Hi,





  y^2 = 13y - 40

  y^2 - 3y + 40 = 0

  factoring

 (y-8)(y-5) = 0

 (y-8)= 0   y = 8

 (y-5)= 0   y = 5



  

 

Hi,

Need more information: either total number tickets sold or the 

proportion each sold, for ex



24 ticket sold

Let x and (24-x) represent the number of $5.50 and $2 tickets sold

Question states***

  5.50x + 2(24-x) = 83

Solving for x

    3.50x = 35

        x = 10, number of $5.50 tickets sold and...

           There were 14 $2 tickets sold by Ron  (24-10)



CHECKING our Answer***

  $5.50*10 + $2*14 = $55 + $28 = $83

 

Hi,

 = (x-3)(10x^2 - 31x + 22)

Found by using synthetic Division:

3	10	-61	115	-66

				

		30	-93	66

	10	-31	22	0



(x-3)(10x^2 - 31x + 22)

      factoring

(x-3)(10x -11)(x - 2)

 

Hi,

solving for a:  Plan a strategy to place variable a on one side of the EQ



  t(a+b) -ab = 0

  at +bt - ab = 0

  a(t-b) = bt

    

 

Hi,

mixed to get 20 gallons

Let x and (20-x) represent the amount of the  35% and 25% solutions respectively

Question states*** 

 mixing to get 20 gal of 32% alcohol

   .35x + .25(20-x) = .32*20G

Solving for x

     .10x  = .07*20G =  

      x = 14G, the amount of the 35% Solution.  6G of the 25% solution



CHECKING our Answer***

.35*14 + .25*6  = 4.9 + 1.5 = .32*20 = .64

 

Hi,

mixed to get 120 Liters 

Let x and (120-x) represent the amount of the  33% and 15% solutions respectively

Question states*** 

 mixing to get 120 Liters of 21% acid?

   .33x + .15(120-x) = .21*120L

Solving for x

     .18x  = .06*120L =  7.2L

      x = 40L, the amount of the 33% Solution.  80L of the 15% solution



CHECKING our Answer***

  .33*40 + .15*80 = 13.2 + 12 = 25.2 = .21*120

 

Hi,

sold 57 pizzas

Let x and (57-x) represent the number of $14 and $12 sold respectively

Question states*** 

   $14x + $12(57-x) = $722

Solving for x

    2x = 38

      x = 19,number of $14 sold.  38 $12 pizzas sold  (57-19)

CHECKING our Answer***

  $14*19 + $12*38 = $722

 

Hi,

one car traveled, on average 8mph faster than the other car

Let x and (x + 8mph) represent the respective speeds of these cars

Question states*** Note:  D = r*t  OR t = D/r

   2x + 2(x+8) = 208

Solving for x

    4x = 192

      x = 48mph,  the faster car is traveling at 56mph  (44mph + 8mp)

CHECKING our Answer***

  96mi + 112m = 208mi

 

Hi,

The measure of one angle is 30° more than twice the other

Let x and (2x +30°) represent the measures of these angles

Question states*** "Angles are supplementary

  x + (2x +30°) = 180°

Solving for x

    3x = 150°

      x = 50°,  It's supplementary angle is 130°     (2*50°+30

CHECKING our Answer***

  50° + 130° = 180°

 

Hi,

There were 3 times as many $4.00 sold than $6.00 

Let x and 3x represent the number of $6 and $4 tickets respectively

Question states***

 $6x + $4(3x) = $2052

Solving for x

    18x = 2052

      x = 114, number of $6 tickets.  342  $4 tickets sold   (3*114)

CHECKING our Answer***

   $6*114 + $4*342 = $2052

 

Hi,

28 bottles in ALL,of which: 16 are diet soda, 8 are regular soda, and 4 are water.

Chosing 1 bottle..

P(diet soda) = 16/28

P(reg soda) = 8/28

P(water) = 4/28

reduce the fractions and You are done.

 

Hi,

Mixing TO GET 8 L OF A FERTILIZER 

Let x and (8L-x) represent the amount of the 12% and the 8% respectively

Question states***

Mixing to form 8 L OF A FERTILIZER CONTAINING 11% NITROGEN

 .12x + .08(8-x) = .11*8L

     .04x = .88 - .64  Will let You finish it Up

 

Hi,

1 and 2 are "supplementary". If m 1 = 60° and m 2 = (2x + 20)

What is the value of x?

