Hi, Here is one as an example that was just previously posted

x2+12x-5=0

x2+12x = 5

4x2+48x = 20

4x2+48x+144 = 164 

 = ± sqrt(164)

      2x + 12 = 2sqrt(41)

           x = -6 +sqrt(41)

      2x + 12 = -2sqrt(41)

            x = -6 -sqrt(41)



Checking using 'Completing the Square'

(x+6)^2 = 5 + 36

   x+6 =  ±sqrt(41)

    x = -6 ±sqrt(41)

 

Hi

Re: TY, graph was for demonstration only, in this case:

Note: The factor theorem states that a polynomial f(x) has a factor (x − k)if and only if f(k) = 0

IF -x^2(x+2)(x-1)(x+1)= 0   || IF f(k) = 0, then the resulting "k(s)" are x-intercepts!

 -x^2 = 0     ||x = 0

0r (x+2) = 0  || x = -2

0r (x-1) = 0  ||  x = 1

0r (x+1)  = 0 || x = -1

-x^2(x+2)(x^2-1) = -x^2(x+2)(x-1)(x+1)  |||x-intercepts are -2,-1,0,1

Might recommend checking out downloading this FREE graphing software

 www.padowan.dk 

 

Hi

IF this is what You meant (please use parenthesis when posting for clarity)

f(x)=   ||Domain is all real number except x=5



f(x)= 

 f(x) = x^2 + 5x + 25

f(x) = (x+5/2)^2 - 25/4 + 100/4

f(x) = (x+ 5/2)^2 + 75/4   Parabola opening Upward V(-5/2,75/4)

Range is y ≥ 75/4





  

 

Hi

Question not clear..please repost

 

Hi

go where, how far??

 

Hi

Has to be 'something' You are leaving out...

Please repost

 

Hi

f(x)=3-6x

 y = 3 - 6x   ||Finding the Inverse (interchanging the x and y )

 x = 3 - 6y'

 6y' = 3-x

 y' = (3-x)/6

f '(9) = (3-9)/6 = -6/6 = -1

 

Hi

x2+12x-5=0

x2+12x = 5

4x2+48x = 20

4x2+48x+144 = 164 

 = ± sqrt(164)

      2x + 12 = 2sqrt(41)

           x = -6 +sqrt(41)

      2x + 12 = -2sqrt(41)

            x = -6 -sqrt(41)



Checking using 'Completing the Square'

(x+6)^2 = 5 + 36

   x+6 =  ±sqrt(41)

    x = -6 ±sqrt(41)

  

 

Hi

Standard Form of an Equation of a Circle is  

where Pt(h,k) is the center and r is the radius

x^2+y^2-10y-24=0   ||Putting in standard form

x^2  +y^2-10y +25 = 24 + 25

   C(0,5)  and r = 7

 

Hi

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.

7y=4x-7   0r   y = (4/7)x - 1,  m = 4/7  and -1 is the y-intercept

 

Hi

30% orange juice, another is 10% orange juice

Mixing Algebraically

  .30x + .10(20L-x) = .27•20L  

            .20x = .17•20L 

               x = 17L of the 30%  and 3L of the 10%

and

 

Hi

how many ways can a sample of 4 chocolates be selected from a box of 12 chocolates?

 12C4  ways

 

Hi

 

Hi

Done quickly, check for typos

1) Conjugates of the rational roots given:  7-sqrt(3  and 2+sqrt(6

2) M(1990) = (1/25)18 + 7  using for reference (1997,8)&(1972,7), 1990 being 18 yrs from 1972 

3) y = ( x + 8 )^3 + 9  One root(see below Blue) 

4)  (x-5)(x-1) = x^2 - 6x + 5

5)  (x - (-1+4i))(x-(-1-4i)) = x^2 +2x + 17

6)  x^4 - 9x^2-400) = (x^2 - 25)(x^2 + 16) = 0  x = ±5  0r  x = ±4i

7)

8) y = x^3 (see below Green) y = 3(x-4)^3 - 3  Purple

9) 500 = k(10)^3, k = .5   ,  P = .5(12)^3

 

Hi

John has 55 coins consisting of dimes, nickels and quarters.  

numbers of quarters are five more than twice the number of dimes

   

x + y + z = 55   Yes, good work  

  0r   y =  = (50-3x)

and the total value is 8.25. 

