Hi

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function

f(x)=2x^2-12x+20

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

f(x)=2(x^2-6x)+20   |completing square to put into vertex form

f(x)=2[(x-3)^2 - 9] +20

f(x) = 2(x-3)^2 -18 + 20

f(x) = 2(x-3)^2 + 2   |Vertex is Pt(3,2)  Line of symmetry is x= 3

Hi

What is : 7 more than a number

Letting x represent the number, it would be: x + 7

Hi

Let x represent pages that can be printed in 30 minutes

Question states*** 

a printer can print 50 pages in 2 minutes

Sets Up the Proportion

  

     2x = 1500

      x = 750, pages that can be printed in 30 minutes



   

Hi

Question states***   

 6 people  build a house in 8 days: 

 that is 1/8 built per day and (1/8) /6 = 1/48 built per person per day

how many people does it take to build a house in one day? 48 people.

 

Hi

3 people working together at the same rate can do a job in 5 1/3 OR 16/3 days:

that is: 3/16 of the job per day with each person doing (3/16)/3 = 3/48 = 1/16 per day

what fraction of that job can 2 of these people do in 1 day?

  2*1/16 = 2/16 = 1/8 of the job 

Hi

Let x represent the time it would take Peter solo

Question states*** Per hour the Equalizer

 1/5 + 1/6 + 1/x = 1/2

Solving for x  

 6x + 5x + 30 = 15x   |Multiplying thru by 30x so as all denominators = 1

         30 = 4x

         x = 30/4 or 7.5 hrs, time it would take Peter solo



CHECKING our Answer***

   6/30 + 5/30 + 4/30 = 15/30 = 1/2

Hi

Z = {17, 18, 19, 20, 21, 22, 23, 24, 25} in set-builder notation:

  {x Z |x ≥ 17 and x ≤ 25} 

Verbally this says: 

"the set of all x's that are a member of() the set of Integers(Z), 

such that(|) x is greater than or equal to 17 and less than or equal to 25"

 

Hi

Let x and (x+20mph)represent their respective speeds.  t = D/r

Question states***

  330/x + 330/(x+20) = 3hr

Solving for x

 330(x+20) + 330x = 3x(x+20)

  660x + 6600 = 3x^2 + 60x

   3x^2 -600x - 6600 = 0

  3(x^2 - 200x - 2200) = 0



  x = 210.4536   |negative solution tossed out for speed

CHECKING our Answer***

  330/210 + 330/230 = 3hr  |to the nearest whole number

Hi

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

 y = 1/4(x+2)^2+6   |Vertex is Pt(-2,6), Axis of symmetry is x = -2



 y = 2(x+2)(x+4)

 y = 2(x^2 + 6x + 8)

 y = 2[(x+3)^2 - 9 + 8]

 y = 2(x+3)^2 - 2   |Vertex is Pt(-3,-2), Axis of symmetry is x = -3

Hi

  8 = 2^(x-4)

 2^3 = 2^(x-4)

   3 = (x-4)

   7 = x



CHECKING our Answer***

 8 = 2^(7-4) = 2^3

Hi

64^x=16^(x-1)

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

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

    6x = 4(x-1)

     2x = -4

      x = -2

CHECKING our Answer***

  64^-2 = 16 ^-3

   1/4096 = 1/4096

Hi

graph (y=1/5x-2).

 



  y = (1/5)x - 2  |y-intercept is Pt(0,-2)

Note: as y increases/decreases by 1, x increases/decreases by 5   

Pt(5, -1) and Pt(-5, -3) on the Line.  Plotting Pts and connecting with line

Hi

Graph the line that passes through (3,1) parallel to a line whose slope is -0.5

 



  y = -.5x + b  |using order pair Pt(3,1) to solve for b

  1 = -1.5 + b

  2.5 = b

  y = (-1/2)x + 5/2  |y-intercept is Pt(0,5/2)

Note: as y increases/decreases by 1, x increases/decreases by 2 in opposite direction

  Pt(2, 3/2) and Pt(-2, 7/2) on the Line.  Plotting Pts and connecting with line

Hi

Paul is 12. His father is 33

Let x represent How many years ago was the father 4 times as old as the son? 

Question states*** 'x' years ago...

   33-x = 4*(12-x)

  Solving for x

   33-x = 48 - 4x

        3x = 15       

           x = 5, the years ago the father was 4 times as old as the son        

CHECKING our Answer***

  33-5 = 28 = 4*(12-5)

Hi

Maria is now 3 years younger that her sister Ann.

Let x and (x-3) represent Ann's and Maria's ages NOW respectively

Question states***four years ago...