60° + (2x+20) = 180°

      2x = 100

       x = 50°

 

Hi,

 

Hi,

A is at (4,6) 

B is at (-4,0)

D = 

 D = 

 

Hi,

Different ways to solve this system. EQs lend to elimination, substitution methods

x+y+z=4

x+y-z=6



 x +y+z=4  

-x -y+z =-6   |multiplying 2nd Eq thru by -1 to eliminate both x and y

    2z = -2  z = -1



2x-3y+(-1)=-1  |substituting z = -1

 x+y+(-1)=4

therefore:

2x-3y = 0

 x+y = 5



2x-3y = 0

-2x-2y = -10   Multiplying 2 EQ thru by -2 to eliminate x

   -5y = -10   y = 2  and x = 3   (x + y = 5)

 

Hi

 = 

 

Hi

find the LCM (7+6w),(49-36w^2), and (7-6w)

Note:  (49 - 36w^2) = (7-6w)(7+6w)

     (49 - 36w^2) is the LCM

 

Hi

solving by:

60 + .20(x-550)=120 +.15(x-800)

1) removing the parenthesis

60+.20x-110 =120+.15x-120

2)combining Like terms

 .20x - 50 = .15x               

3) Isolating the variable on one side of the EQ

     .05x = 50

        x = 50/.05

        x = 1000

 

Hi,

Using the vertex form of a parabola,  where(h,k) is the vertex

y = x^2 + 4x – 1

f(x)= (x+2)^2 -4 - 1

f(x)= (x+2)^2 -5  V(-2,-5) minimum  a =1 a>0 Parabola opens upward

                    Line of symmetry x = -2

 

Hi,

Using the vertex form of a parabola,  where(h,k) is the vertex

f(x)= -x^2+6x+6

f(x)= -[(x-3)^2 -9]+6

f(x)= -(x-3)^2 +15  V(3,15) maximum  a = -1 a<0 Parabola opens downward

                    Line of symmetry x = 3



f(x)= 2-x^2

f(x)= -(x-0)^2 + 2  V(0,2) maximum  a = -1 a<0  Parabola opens downward

                    Line of symmetry x = 0  (y-axis)

 

Hi,

f(x) = x3 + 5x2 + 6x + 2  | x = -1 a root as -1 + 5 - 6 + 2 = 0

Using synthetic division

(x3 + 5x2 + 6x + 2)/(x+1) = x^2 + 4x + 2 



-1	1	5	6	2

		-1	-4	-2

	1	4	2	0

(x+1)(x^2 + 4x + 2)

   



zeros are: -1, -2+sqrt(2),-2-sqrt(2)

 

Hi,

(2x3 - 23x2 + 71x - 30)/(x-5) = 2x^2 -13x + 6

Using synthetic division to determine the 2x^2 -13x + 6

5	2	-23	 71	-30

		 10	-65	 30

	2     -13	  6	  0



(x-5)(2x^2 - 13x + 6) = 0

factoring

(x-5)(2x -1)(x-6) = 0

(x-5)= 0     x= 5

(2x -1)= 0   x= 1/2

(x-6) = 0    x= 6

 

Hi

Long Division is performed in a similar fashion as with numbers

(2x^3-29x+12)/ (x+4) = 2x^2 -8x + 3

 



          2x^2 + (-8x) +   3    

        __________________________

x + 4 |  2x^3           -29x    +12      

      - (2x^3 +  8x^2)

       ---------------

                -8x^2 -  29x

             - (-8x^2 -  32x))

                --------------

                          3x  + 12

                       - (3x  + 12)

                          --------

                               0

 

Hi

15C4 = 15!/(4!11!) = 15*14*13*12/(4*3*2*1) = 15*7*13 = 1365

Can be done quickly on a scientific calculator as well.

 

Hi

 

 

Hi,

invest $130 at 4% compounded continuously

 A = Pe^(rt) where P is the amount Invested, r the rate, t the number of years



$600 = $130 e^.04t

ln(600/130) = .04t

 1.5294/.04 = t

   38.2349yrs = t

 

Hi,

A bag contains four marbles: one red, one black, one white, and one orange. 

Two marbles are to be selected at random from the bag, with replacement.

Sample Space: RR,BB,WW,OO, RB,BR,RW,WR,RO,OR,BW,WB,B0,OB, WO,OW

P(2B) = 1/4*1/4 = 1/16

 

Hi,



    log 3x+5=3  then  10^3 = 3x+5

 3x+5 = 1000

   3x = 995

    x = 331 2/3 = 331.6667

 

Hi,

Note: 2 2/3 = 8/3

 

Hi,

One number is 6 more than twice another

Let x and ( 2x+6) represent the numbers

Question states***

 x(2x+6) = 2[x + (2x+6)] + 6

Solving for x

 2x^2 + 6x = 6x + 18

  2x^2 = 18

   x^2 = 9

    x = ± 3

Numbers are 3 and 12   OR -3 and 0

CHECKING our Answer***

   3*12 = 2*15 + 6 = 36

   -3*0 = 0 = 2*(-3) + 6