Hi

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

  Vertex is Pt(3,0) and x = 3 the line of symmetry

Hi

y = -4/x      Green hyperbola

y = -4/(x-2)  Blue hyperbola    |shfting 2 horizontally

y =  -4/x +3  purple hyperbola  |shifting 3 vertically

y = -4/(x-1) - 2  yellow        |shifting 1 horizontaly and -2 vertically

Hi

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

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

isolating y on one side of the equality by performing allowable operations correctly

For ex:  2y -4x < 4  

           y < 2x + 2  |Line: y = 2x + 2, slope m = 2/1  y intercept Pt(0,2)

ONe can graph the line and shade below it: (y < 2x+2) to illustrate 

the graph of the Inequality



 
Solved by pluggable solver: Plot Any Inequality
Graphing function : 

  

  




As to systems of Inequalities, the shaded area they have in common, represents

the solution for the Inquality

For ex. system of Inequalities

 y < 2x + 2  Green line

 y > 2x - 2  Blue line

Solution would be shaded area below green line and above blue line

Solution would be the shaded area between the two lines and not including the lines 

Hi

 

    |squaring both sides of the equation

 (S/2)^2 = I - 5    | 17/2 = 8.5

  (8.5)^2 + 5 = I

  72.25 + 5 = I

     77.25 = I

Hi

Standard Form of an Equation of a Circle is 

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

1.)Center Pt(0,0) and r = 6    x^2 + y^2 = 36

2.)Center Pt(-2,4)and r = 4    (x+2)^2 + (y-4)^2 = 16

Hi

Total Cost = $29,220 

Listing the decimal forms in an Excel Worksheet Column, highlighting and Inserting "Chart" 

selecting Pie Chart will give a great presentation.  

Cannot show that here. These decimals will add up to 1.00 (the whole pie)

tuition fee:  1600/29220  =  .055 (rounding to nearest thousandths) OR 5.5% of circle

food: 7200/29200 = .247

transportation:  6720/29220 = .230

Projects/school supplies:  5400/29220 = .185

books:  4800/29220 = .164

others: 3500/29220  = .120

Hi

Now, he is 4 times his daughters age

Let x and 4x represent daughter and father's ages NOW

question States*** 

 4x - 7 = 11(x-7)     |seven  years ago...

solving for x

  4x - 7 = 11x - 77

      70  = 7x

      x = 10, daughter's age now.  Father is now 40.   (4*10)



CHECKING our Answer

  33 = 11*3

Hi

two longest sides are five less than three times the width

Let x and (3x-5) represent the width and length respectively

Question states

 (3x-5) + x + x = 410 ft    |using the henhouse as a length of the fence

solving for x 

      5x = 415 ft

       x = 83 ft, the width.  the length is 244ft ( 3*83-5)

CHECKING our Answer

  244 + 83 + 83 = 410

Hi

100 numbers, of which 15 of them are < 16

P(number <16) = 15/100 = 3/20

Hi

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 = .9 and q = .1

nCx = 



P(exactly 4 out of 7 time) = 35 (.9)^4(.1)^3 = .0229635

Hi

Let x and (500-2x) represent the width and length of pen

Question states***

  x(500-2x) = 15625    |area = width*length

solving for x

 500x - 2x^2 = 15625

   2x^2 - 500x + 15625 = 0



x =  36.6m and 213.4m (rounding to nearest tenth and tossing out larger solution)

Length of Pen = 500m- 2*36.6m = 426.8m



CHECKING our Answer

426.8m + 36.6m + 36.6m = 500m of fencing    |pen is against his barn wall

Hi

Let x represent the width and y the length

Question states***Write as we Read

3x+30m = 84m

   x = 18m, the width

 2y + 36 = 84m         | P = 2*length + 2*width

   y = 24m, the length

Hi

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

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

I.Putting the Inequality in terms of y gives us slope-intercept format 

 	         In terms of y	   Slope	  y-intercept	 shaded area

x-2y>3	        y < x/2 - 3/2	    m = 1/2	  (0,-3/2)	   Below line

x+3y-7<0	  y <-x/3 + 7/3	    m = -1/3     (0,7/3)	   Below line

y<(-1/2)x-1	  y <(-1/2)x-1	    m= -1/2      (0,-1)	        Below line

(-1/2)x+y-1<0	y < x/2 + 1	    m = 1/2	   (0,1)	   Below line

x>-y+2	           y > -x+2          m = -1	    (0,2)	  Above line

II. Graph line: 

   Plot the y-intercept Pt and  

   Use slope to find two other points starting from y-intercept Pt

III. Shade Area defined by the Inequality (above or Below line) 

 (Note: the inequalities listed here do not include the line)

have completed grahing for the first, the remainder are done in the same way.

