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Well, GM.....the dirty little secret is that EVERYONE on this site sometimes struggles with probabiity....I'm not  very  good at it, either, so I usually qualify my answers with a "Here's what I think"  disclaimer.....(or words to that effect )

By Vieta.......

The sum of the roots, a + b =  -6/2  = -3

And the product of the roots  = ab =  -14/2  =  -7

So

(2a - 3)  ( 4b - 6)   = 

8ab - 12b - 12a  + 18  =

8ab -12 ( a + b)  + 18   =

8 (-7)  - 12 ( -3)  +  18  =

-56  + 36  +  18  =

-2

I think it is something close to 3!

Initial square area    1 cm  x   1 cm =   1 cm²

  After  70 minutes side is   1 + 2(70) = 141 cm      Last square area = 141 x 141 cm = 19,881 cm²

    ^{You can calculate the difference..........}

Use Quadratic Formula to find    roots (a   and  b)  = - 3/2 +- sqrt(37) / 2

                                  Use these values in    (2a-3)(4b-6)      to find the answer .....

75.6 % OFF means you pay only    100 - 75.6 = 24.4 % of original price

24.4% *  p   = 10.99

.244  p = 10.99

p = 10.99/.244 = $ ...........      this is the price for 17 issues         now divide this number by 17 to find the 'each magazine ' price.

the function f(x)= x+4 over x^2-4 is continuous for   

      x + 4               x + 4  

    ––——   =   —–————       This is continuous for all x except +2 and –2.  

     x² – 4         (x + 2)(x – 2)  

_...

I think there are 6 such values

Rearrange the L1 equation as \(y=-\frac{5}{8}x-\frac{13}{8}\)

The slope of L2 must be \(m=\frac{8}{5}\) so its equation will be \(y=\frac{8}{5}x+b\)

We know it goes through point (10, -10), so  \(-10=\frac{8}{5}\times10+b\)

Can you take it from here?

Use k in all your answers

What is the common ratio of the first one  ?

What is the common ratio of the second one  ?

You want a single number for the sum of these.

What is an expression for a_3?

What is an expression for b_3?

Now what?

Answer these then see if you can continue.   [ It will be useful to remember that x^2-y^2 = (x-y)(x+y)  ]

These questions are not worded properly.   

I mean this question and at least one other similar question that you have posted.

If you want to do fractions on a calculator there are many better calculators to use. 

This calc is good for many things but fractions is not one of those things.

The question does not make sense to me.

The probabilities are based on the sample of 201 people. 

0.784*201 = 157.584

How can you have 0.584 of a person?

THX Guest for showing me my error, and sorry if i confused you....

I meant =

each square =2 triangles

there are 12 squares so 12x2=24

there are 12 regular triangles

24+12+?

You can solve the addition 24+12+? problem to get your answer Guest!

Hi Guest!

1. First on the 2.0 caculator you just put in a normal fraction equasion (ex.2/5+7/8 = 1.275)

2. Then you hit the enter button on your keyboard or click the caculate button on your screen.

3. Last the answer it gives you is  2/5+7/8 = 51/40 = 1.275

(0.1)2-8(0.1)+1 = 2 / 5 = 0.4

I put this into the calculator......

I just thought maybe you would need the fraction too.....

If the first term is a and the common difference d, the progression will be

a, a + d, a + 2d, a + 3d, a + 4d, ... so 

\(\displaystyle \frac{a_{5}}{a_{3}}=\frac{a+4d}{a+2d}=3\\ \text{so} \\a+4d=3a+6d, \\2a+2d=0,\\d=-a.\)

The progression will be a, 0, -a, -2a, -3a, ... in which case 

\(\displaystyle \frac{a_{4}}{a_{2}}=\frac{-2a}{0},\)

which you might take to be meaningless (since your not allowed to divide by zero), or infinite ?

ABCD trapezoid, bases AD = 4 and BC = 12.  Also, diagonals AC and BD are perpendicular.  Find the area of ABCD.

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

ABCD trapezoid is an isosceles trapezoid with perpendicular diagonals.

Height      h = 1/2(AD + BC) = 8

Area       A = 1/2 [ h (AD + BC) ] = 64 u² 

(0.1)(2)−(8)(0.1)+1

=0.2−(8)(0.1)+1

=0.2−0.8+1

=−0.6+1

=0.4

Since Ad and Bc are perpendicular....the length  of  one diagonal   is    12/sqrt (2)  + 4/sqrt (2)  =  16/sqrt (2)  = 8 sqrt (2)  = sqrt (128)

And the length of  portion of the base  from the red line to C =   8

So....the height of  the trapezoid is

h = sqrt [ ( sqrt (128))^2  - 8^2 ]  =  sqrt [ 128 - 64  ] =  sqrt [ 64]  = 8

So....the area of the trapezoid is

(1/2)  * height * ( sum of base lengths)  =

(1/2) (8)  ( 12 + 4)  =

4 (16)   =

64 units^2

Let the side of the square  = S

Connect  the  bottom left vertex of the large equilateral triangle  with the vertex where the bottom square and leftmost square meet

This forms a  30-60-90   right traingle

We can find the  distance  from the bottom left vertex of  the  large equilateral square to the bottom left vertex of the bottom square  =  S* sqrt (3)

So....the  side of  the  equilateral triangle is   ( 2sqrt(3)S  + S ) =  S ( 2sqrt (3) + 1) =  S [ sqrt (12) + 1 ] 

And the side of  the  smaller  equilateral triangle    = S

The triangles are  similar figures  and  their scale factor  =  [ S ]  / [ S *( 2sqrt (3) + 1) ]  =  1 / [ sqrt (12) + 1 ]

The ratio of the area of the  smaller equilateral triangle to the larger = [ scale factor] ^2   =

[ 1 / [sqrt (12) + 1 ] ]^2    =

1 / [ 12 + 2sqrt (12)  + 1 ]  =

1/ [ 13  + 2sqrt (12) ]   =

1/  [ 13  + sqrt (48) ]   =

13 -sqrt (48)

___________  =

169   - 48

13 -sqrt (48)

_________  =

   121

13  - 2sqrt (3)

___________   ≈  .05  ≈  1/20

    121

The answer is 60sqrt3

f(x)  =  (ax^4  + bx^3  + 3)  / ( x^3  -2)

We  need to  use long divsion

                 ax  +  b

x^3- 2   [  ax^4  +  bx^3   +  0x^2  +  0x  +   3  ]

                ax^4                                -2x

              __________________________________

                             bx^3                 2x 

                             bx^3                           -2b

                      ___________________________

                                                   (  2x    +  2b )    this remainder is ignored 

So  .....ax + b  =  x   -  5

So

a =1   and  b =  -5

See  the graph here  :   https://www.desmos.com/calculator/yi1t4tgsu5

Let's suppose  that  they can sit together

John and Paul can occupy  any of 7 positions and for each of these,they can sit in 2 ways...and for all these  arrangements  the other people can  sit  in 6!  ways

So....the total arrangements where they sit together =  7 * 2 * 6!  = 10080 ways

And the total possible arrangements  = 8!   = 40320

So....the ways  which they don't sit together  =   total arrangements - those where they sit  together  =   40320  - 10080   = 30240

Sorry,,,,,   No I didn't do the multiplication you had answered....

                       I was questioning how you multiplied 12 x 2    and got 48 

Thanks !