Hi

find points by choosing x-values and determining the y-values

 y = -4x-5  Points (0-5), (-1,-1) and (-2,3) on this line (blue)

 y = x - 5  Points (0-5), (1,-4) and (2,-3) on this line (green)

Lines intersect at Pt(0,-5) This ordered pair is the solution for this system

Plot points, connect with the corresponding lines 

 

Hi

x - y = -2

  y = x + 2

x	y	

0	2	(0,2)

-1	1	(-1,1)

-2	0	(-2,0)

Plot points, connect with the line representing y = x + 2

 

Hi

2x + y = -6

  y = -2x - 6

x	y	

0	-6	(0,-6)

-1	-8	(-1,-8)

-2	-2	(-2,-2)

Plot points, connect with the line representing y = -2x-6

 

Hi

the least commom denominator for 3/4 and 3/8 is 8

   3/4 = 6/8

 the two numbers in 'Like' form are 6/8 and 3/8

 

Hi



The perimeter of a standard high school basketball court is 268 ft.

 The length is 34 ft longer than the width

Let x and (x+34) represent the width and length respectively

 2*(x+34) + 2*x = 268ft

    4x = 268 - 68

    4x = 200

     x = 50 ft, the width.  the length is 84 ft

CHECKING our Answer***

  2*84ft + 2*50ft = 268ft











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Hi



Let x and y represent the width and length respectively

 P = 2*y + 28x

AND  x*y = 96yd^2

    6yd = 96yd^2/y   |Its width is 6 yd.

   y = 96yd^2/6yd = 16yd

 2*y + 2*x = P

  2*16yd + 2*6yd = 44 yd 

 

Hi



A rectangle has a perimeter of 24 feet.  

Let x and y represent the width and length respectively

 2*y + 2*x = 24

 2(y+x) = 24

  y + x = 12

Possible combinations of the dimensions and resulting Area

 Rectangle in shape of a square with all sides = 6 has the greatest area.

width	length	Area

1	11	11

2	10	20

3	9	27

4	8	32

5	7	35

6	6	

7	5	35

8	4	32

9	3	27

10	2	20

12	1	12









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Hi



A rectangle has a perimeter of 30 feet.  

Let x and y represent the width and length respectively

 2*y + 2*x = 30ft

 2(y+x) = 30ft

  y + x = 15ft

     y = 15ft-x

Area(rectangle) = L*W = (15-x)x

        A = x(15ft-x)









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Hi



length of a rectangle is 4 times the width

Let x and 4x represent the width and length respectively

 2*4x + 2*x = 50cm

   10x = 50cm

     x = 5cm, the width.  The length is 20cm





CHECKING our Answer***

  2*20cm + 2*5cm =  50cm







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Hi

11	16	18	11	10	14	12	11

 SD = 2.8504 using data Analysis in Excel

Caculators work as well

 

Hi

 x parent  and y child

x	x^2	y	y^2	xy

14	196	13	169	182

10	100	14	196	140

7	49	7	49	49

13	169	15	225	195

13	169	20	400	260

9	81	6	36	54

12	144	18	324	216

78	908	93	1399	1096



r =  = .7493



  y = 1.54x -3.84

parent 16 years of education... the child ~ 21

 

Hi

All of the letters of the word MISSISSIPPI are placed in a bag

11 Letters: 4 of which are s and 1 of which is a m

Without replacing the first letter that was pulled

 P(pulling  s and then  m) = 4/11*1/10

 

Hi

A manufacturing machine has a 1% defect rate. 

4 items are chosen at random

P(at least one will have a defect)

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p = .01 and q = .99

nCx = 

 P(at least one defective) = 1 - P(none defective) = 1 - (.99)^4 =.0394 

P(at least one defective)= .0394

 

Hi

A quiz consists of 20 multiple-choice questions, each with 5 possible answers

 P(passing) if the minimum passing grade is 70 %. |that is, 14 or more correct

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p = 1/5 = .2 and q = .8

nCx = 

For example:

 P(x = 14) =  30C14(.2)^14(.8)^6 = 38,760(.2)^14(.8)^6 = .0000016647

 P(x ≥ 14) = P(14)+P(15)+P(16)+P(17)+P(18)+P(19)+P(20) = .000001845

 

Hi



 mean of 150 and a standard deviation of 30. 

