Hi,

 

 Ellipse C(-1,-3) Vertices(-1,2),(-1,-8) and (2,-3),(-4,-3)





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,

four times the angleis equal to twice its supplement  



   4x = 2(180° - x)

   6x = 360° 

    x = 60°       (supplement is 120°) 

 

Hi,



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Hi,

Note: Midpoint Pt(x,y):  ( , )

endpoint: (-4,3) midpoint: (6,3) (-4 + x)/2 = 6  and (3+y)/2 = 3  Pt(16,3)



endpoint: (5,0) midpoint: (-3,-5) 



endpoint: (4,1) midpoint: (3,0)

 

Hi,

A rug is to fit in a room so that a border of consistent width is left on all four sides.  

If the room is 9 feet by 25 feet and the area of the rug is 57 square feet,

how wide will the border be?

 (9-2x)(25-2x)  = 57ft^2

 9*25 - 68x + 4x^2  = 57

        4x^2 - 68x +168 = 0

         x^2 - 17x + 42  = 0

Factoring

      (x - 14)(x-3) = 0

               x = 3' the width of the border.  (throwing out 14 for the border)

CHECKING our Answer***

        3 * 19 = 57ft^2



        

      

  

 

Hi,

The average home price in Linden Hills, Minneapolis in 2007 was $381,000

The average home price in Linden Hills, Minneapolis in 2011 was $296,000



(0,381,000)

(4,296,000   m = 85,000/-4 = -21,250

Generate a linear function that relates year (x) to home price (y). 

 where x is the number of years after 2007  

 Estimate what the average home price was in 2009. $338,500

 Estimate what the average home price will be in 2035. -21250*28 + 381,000 

 If this trend continues, estimate what year you would predict the average home price will reach $250,000.

  250,000 = -21250x + 381,00

  -131,000/ -21250 = x = 6.165  2007 + 7 = 2014

 

Hi, Previously Posted

The number of ways of selecting 2 boys or 2 girls from a group of 4 boys and 5 girls

   4C2*5C2 = 6*10 = 60 ways 

 

Hi, Previously Posted

The number of ways of selecting 2 boys or 2 girls from a group of 4 boys and 5 girls

   4C2*5C2 = 6*10 = 60 ways 

 

Hi

What is the sum of the measures of the interior angle of a polygon with 7 sides?

Note: In general 180°(n-2) is the sum of the interior angles of a polygon with n-sides

  180°(7-2) = 180*5 = 900°

 

Hi,

One-fifth of a numberplus one-third of the numberis 140.

Question states***

   || |Multiplying thru by 15 so as all denominators = 1

    3x + 5x = 140*15

        8x = 140*15

         x = 140*15/8 

         x = 262.5

CHECKING our Answer***

 

 

Hi,

The number of ways of selecting 2 boys or 2 girls from a group of 4 boys and 5 girls

   4C2*5C2 = 6*10 = 60 ways 

 

Hi,

A bag contains 17 marbles - 6 blue, 7 red, and 4 green marbles.

If four marbles are drawn randomly (without replacement)

 P(3 are green) = 

 

Hi,

Let x represent the amount invested at larger interest rate

 Question states***

 .10x + .08(20000 - x) = $1760

       .02x = 1760 - 1600

      .02x = 160

         x = $8000 (smount at 10%).  Amount at 8% was $12,000

And

CHECKING our Answer***

 $800 + $960 = $1760

 

Hi,

Going north with jet stream, a plane makes a 1200 mile trip in 3 hours. 

Going south against the jet stream, the plane makes the trip in 4 hours.

 D = rt   or D/t = r

 1200/3  = r + s

 1200/4  = r - s 

  400 = r + s

  300 = r - s

   700 = 2r

 r = 350mph, speed of plane and speed of jet stream is 50mph  (350+s = 400)

 

Hi,



P = 

The ply wood boards used to build it are 48 inches. or 4'

  linear length of boards needed

 4' by 8' will yield  pieces 4' by 4' 

    40.5/2 = 20.25, will need 21 pieces of plywood

     

 

Hi,

In a classroom there are two kinds of seats; single and double. 