x-2y>3	     OR   y < x/2-3/2  m = 1/2	  (0,-3/2)	Below line

Note: m = 1/2, as y increases/decreases by 1, x increases/decreases by 2 





 
Solved by pluggable solver: Plot Any Inequality
Graphing function : 

  

  

Hi

Note: A= p(1-r/n) ^nt

amount owing on a loan of 7400,after 3 years: t = 3

with annual interest=0.109 compounded monthly: n =12 r/n = .009 

amount owing =7400*(1-0.109/12)^(12*3)= $5328.05

Hi

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

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

for ex:    -5x - 5y = -47:  |  y = -x + 47/5   

Slope m = -(1/1)  LIne perpendicular to it wil have a slope m = 1 (negative reciprocal)

 New Line:

 y = 1*x + b  |using ordered pair Pt(5,4) to solve for b

 4 = 5 + b

-1 = b

y = x -1



 

Hi, previously posted

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1] 

Note: i = .0675/12 = .005625  and (1+i)^n = (1.005625)^300 = 5.38

M = 103500*.005625*5.38/ 4.38 = 715.10, is the mortagage payment 



Propery Tax =  16.3081*129500/1000 = 2111.90/yr  OR 175.99/mo



his monthly housing costs = M + PTax = 715.10 + 175.99

Hi

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1] 

 i = .0775/12 = .006458    (1 + i)n = (1.006458)^240 = 4.6877

M = 93000*.006458*4.6877/3.6877 

Many mortgage calulators on line to check Your answer

Hi

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1] 

Note: i = .0675/12 = .005625  and (1+i)^n = (1.005625)^300 = 5.38

M = 103500*.005625*5.38/ 4.38 = 715.10, is the mortagage payment 



Propery Tax =  16.3081*129500/1000 = 2111.90/yr  OR 175.99/mo



his monthly housing costs = M + PTax = 715.10 + 175.99

Hi

Combining Like terms

(7+9i) + (4-15i) 

 7 + 9i + 4 -15i 

 (7 + 4) +( 9i-15i)

    11 - 6i

Hi

Speed in mph = 322mi/7hr = 46mph

Hi

Simplify

 8-3[-2(5-7)-5(4-2)]      |important to work inner parenthesis first

 8-3[-2(-2)-5(2)]

 8-3[ 4 -10 ]

 8-3[ -6 ]

 8 + 18 = 26

Hi

The annual property tax = 11.4898*$197,$500/1000 = $2269.24

Hi

Using the point-slope formula,  to find slope

(–1, 3) and 

(2, –5)   m = 3  -(-5) /-1-2 = 8/-3  Slope m = -(8/3)

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

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

y = -(8/3)x + b    | using ordered pair Pt(-1,3) to solve for b

3 = 8/3 + b

1/3 = b

y = -(8/3)x + 1/3

Note: as y increases/decreases by 8, x value changes by 3 in the opposite direction

Hi

one leg is 14ft longer than the other leg

Let x and (x+14) represent the lengths of the legs

Applying the Pytahgorean Theore,

x^2 + (x+14ft)^2 = (34ft)^2

solving for x

   2x^2 + 28x + 196 = 1156

   2x^2 + 28x - 960 =  0

   x^2 + 14z - 480 = 0

 

 x = -30 and x = 16  |tossing out negative solution:  x = 16

the lengths of the leg are 16ft and 30ft   (16ft + 14ft)

Hi

x^2 + 5x -3 = 0

 



 x = 0.541 and x = -5.541

Hi

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

y = –2x^2-4x+3         |completing square to put into vertex form

y = –2[x+1)^2 -1]+3 

y = –2(x+1)^2 +5  Vertex Pt(-1,5)  Axis of symmetry is x = -1

Hi

Solving the equation:

x^2 + 144 = 0 

   x^2 = -144

   x = ± 

    x = ± 12i

Hi

Let x represent the original cholesterol level

question state *** 

 .18x = 30

   x = 30/.18

   x = 166.67

Hi

Let x represent the percentage decrease

 1350 - x*1350 = 1200

     1-x = 1200/1350

           x = 1-.889 = .111 or 11.1 % decrease

Hi

Note: nCx = 

 small =  8C3 different pizzas = 56

medium =  8C4 different pizzas = 70

large =   8C5 different pizzas = 56

Total number of different pizzas = 56 + 70 + 56

Hi

third side PR <26cm

Note: the sum of the lengths of two sides of a triangle must be greater than 3rd side