Hi,





 



 y = -2  or y = -1



CHECKING our Answer*** by factoring



 (y+2)(y+1) = 0

 y = -2  or y = -1

 

Hi,

 y = (1/4)x (Green)  and x = -12 (Blue)  ||solving this System

substituting x = -12

  y =  = -3

 Ordered pair (-12,-3) the solution for this System of EQ

 

Hi,

Using Common Denominator..

   |||Multiplying thru by x^2 so as all denominators = 1

  7x^2 = -12x - 1

 7x^2 + 12x + 1 = 0



 

 



 

  x = -0.0878 or x =  -1.6265

 

Hi,

Combining Like Terms:

   ||subtracting 2x and 7 from both sides of = sign

     -16 = 2x

      -8 = x 

     

 

Hi,

 

 

Hi,

f(x)=x^4+13x^2+36    || Let X = x^2

f(X) = X^2 + 13X + 36









   X = -9 or X = -4

   x^2 = -9

   x = ± 3i

   x^2 = -4

   x = ± 2i

D) f(x)=(x+2i)(x-2i)(x+3i)(x-3i)

 

Hi,

 

Hi,

^2



F	First terms  6

O	Outside terms 

I	Inside terms  

L	Last terms   27

 ^2 =   33 + 18sqrt(2) 

 

Hi,

Determine whether each pair of equations represents perpendicular lines.

y=5-3x, 3x-y=8 

  y = mx + b

  y = -3x + 5    m = -3

& y = 3x - 8     m = 3    

 NO, this pair of equations do not represent perpendicular lines 

 

Hi,

 56° + (y+12°) + y = 180° 

      2y + 68°  = 180° 

         2y = 112° 

          y = 56° 

CHECKING our Answer***

56° + 68° + 56° = 180° 

 

Hi,

A 15-foot ladder is leaning against a 30-foot wall. 

The bottom end of the ladder is 9 feet from the wall.

Applying the Pythagorean Theorem:  

 12 feet above the ground the ladder touches the wall 

 

Hi,



  x(x-1) - 3(x-2) = 2(x-1)(x-2)= 2(x^2 - 3x + 2)

  x^2 - x - 3x + 6 = 2x^2 -6x + 4

                  x^2 -2x -2  = 0

          

          

             



          

 

Hi,

     || isolating the Radical on one side of the EQ

    || Squaring both sides of EQ

      (x-2) = 1

       x = 3

 

Hi,

   ||Rationalizing the denominator using the conjugate

 =  =  

 

Hi,

You have 12 black and 6 blue socks in a draw.   Total

pick out 2 socks in the dark. What is the probability you get a pair the same colour?

P(2 black 'or' 2 blue) = 

 

Hi,

 

Hi,

x = 2     || Note Vertical line at x = 2

y = x - 2

Finding the y-intercept  (, _)  

y =  -2 = -2 

      y = -2    || the y-intercept  (, -2) 



Finding the x-intercept  ( _, )   

  = x - 2

     x = 2    ||   the x-intercept is (2 , ) 

Plot (0,-2) and (2,0) and connect with a Line

Lines Intersect at (2,0), the ordered pair that is the solution for this System of EQs

 

Hi,

The number of people at a party is given as 180, correct to the nearest 20.

 What's the lowest and highest possible numberof people at the party? 

   160 <  < 200

 

Hi,

The quotient of 3 and 8 is the same as t plus 5.  

 

Hi,

she has 6 more pennies thannumber of nickels. She has the same number of nickels as dimes. 

2.) let n=the number of nickels she has. Represent the number of pennies in terms of n. + 6  

 3.) represent the number of dimes in terms of n.   dimes

1.)what coin does she have the most of? pennies

 

Hi,

x-y = 3   Careful..(0,) on this Line,and also (3,0) Plot, Connect (Blue)

x+y = 5   Yes, (5,0) on this Line and also (0,5) Plot , Connnect (Green)

Lines Intersect at (4,1), the ordered pair that is the solution for this System of EQs

 

Hi,

For example: collecting Like terms: 1-9   or 1 + (-9) on a number Line...

 Starting at 1 and going 9 units to the, one is on         



Likewise:  when collecting Like Terms

 

Hi,

y= -x^2 - 4x - 3   Completing Square to put into Vertex Form

y = -(x+2)^2 + 4 - 3

y = -(x+2)^2 + 1  ||Parabola opens downward (-1 <0) along x = -2 , V(-2,1



See below descriptions of various conics                         

Standard Form of an Equation of a Circle is  

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





 Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center. (a positioned to correspond with major axis)

 a and b  are the respective vertices distances from center

 and ±are the foci distances from center: a > b



Standard Form of an Equation of an Hyperbola opening right and  left is:

   where Pt(h,k) is a center  with vertices 'a' units right and left of center 

and foci  units right and left of center along y = k



Standard Form of an Equation of an Hyperbola opening up and down is:

   where Pt(h,k) is a center  with vertices 'b' units up and down from center, 

and foci units units up and down from center, along x = h



the vertex form of a Parabola opening up(a>0) or down(a<0),  where(h,k) is the vertex.

The standard form is , where  the focus is (h,k + p)



the vertex form of a Parabola opening right(a>0) or left(a<0),  where(h,k) is the vertex.

The standard form is , where  the focus is (h +p,k )

 

Hi,

What is the graph of

f(x)=1/3(x-4)^2-1   Parabola Opening up along x = 4, V(4,-1)





See below descriptions of various conics                         

Standard Form of an Equation of a Circle is  

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





 Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center. (a positioned to correspond with major axis)

 a and b  are the respective vertices distances from center

 and ±are the foci distances from center: a > b



Standard Form of an Equation of an Hyperbola opening right and  left is:

   where Pt(h,k) is a center  with vertices 'a' units right and left of center 

and foci  units right and left of center along y = k



Standard Form of an Equation of an Hyperbola opening up and down is:

   where Pt(h,k) is a center  with vertices 'b' units up and down from center, 

and foci units units up and down from center, along x = h



the vertex form of a Parabola opening up(a>0) or down(a<0),  where(h,k) is the vertex.

The standard form is , where  the focus is (h,k + p)



the vertex form of a Parabola opening right(a>0) or left(a<0),  where(h,k) is the vertex.

The standard form is , where  the focus is (h +p,k )

 

Hi,

If I have 4 frames and put them in a line 

how many different arrangements can I make?   = 4! = 24 ways

 

Hi,

tank that measures 30 feet wide x 30 feet long x 21 feet deep. V = 

  900*21ft = 18,900  and 900*(.80*21) = 900* 16.8ft =  15,120

     21 - 16.8 = 4.2ft = 48in + 2.4in  = 50.4 inches below the top of the tank

 

Hi,

|6z+30|= 48

 6z+30 = 48   z = 3

 6z+30= -48   z = -13

Your solution: z = 3 or z = -13,  Yes!  Good work.

 

Hi,

Solve using quadratic formula: 

6x^2 + 7x - 11 = 0



   || Yes. Good Work.  Keep going...



  Leave in this format

   or use your calculator

   

 

Hi,

Five English books and three Mathematics books are placed at random on a shelf.

Ways of doing this(using the 3 Math books as 1 unit) = 6!

 Find the probability that Mathematics books are together?

    

 

Hi,

  5.355<  < 5.445    ||Note:(.445-.355)/2 = .045= ME

  5.4 -.045<  < 5.4 + .045 

re: n = 200, m = 55200 and SD = 1500 

Find a 95% confidence interval for the true mean annual income of the nursing school alumni.

  ME = 1.96(1500/sqrt(200))}}} = $207.89

55200 - ME <  < 55200 + ME