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Discriminat of the Quadratice Formula must be > 1 for this to be true

b^2 - 4ac  >0

15^2 - 4(8)(c) >0

225 - 32 c >0

32c <225

c < 225 / 32

c < 225/32 = 7.03125        sooo     7   6   5   4   3   2  1     the product of these is  7!

I think that presentation is confusing too!

Try expanding this    \((x+7)^2\)  and you will get     \(x^2+17x+49 \)

Do it to make sure you know how and to check I did it right.

so I have    \(x^2+14x+49=(x+7)^2\)

Notice if I half the 14 I get 7

If I square the 7 I git 49

so

\(x^2+14x+(\frac{14}{2})^2=(x+\frac{14}{2})^2\)

\(​​​​\)

If there is no number in front of the x^2 except for an invisible 1 then this will always be true.

Consider your example:

\(x^2 - 7x + c = (x + a)^2\)

c will be  half of -7

a will be (half of -7) squared.

So you complete this bit for me please.

the same question was posted on Aug 26, 2018 by Lightning.

It was answered by deirdust (signed as Daisy) and she wrote-

  1   2   3   4   5   6   7   8   9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 

By the chart, you can see that there are:

Fifteen 1's

Fifteen 2's

Fifteen 3's

Fifteen 4's

Five 5's

Five 6's

Five 7's

Five 8's

Five 9's    and 

Four 0's (Of course, the zero's would not matter, because they are asking for the sum).

So we are trying to find s, the sum of the digits. We can get the equation s=15(1)+15(2)+15(3)+15(4)+5(5)+5(6)+5(7)+5(8)+5(9), which is equal to s=15+30+45+60+25+30+35+40+45, which we can finally get s=325

-Daisy

Hope this is helpfull!

-Abi

In trapezoid ABCD, sides AB and CD are parallel, angle A = 2(angle D), and angle C = 8(angle B). Find angle B

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

∠A = 120º          ∠B = 20º          ∠C = 160º            ∠D = 60º

it is 92, M and N are 23 and 4

to solve: M has to be prime and N has to be a square, we start off with 4 as that is the smallest square ( we dont count 1) and already, 23 is the biggest prime when multiplied by 4 that the answer is still less than 98

source: i already took the MOEMS and got a 5 (I put 92 as my answer for 2E)

Thank you!

Note  that   l a - b l=   l b - a l   =  b  - a

So

(b -a) + ( b + a)  =  

2b

It should be  noted that  x, y  must both be larger than 20

Let     20  = z   , x = z + a    and  y = z + b

So we have this

1/ ( z + a)   +  1/(z + b)  = 1  / z

(z + b)  + ( z + a)                       1

_________________ =         ____

  z^2  + az + bz + ab                   z

2z  +  a + b                               1

_______________     =         ____     cross-multiply

z^2 + az + bz +ab                    z

2z^2 + az + bz     =  z^2 + az + bz + ab

z^2  =    ab

So  400  = ab

Smallest two factors of 400  added together is   25  and  16

The smallest possible  value  for  x + y  is   20 + 25  = 45    and  20 + 16 = 36

So....the smallest  sum for x +  y  =  45 + 36 =   81

If  they  are perpendicular,they have negative reciprocal  slopes....so....

Put in form   y =  mx + b

2 y + x  +  3    =  0                                  8y +  ax  +  2   = 0

2y  =  -x  - 3                                           8y =  -ax  -  2

divide through by  2                              divide through by 8

y  = (-1/2)x - 3/2                                  y= -(a)/8  - 1/4

We  can  solve this

(-1/2) * ( -a/8)   =  -1

(1/16) a  =  -1             multiply both sides by 16

a = -16

The answer is x = 6

I used the caculator on this site.......

Answer= 0.7272727272727273

I just used the caculator on here......

The smallest x and y are:

x = 36   and   y =45

x  +  y =36  +  45==81

I think that it would be 5/30

1. I saw that there were 5 dice so that would be my numerator because that would be how many chances you get.....

2. I fond the (LCM) Least Common Multiple for 6 and 5, and that is 30 so that would be my denominator.

[5 nCr 1] * 5^4 =3125 / 6^5, or:

[5 nCr 1 * (1/6)^1 * (5/6)^4 =0.401877572, which is exactly the same as: 3125 / 6^5.

As follows:

The area of trapezoid ABCD is 45.

= 4 /5.5  = 8 / 11 = 0.7272727272727273

The quad formula is  fine.....I always like to see if  I can factor, first, before resorting to the "Q"....

(5x - 6) ( 2x + 1)     =   0

Setting each  factor to 0  and solving  for  x produces

5x  - 6   = 0                      2x  +  1   =   0

5x   =  6                          2x  =  -1

x =  6/5                          x  = -1/2

THX, guys.....I really appreciate  that  !!!

5a + 2b   = 0     (1)

ab  = -10   ⇒    b  =  -10/a   (2)

Put (2) into (1)  for   b   and we  have

5a +  2 ( -10/a)   = 0        

5a  -  20/a   =   0     multiply through by a

5a^2   -20    =   0      divide  through  by 5

a^2  - 4     =   0        factor as a difference  of  squares

(a - 2) ( a + 2)  =   0  

Setting each factor  to 0 and  solving  for a  produces  a  =  2     or  a   =  -2

a  = 2   is the  greatest  value  for a   

3x - x^2 + x^2 - 6x  =  -18      simplify

-3x  =  -18       divide both sides by -3

x  =  6

I managed to do this question the wrong way around.

I have 5 red and 4 blue beads. 

oh dear, they are meant to be balls, never mind, mine are balls with holes to turn them into beads.

I have thought of it as a bangle so rotations are the same.

Plus the bangle can put on either way so that cuts down on possibilities as well.

At first I just thought of it as a standard permutation question but it became clear to me that standard 'simple' formula methods were not going to work.

So I resorted to drawing all the possibilities.

This is what I came up with.

If anyone says I have missed any, or that I have double-counted I am all ears.

Only one of these has all the blue separate.

So if you know anything at all about probability you can finish it yourself.

Happy Birthday CPhill!

-Abi