Hi

1) x+7y=62 and 

  -x+2y=10   9y = 72, y = 8 and x = 6, (6,7) the solution

2) 3x+4y=12 and 

  -3x+ y=33   5y = 45, y = 9 and x = -8  (12-4*9)/3 ) (-8,9) the solution

3)4x-8y=1 and 

  4x-8y=2



  4x-8y= 1 

 -4x+8y= -2   |Multiplying 2nd Eq thru by -1

     0 ≠ -1  there is NO solution

 

Hi

june 2006/1982-84 =  = Rose 159.3%

 

Hi, Previously Posted

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.

vertices: (1,-8), (1,-2)  b = 6/2= 3 then Center is (1,-5) 

  

 foci: (1,-10),(1,0)  a^2 = 16

   

  

 

Hi, Previously Posted

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.

    Center(-7,3)

 Foci distance from center = 

 Foci are (-7,7) and (-7,-1)

  

 

Hi, Previously Posted

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.

vertices: (1,-8), (1,-2)  b = 6/2= 3 then Center is (1,-5) 

  

 foci: (1,-10),(1,0)  a^2 = 16

   

  

 

Hi, Previously Posted

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.

vertices: vertices: (0,+-5) b = 5  AND Center is (0,-0) 

  

foci: (0,+-7)  a^2 = 24   (25+24 =49)

   

  

 

Hi

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.

vertices: vertices: (0,+-5) b = 5  AND Center is (0,-0) 

  

foci: (0,+-7)  a^2 = 24   (25+24 =49)

   

  

 

Hi

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.

vertices: (1,-8), (1,-2)  b = 6/2= 3 then Center is (1,-5) 

  

 foci: (1,-10),(1,0)  a^2 = 16

   

  

 

Hi

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.

    Center(-7,3)

 Foci distance from center = 

 Foci are (-7,7) and (-7,-1)

  

 

Hi

Maximum heart rate R is R=220- A, where A is the person’s age

and R is the heart rate in beats per minute.

R(20) = 220-20 = 200

R(70) = 220-70 = 150

 Ordered pairs 

(70,150) and 

(20,200)   m = -50/50 = -1   |Using the point-slope formula, 

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

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

  As stated: R = -A + 220

Plot (70,150) and (20,200)and connect with line.

Graph says as age increases, that Maximum heart rate number decreases

 

Hi



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.

  and  

 x^2/4 + (x^2 - 6x + 9)/9 = 1

  9x^2 + 4x^2-24x+36 = 36

      13x^2 -24x = 0

     x(13x -24) = 0   x = 0 and x = 24/13  

(0,3)  and (24/13,15/13) the solutions for this system

 

Hi



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.

 4x^2 + 8x + y^2 + 2y + 1 = 0  

4(x+1)^2 -4 + (y+1)^2 -1 +1 = 0

4(x+1)^2 + (y+1)^2 = 4

  sqrt(4-1) = sqrt(3) = 1.732

 Center (-1,-1) foci (-1, -2.732) and (-1,.732)

 

Hi



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.

 endpoints of the major axis: (2,4),(2,12) 12-4 = 8/2 b = 4 Center( 2,8)

    

foci (2,5),(2,11)  f = 3    a^2 = 7

      

 

Hi



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.

    f = sqrt(36-11) = sqrt(25) = 5

  Center(-5,-1) and foci are (-5, -6) and (-5,4)

 

Hi



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.

foci: (+9,0) major axis along the x=axis

major axis of length: 24  2a = 24  a = 24/2 = 12

  

  f = sqrt(144-b^2) =  9       b^2  = 63

    

 

Hi

ln x- ln(x-1)= 2

ln (x/(x-1) = 2

  e^2 = x/(x-1)

 7.389 = x/(x-1)

 7.389(x-1) = x

  6.389x = 7.389

       x = 1.1565

 

Hi

You invest $1,000.00 in one account and $4,000.00 in another account.

Both accounts have the same interest rate over the same amount of time.

How will the interest earned compare?   Interest earned on the $4000 account

will be 4 times that earned on the $1000 account

Note:  $4,000 = *$1,000 

 

Hi

Let x represent how tall the flagpole is

Question Sets Up the Proportion

   |Cross Multiplying 

   4x = 60

    x = 15ft tall



CHECKING our Answer***

 15/10 = 6/4 = 3/2

 

Hi

2^(3x-5)= 16

2^(3x-5)= 2^4

 3x-5 = 4

  3x = 9

   x = 3





ewatrrr@aol.com

private/pay tutoring Inquiries only, please. 

 

Hi

On which class did she spend almost 1/4 of her time studying?  1/4 = .25 or 25%

You are exactly correct, it would be the history at 24%

 

Hi

  Let z = (x+1)







   z = -60/24 = -5/2 therefore x = -7/2    (x = z -1)

 

Hi

{64,32,16,8,4,2,1,,...}

 

Hi

 Noticing 

 {125,25,,1,}

 

Hi

Finding Any Restrictions 

Note: generally the restrictions would be when the DENOMINATOR = 0

      as there can be NO zero in a denominator

   Restrictions:  x≠ 3 and x≠ -3

   Restrictions:  x≠ 0, -4,-3,-1/2

  Restrictions:  x≠ 2, -2

             Note: x^2-4 = (x-2)(x+2)

 

Hi

 1,2 and 4 Set Up for Cross Multiplying to solve:

   4x = 2(x+1)   2x = 2   x = 1

   3(3x+2) = 4(x-1)    5x = -10  x = -2



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

  3x^2 - x -2 = 0

factoring

 (3x+2)(x-1) = 0

 (3x+2)= 0   x = -2/3

  (x-1)= 0   x = 1



3. 3x/(x+1) = 0  x = 0 would work

 

Hi

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

axis of symmetry for y=x^2-2 is  the y-axis

the vertex for y=x^2-2 is Pt(0,-2)

 

Hi

Using the point-slope formula, 

(0, 5) and 

(–2, 11)  m = -6/2 = -3



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

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

 y = -3x + b

 5 = -3*0 + b

  5 = b

 y = -3x+5

 

Hi

Using the point-slope formula, 

(2, 5) and 

(–1, 5   m = 0/3 = 0

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

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

 y = 0*x + b

 5 = b

  y = 5

 

Hi

train travels 20 miles faster than a car.

Let x and (x+20) represent speed of car and train respectively

Question states***  Note: D = r*t OR t= D/r

  |Cross Multiplying for solving

  120c = 90(x+20)

   30x = 180

     x = 60mph, speed of car.  The  speed pf the train is 80mph  (60mph+20mph)



CHECKING our Answer***

 90/60 = 120/80 = 3/2









ewatrrr@aol.com

private/pay tutoring Inquiries only, please. 

 

Hi

Factor Completely 

4w^2-9w+5

(4w-5)(w-1)

  Note:SUM of the outside terms(-4w) and the inside terms(-5w) = -9w

       F	First terms

       O	Outside terms

       I	Inside terms

       L	Last terms

 

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