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The two solutions of the equation $x^2+bx+18=0$  are in the ratio of 2  to 1  for some values of b. What is the largest possible value of b.

Hello Guest!

$x=-\frac{b}{2}\pm \sqrt{(\frac{b}{2})^2-18}\\ \ $

b = - 9 :    x1 = 6        x2 = 3       x2 : x1 = 1 : 2

b=    9 :    x1 = - 6      x2 = - 3     x2 : x1 = 1 : 2

The largest possible value of b is 9 (for x1: x2 = 1: 2).

$b\in \mathbb R\ |b\le-6\sqrt{2}\ and\ 6\sqrt{2}\le b$

  !

The largest possible value of b is -9.

Step 1: Assign variables:

Let x = time taken by Peter

Step 2: Use the formula:

$\frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2}$. Let's see if you can solve it from here. I know you can! 

https://web2.0calc.com/questions/kimberly-borrows-dollars-from-lucy-who-charged-interest

Although this one is "..., who charged interest of 5% per month..." I know you can solve it with 6% per month!

If the product (3x^2 - 5x + 4)(7 - x) can be written in the form ax^3 + bx^2 + cx + d, where a,b,c, and d are real numbers, then find 8a + 4b + 2c + d.

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$(3x^2 - 5x + 4)(7 - x)\\ =21x^3-35x+28-3x^3+5x^2-4x\\ \color{blue}=18x^3+5x^2-39x+28$

     a           b           c          d

$\color{blue}8a + 4b + 2c + d\\ =144+20-78+28$

$=114$

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1/3)⁴  =  1⁴  / 3⁴     =  1/ 81

Cedric in 15 years     12000 (1.05)¹⁵  = $ .........

Daniel                        12000 + 12000(.09)(15) = $........

The area of the triangle is 72.

(a,b,c) = (2,-1,5)

The probability is 3/40.

There are 408 ways to place the beads.

a(2)^r = 1       2^r = 1/a 

a(128)^r = 5     a(2⁷)^r = 5

                       a (1/a)⁷ =5

                          1/a⁶ = 5

                           1/5 = a⁶

                                  a = .76472449              .764724491 * (2^r) = 1      r = .38699

Angle B = 28 degrees

Assuming all of the books are distinguisible

6 ways to have math on each end

   then there is 7 books left     7 P 7 = 5040  ways to arrange the 7 books

5040 x 6 = 30 240 ways  (I think)

Try to find the number of ways from E to F and the number of ways from F to G, then mulitply.

E -> F

4 choose 2 = 6

F -> G

5 choose 2 = 10

6 * 10 = 60.

Hope this helps!

x³ * x⁵   + (x³)² =

x⁸   + x⁶     

.75 gallons per hour ?   REALLY?

anyway     gallons left after 't' hours        gallons_left  =  11 - .75 t

    after 4 hours    11 - .75(4) = ....... gallons left

10000 e^.045(10)   = 15683.12      they will not make it to double 10 000 in 10 years

                              ...they need more time or a higher interest rate to double thier initial investment

Claire gets there in 3 hours

   Megan stil has 3 miles to go

       the two of them will cover those 3 miles (and meet)   in 3 miles/ (6+ 5 m/hr)= 3/11 hr 

              at 6 m/hr  claire will have travelled back from outpost  :     6 m/hr *  3/11 hr = 18 /11 miles = 1 7/11 miles

(x-3+sqrt3)(x-3-sqrt3) =   x^2 -6x -2

multiply thru bu -2

-2x^2 + 12x + 4 = 0        vertex   ''x'' = - b/2a = 3  (right between the roots)

    use this value of 'x' in the equation to calculate ''y'' of the vertex

The maximum value is 8*sqrt(3).

You need a minimum of 8 cuts.

1/   ABC

2/   ABD

3/   BCD

4/   BDE

5/   CDE

6/   DEF

7/   CEF