/25  =  600/625  =  24/25