5y + 10x + 25z = 825   ||Careful, Cents does makes sense..however,  $8.25 is 825¢

Substituting

5(50-3x) + 10x + 25(2x+5) = 825

 250 - 15x + 10x + 50x + 125 = 825

            45x = 825-125-250

            45x = 450

              x = 10, number of dimes.   20 nickels and 25 quarters

and

 

 



      

 

Hi

 p(x)=2x^4-x^3+2x-1    x = -1  and x = 1/2 are roots

Using synthetic division

-1	2	-1	0	2	-1

		-2	3	-3	1

1/2	2	-3	3	-1	0

		1	-1	1	

	2	-2	2	0

results in

   2x^2 - 2x + 2

	

 

Hi

 

 

Hi

expected net winnings 

 = -$70

Profit to the college foundation is  = $50,400

 

Hi

A college foundation raises funds by selling raffle tickets for a car worth $36,000. 

Given that 720 tickets are sold for $120 each.  

Find the total profit for the foundation, if they had to purchase the car.

  is the total dollar profit

 

Hi

x^2-6x+9 = (x-3)(x-3)

Check factoring Using FOIL

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

 

Hi



 1) n (A) 50

 2) n (B) 110

 3) p (A) 50/140

 4) p (B) 110/140

 5) p (AǀB) 

 6) p (BǀA) 

P(X|Y) = P(X and Y)/P(Y)

 

Hi

x^2 + y^2 - 4x + 2y = 15

x^2 - 4x + 4 + y^2 + 2y + 1 = 15 + 4 + 1

  C(2,-1)  r = sqrt(20) = 2sqrt(5)

 C(2,-1)

  (4,-5)  m = 4/-2 = -2

tangent Line  m = 1/2

 y = (1/2)x + b   ||Using the  (x,y) ordered pair (4,-5) to solve for b

-5 =(1/2)4 + b

-7 = b

 y = (1/2)x -7

 

Hi

   W

6  $3   1/6  

5  $2   1/6  

4  $1   1/6    Expect winnings 6/6  or $1



A game in which the expected net winnings are zero is called a fair game.

b) what is a fair price to play this game. $1

   Net

6  $2   1/6  

5  $1   1/6  

4  $0   1/6  

3 -$1   1/6  

2 -$1   1/6  

1 -$1   1/6  expected net winnings are zero

 

Hi

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.

line that passes through the point (-6,9) and has a slope of -9.

 y = (-9)x + b

9 = (-9)·-6 + b   |Using ordered pair (x,y):(-6,9)  to solve for b

 63 = b

 y = -9x + 63

 

Hi

A basketball team has won 50 games of 75 played. 

The team still has 45 games to play. 

How many of the remaining games must the team win.  being that amount

 in order to win 60% of all games played during the season? 

 (total games won)/(total games played) = 60%



  

  

           x = 22

and

 72/120 = .60 or 60% win record

  

 

Hi

(2000,41000)

(1980,18000)  m = 23000/20 = 1150

 

Hi, Previously Posted



Check factoring Using FOIL

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

 

Hi

y=2x-5  ||(x,y) ordered pairs (0,-5) and (5/2,0) on this Line.  Plot points & connect with Line

y=-x+3. || (x,y) ordered pairs (0,3) and (3,0) on this Line.  Plot points & connect with Line

Explain why solving a system of equation graphically can be difficult: 

fractional values may be involved in the (x,y) ordered pair of the Intersection

2x-5 = -x+3 , x = 8/3  and y = 1/3 , Pt(8/3,1/3) point of Intersection

 

Hi

4x - y = 8   0r   

 2x + 3y = 9 

 2x + 3(4x-8) = 9

you substitute (4x-8) into the second equation?

 

Hi 



Check factoring Using FOIL

F	First terms

O	Outside terms

I	Inside terms

L	Last terms