There are twice as single seats as double seats.

THe room can accomodate 76 pupils. How many each kind of seats are there?

Question states*** 

Students = Students

      76 = single seats + 2(double seats)

      76 = 2x + 2(x)

      76 = 4x

       x = 19 double seats and 38 single seats

CHECKING our Answer***

 38 + 2*19 = room for 76 Students

 

Hi,

A speculator bought stocks and later sold them for 19170.00, making a profit of 6.5%.  

How much did the stocks cost him? 

 

Hi,

what acute angle does a line of slope -3/4 make with a horizontal line?

 tanθ = 3/4,  θ ~ 36.87°

 

Hi,

 7 coins: 1 dime, 2 quarters and 4 nickels

One coin is taken from the jar at random.

 P(nickel) =

 

Hi,

 10 marbles: 3 green, 1 red, 5 yellow and 1 blue

If one marble is taken out of the bag randomly

P(green 'or' red) = P(green) + P(red) = 

 

Hi,

 9 marbles: 3 green, 3 blue, 3 white 

without replacement

 P(white, then blue) = 

 

Hi,

3x-2y=0,   Green y = (3/2)x

 x+2y=8    Blue  y = (-1/2)x + 4

 4x = 8

  x = 2  and y = 3   (6-2y = 0, 2y = 6, y  = 3)

 Ordered pair (2,3) is the solution to this system fo Equations

 

Hi,

 four-digit whole number <1300, sum of digits 1s 14

 1 2 x 3

 1 +2 + x +3= 14

       x = 8

 1283 would satisfy the conditions

 

Hi,

Note: Midpoint Pt(x,y):  ( , )

for ex:

(-3, 4) and (-8, 4)  Midpoint is (-11/2,4)

(8, a + 7) and (5, a + 11)  midpoint is (13/2, (a + 9))

(-14, -17) and (-10, -30)  midpoint is (-12, -47/2) 

 

Hi,

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)

Parabola with Vertex at origin, focus: (0, -1/4)

 4py = x^2   and p = -1/4, 

 y = -x^2 

 

Hi,

solving algebraically:  Parabola with V(8,3) and passing thru (5,0) 

 y = a(x -8)^2 + 3

 0 = a(5-8)^2 + 3

 -3/9 = a

 y = (-1/3)(x-8)^2 + 3

 0 = (-1/3)(x-8)^2 + 3

      -3 = (-1/3)(x-8)^2

       (x-8)^2 = 9

        (x-8) = ± 3

          x = 5 and x = 11 

    (11,0) are the coordinates of the other x- intercept.  

 

Hi,  

Re: TY  Note: Graph demonstrates Profit Peaks at ~16 tiles and then decreases as more tiles are sold

Careful, the (-1) stays in effect 

P(x)= (-1)x^2 + 33x - 20

P(20)= (-1)20^2+(33*20)-200

P(20)= -400+660-200 = 60

P(25)= (-1)25^2+(33*25)-200

 P(25)= - 625+825-200 = 0

 

Hi,

 y = x

 y = mx + b   |Standard slope-intercept form

   m = 5/1 = 5     (Note:  in this case b = 0)

 

Hi,

If the profit equation is 

P(x)= -x^2+33x-200

   |Idea is to replace x with 25 and then find P(25)

 

Hi,

3) x+ y=2

  2x+2y=4 

5) y=3x-5

 -3x +y =-5

 -6x+2y=-10     | 3) and 5) The systems are identical Lines, Infinite amount of Solutions



2) 4y-6x=1

   2y-3x=4    | multiplying 2nd thru by -2,   0 ≠ -7  NO solution



1) 2x+y=10

   2x-3y=5   (4.375,1.25)     

4) 4x+5y=12

   2x-y=6     (3,0)

 

Hi,

The amount of water in a wading pool by given by the function w(t)=30+t,

 where "t" is time in minutes and t= 0 corresponds to when a faucet is turned on...

using Gallons

a. What is the rate of change of the water in the pool? 5gal/min

b. Is this an increasing or decreasing function?

c. How much water is in the pool an  after the faucet has been turned on?