   (x-3) - 4 = x/2

  Solving for x

     x - 7 = x/2 

         x/2 = 7         

           x = 14, Ann's age now.  Maria is 11  (14-3)         

CHECKING our Answer***

  11-4 = 14 = 7

Hi

Find three consecutive integers 

Let x, (x+1), (x+2) represent the three consecutive integers respectively

Question states***

  2(x+1) + 3(x+2) = 6x - 5

  Solving for x

     5x + 8 = 6x - 5           

         13 = x  The three consecutive integers are 13,14,15          

CHECKING our Answer***

    2*14 + 3*15 = 73 = 78 - 5

Hi

Find three consecutive integers 

Let x, (x+1), (x+2) represent the three consecutive integers respectively

Question states***

  8[x+ (x+1)+ (x+2)] = 21x + 108

Solving for x

    8(3x + 3) = 21x + 108

      24x + 24 = 21x + 108

           3x = 84

             x = 28  The three consecutive integers are 28,29,30

          

CHECKING our Answer***

   8*87 = 696 = 588 + 108

Hi

Find three consecutive integers 

Let x, (x+1), (x+2) represent the three consecutive integers respectively

Question states***

  x + (x+1) = (x+2)/2 + 9

Solving for x

     2x + 1 - x/2 = 1 + 9

        (3/2)x = 9

             x = 6  The three consecutive integers are 6,7,8

          

CHECKING our Answer***

 6+7 = 4 + 9

Hi

one is twice another number

Let x and 2x represent the smaller number and larger number respectively

Question states***

 2x - 10 = x+2

Solving for x

      x = 12, the smaller number.  The larger number is 24.

CHECKING our Answer***

 24-10 = 12 + 2 = 14

Hi

mean = 7.9473   (151/19)

median = 8     |(19+1)/2  or tenth term

mode = 4  (most frequent)

midrange (16-3)/2 = 7.5

1st quartile = 4      |(19+1)/4 or the 5th term  | 25% are less than this

3rd  quartile = 9     |25% are greater than this 



3	4	4	4	4	6	6	7	7	8

8	9	9	9	11	12	12	12	16	

Hi

 



1.what is the equation of line passes through points (4,-6) and has a slope of -3 

  y = -3x + b   |using ordered pair pt( 4,-6) to solve for b

 -6 = -12

 6 = b   | y = -3x+6  OR 3x+y = 6



2.what equation represent a line parallel to the graph of 2x-4y=16

 2x-4y=16  OR y = (1/2)x - 4   |these 'parallel' lines would have m = (1/2)

New Line

  y = (1/2)x + b  | b can be any real value for this line

Hi

What is the equation of a line with a slope of -5 and containing point (2,4)?

 



  y = -5x + b   |using ordered pair pt(2,4) to solve for b

  4 = -10

 14 = b   | y = -5x+14  OR 5x+y = 14

Hi

Find the slope and y-intercept of the line.  Graph the line: 1/4y=x-2

 



 1/4y=x-2  OR y = 4x - 8   |slope m = 4 and the y-intercept is Pt(0,-8)

Hi

Find the equation of the line that has the given properties.  Express the

 equation in slope-intercept form: slope=-7; y-intercept=4

 



 slope=-7; y-intercept=4    | y = -7x + 4

Hi

One number is 10 times as large as another

Let x and 10x represent the numbers

Question states***

 10x - x = 81

Solving for x

     9x  = 81

      x = 9  The numbers are 9 and 90.



CHECKING our Answer***

   90 - 9 = 81

Hi

Verical lines have undefined slopes:  the x-value NEVER changes

m = change(y)/change(x) (cannot divide by zero!)

Hi

My recommendation would be to follow the following steps:

I.Defining the variable(s), might recommend using x for consistency

 majority of problems can be written in terms of one variable,

 Some require two variables and two equations, rare to see them here.

II.Stating the Question Algebraically

III.Solving for x

IV.CHECKING the Answer***



Example:  a movie was was attended by 212 people. 

Children's tickets were $4 and adult tickets were $8. If the amount from

 tickets sales was $1448, how many children and how many adults attended?



I.Let x and (212-x) represent the number of adult and children's tickets respectively

II.Question states***

 8x + 4(212-x) = 1448

III.Solving for x

     4x = 600

      x = 150, number of adult tickets. 62 children's tickets. (212-150)  

     

Iv.CHECKING our Answer***

    $8*150 + $4*62 =  $1200 + $248 = $1448

Hi

Using the point-slope formula, 

 



1) What is the equation of the line whose y-intercept is 3 and slope is 1

y = x + 3  

2) What is the slope of a line parallel to the line whose equation is y - x = 5

 y-x=5  Or y = x+5  |slope of these parallel lines is m = 1

3)What is the equation of a line that passes through points (-1, 2) and (5, 2)?

(-1, 2) and 

 (5, 2)  m = 0   y = 2 OR y-2 = 0

4)What is the equation of a line with a slope of -2 and a y-intercept of 8?

   y = -2x + 8    OR 2x+ y -8 = 0

5)What is the equation of the line that passes through the point (1, 1) 

  and has a y-intercept of 2, thus Pt(0,2)

 (1,1)

 (0,2)  m = -1   

 y = -x + b    |using ordered pair Pt(0,2) to solve for b

 2 = b

 y = -x + 2

  

Hi

Write the slope-intercept equation for the line that passes through (5,4) and (7,8)

Using the point-slope formula, 

(5,4) and 

(7,8)  m = -4/-2 = 2

 



y = 2x + b   |using ordered pair Pt(5,4) to solve for b

4 = 10 + b

-6 = b

y = 2x -6

 

Hi

find the linear equation passing through (4,2) (-3,5)

Using the point-slope formula, 

( 4,2) 

(-3,5)  m = -3/7

 



y = (-3/7)x + b   |using ordered pair Pt(4,2) to solve for b

2 = -12/7 + b

26/7 = b

y = (-3/7)x + 26/7 

Hi

Find the slope and y-intercept of the line in the given equation y=4/9x-20

 



y = (4/9)x-20  |slope= 4/9 and y-intercept is Pt(0,-20)