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(x-a)(x-b) ~~ 7 x^2 + x - 5

x^2 - ax - bx + ab =     7x^2 + x -5

7 x^2 - x* 7(a+b) + ab = 7x^2 +  x -5

sooo:     ab = -5     a + b = 1/7  

(a-4)(b-4) =   ab  - 4a - 4b  + 16

                     ab  - 4 (a+b) + 16

                      -5  -4(1/7) + 16 = .................

Thank you guest, but this is actually a small part of a larger question, so I can't use graphing to solve this.

 $ 1500 ( 1+.03)⁵ =   $               

Have you tried a graphing of the equation ?

6 / .08  =    75  boys

75 / .75   =  100  members

Two amounts     x    and   7000- x

.04 x     +     .08 (7000 -x)  =   476       solve for 'x'  the 4% amount                the  8% other amount is 7000 - x

Each day, the  tracrs  plough  6 * 120   =720 hectares

So....in  4  days.....they  must plow   4 * 720  =   2880 hectares =  size of the  field

When  the  two tractors are moved,  then  each  tractor  does  1 /( 5 * 4)  =  1/20  of the  work in one day

So       2880   / 20    = 144  hectares  / day 

f(x - 1)   = 5(x - 1)  -12  =   5x  - 17

Find  the  inverse

y = 5x  -12

y + 12 =  5x

(y + 12)  / 5    = x      "swap"  x and y

(x + 12)   / 5   = y    = the inverse

So

(x + 12)   / 5  =  5x  + 17

x + 12  =  5  ( 5x  + 17)

x + 12   = 25x   +  85

x - 25x  =    85   -12

-24x  = 73

x =  -73 / 24

(3x  + 1)^2    =   9x^2  +  6x  +  1

See here  : https://www.desmos.com/calculator/5parnxzdni

The roots  of  this graph   are  at  -2  and  3

This  graph is   ≤ 0    between  these  values

So

-2 ≤ x ≤ 3  is  the solution

The  volume  of the wax  cube  = S^3     where  S is the side  of  the  cube

The    length  of the  3D  diagonal vertex  of the  cube = sqrt (3) S  ≈  1.73S

The  diameter  of  the  sphere  must  be  greater  than  this  for  the  cube to fit inside the sphere

The volume of   the  hemisphere   =   (2/3)pi * r^3

Therefore

Volume of the  cube  =Volume of the hemisphere

S^3  =  (2/3)pi  *  r^3        solve for  r   

S^3 / [ (2/3)pi ]   =  r^3  take  the   cube root

S / [ (2/3)pi] ^(1/3)   =  r    ≈ .782 S

So  the diameter of the sphere = 2(.782) S  =  1.564S

So....the wax cube would not  fit

Solve the inequality\( (x + 2)(x - 3)\le 0 \) Give your answer in interval notation.

Hello QuestionMachine!

\( (x + 2)(x - 3)\le 0 \)

\(x\in \mathbb R|x<-2,x> 3\)

  !

QCA  is a right triangle    with  legs  of   QA  and  QC

QA   = 2

QC  = (10 - p)

Area  =   product of the  legs  /  2   =    2  (10 - p)   /   2     =   10  -   p 

If  we  imagine  a circle  with an equation  of  x^2   + y^2 =   20^2

The   coordinates  at the   bottom of the wheel =  (0, -20)

When the wheel  is  20 vertical feet  from  the  bottom (assuming a  counter-clockwise rotation)  it is at  (20, 0)

This position represents  a  1/4  turn of the  wheel ......so....it must take the  wheel  (1/4) (60)   =15  seconds to  reach  this point

Yes! you too

144 hectares a day

30/pi not 30/3pi, sorry.

In one minutes, the wheel has spun once, so it has traveled \(40pi\) feet.
So we have: 60 sec. = 40 pi feet, so ? sec. = 20 feet.

So ? = 60/2pi = 30/pi sec.

30/3pi is about 9.55. So to the nearest integer, the answer is 10.

10 seconds

great job guest!

Yeah I think that is the correct solution asinus

Plug 2 in for x.

4(4) + 2 + 7 = 25.

It seems like it's not letting me use LaTeX. What it's supposed to say is:

1 < i < 2010

Sorry, something was messed up. I meant \(1  instead of \(1.

to the nearest hundredth then it would be 10.67