*Note:   | z = .5

   .5 = (x-150)/30 

     x = .5*30 + 150

     x = 165

 

Hi



mean of 80 and a standard deviation of 4

*Note:   | x = 89

   z = (89-80)/4 = 9/4 = 2.25

 

Hi



mean of 50 and a standard deviation of 30.

*Note:   | z = 2.5

   2.5 = (x-50)/30 

   x = 2.5*30 + 50

   x = 125

 

Hi



mean of 80 and a standard deviation of 7



*Note:   | x = 88

    z = (88-80)/7 = 8/7 = 1.429

 

Hi

x	x^2	y	y^2	xy

2	4	8	64	16

1	1	10	100	10

6	36	3	9	18

8	64	1	1	8

4	16	6	36	24

5	25	4	16	20

26	146	32	226	96



 = -.99935

 

Hi

x	x^2	y	y^2	xy

1	1	2	4	2

6	36	9	81	54

3	9	6	36	18

7	49	9	81	63

4	16	5	25	20

5	25	7	49	35

26	136	38	276	192



 = .9519

 

Hi



P(A|B) = P(A and B)/P(B)

P(4|it is odd) = 0   as P(A and B) = 0

 

Hi

data: 13, 10, 11, 8, 14, 13, 13, 14, 30 

Meam = 14

SD = 6.3246

 30 is 2.5298 SD from mean of 14   | (30-14)/6.3246

 All fall within that area between the green lines below





34 and a standard deviation of 4: x = 26 then z = -8/4 = -2  

 

Hi

N(x)=-0.3x^2+6.6x+14

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

N(x)= -0.3[(x-11)^2 -121]+14

N(x)= -0.3(x-11)^2 + 50.3   Vertex(11,50.3)

ticket sales peak on 11th day and 50 tickets will be sold that day



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Hi

y= (x^3-x)/2 

y-intercept (0,0)

x-intercept (when y=0)

 x^3-x)/2 = 0

 x(x^2-1) = 0

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

 x = 0   (0,0)

(x-1)= 0 (1,0)

(x+1)= 0 (-1,0) 



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Hi

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

f(x)= -2x^2+2x+8

f(x)= -2[(x-.5)^2 -.25] +8

f(x)= -2(x-.5)^2 +.5 +8

f(x)= -2(x-.5)^2 + 8.5  V(.5,8.5) Line of symetry is x = .5

     a = -2 < 0  Parabola opens downward:  f(x) maximum is 8.5

The value , f(1/2) = 17/2 is the maximum value for f(x)



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Hi

Ordered pairs  (-1, 3), (7,-1) 

Show that each pair is a solution of the equation:2y + x = 5

 2y + x = 5

 2*3 + -1 = 5   |Ordered pair (-1, 3)  works!

 2y + x = 5

 2*-1 + 7 = 5   |Ordered pair (7, -1)  works!

Others: (3,1), (-3,4) etc



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Hi

(6,1) represents an ordered pair: 

the 1st value of 6 the x-value

the 2nd value of 1 the y-value



Below are examples of the following ordered pairs: (1,2),(3,4) and (5,5)

 

Hi

Find the standard equation of an ellipse with a vertices on the major axis at:

 (-1,2), (5,2) and a minor axis with a length of 2

 Standard Form of an Equation of an Ellipse is 

where Pt(h,k) is the center and a and b  are the respective vertices distances from center.

 

 



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Hi

Evaluating by combining Like terms: 

  -3/5 + 4 = -3/5 + 20/5 = 17/5  or 3 2/5







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Hi

Solve the following system of equations

x+y=5     OR x = 5-y AND x^2 = (5-y)(5-y) =  25-10y+y^2

x^(2)-y^(2)=5 OR x^2 = 5+y^2

 25-10y+y^2 = 5+y^2  

       20 = 10y

        y = 2 and x = 3  Orderecd Pair (3,2)    





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Hi

Graph the function

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

f(x)= -(x-1)^2   |y-intercept is (0,-1)

V(1,0), Parabola opens downward a = -1 < 0

x-intercepts: x = (1,0) 









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