Hi,

 is (x-1) or (x+1) a factor of x^100 -4x^99 = 3 

That is: does x = 1 or x = -1 satisfy: x^100-4x^99 - 3 = 0

  1 - 4 - 3 ≠  0 and 1 + 4 -3 ≠  0  Neither are factors

   

                       

 

Hi,

finding the value of x so that f(2x)=2f(x).

f(x)=x^2+99x+18

    (2x)^2 + 99(2x) + 18 = 2x^2 + 198x + 36

     4x^2 + 198x + 18 = 2x^2 + 198x + 36

             2x^2  - 18 = 0

             x^2 = 9

             x = ± 3

 

Hi,

i am more than 15 but less than 30. sum of the age digits = 10

 Age of 28 would satisfy all conditions

 

Hi,



 r =   and C = 2pi*r

 

Hi,

write the equation of the line determined by the given pair of points.

a. (2, -3) and 

   (-1, 1) m = -4/3  |Using the point-slope formula, 

y = (-4/3)x + b   | y = mx + b

1 = (4/3)+b, b = -1/3  |using Pt(-1,1) to solve for b.

y = (-4/3)x-1/3



b. (-3, 0) and 

   (3, 2)  m = -2/-6 = 1/3  |Using the point-slope formula, 

 y = (1/3)x + b      | y = mx + b

 0 = -1 + b, b= 1   |using Pt(-3,0) to solve for b

  y = (1/3)x + 1

 

Hi,

coordinates of Pt(-2,4) under a 90 degree clockwise rotation around the origin?

 Pt(4,2)

 

Hi,



The length of a rectangle is 4cm more than the width

Let x and (x+4cm) represent the width and length respectively

Question states***

P= 2(x+ 4cm) + 2x = 3(x+4cm) + 4cm

         x = 8cm, the width

         

CHECKING our Answer*** length is 12cm  (8cm+4cm)

  2*12cm + 2*8cm = 40cm = 3*12cm + 4cm = 40cm 

 

Hi,



length of a rectangle is 13 more than it's width

Let x and (x+13cm) represent the width and length respectively

 2(x+13cm) + 2x = 90cm

         4x = 64cm

          x = 16cm, the width.



CHECKING our Answer*** length is 29cm  (16cm + 13cm)

    2*29cm + 2*16cm = 58cm + 32cm = 90cm

 

Hi,

only VHS 53

only DVD 103

both VHS and DVD 23 

neither 6 

 

Hi,

circle with center (3,-1)and solution point (-5,1)

 

r is the distance from the Center(3,-1) to the point on the circle (-5,1)

D = = 



Conics in general:

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 and a and b  are the respective vertices distances from center.



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.



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.



the vertex form of a parabola opening up or down,  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 or left,  where(h,k) is the vertex.

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

 

Hi,

  

 V = 2512in^3 = pi*800in^3 and   r = 4in  (diameter = 8in)  

  = h

        50in = h

   

 

Hi,

  

Find the surface area of the cylinder with height 8 m and radius 5.6 m. Use pi.

 S =  = pi*103.12m^2 

 

Hi,

2ab/6a = b/3



y = 1/4, then 15/y =  = 60



price of a jacket was increased from $140 to $168: marked up $28

  28/140 = .20  OR 20% increase

 

Hi,

The sum of the smallest and medium sides is 98 cm more than the longest side

The difference of the longest side and shortest sides is 44 cm

Let (x + 44), (x),[(x+44) + 98 -x] represent long, short and medium side lengths respectively

Question states***

(x+44) + x + 142  = 394cm

          2x = 208

           x = 104, dhort side, long side is 148 and medium is 142



  104 + 142 + 148 = 394 

  

 

Hi,



 P = 72sqrt(3), length of each side is 72sqrt(3)/3 = 24sqrt(3)

 

Hi,



equilateral triangle with side of 12. | Note: Altitude bisects the base 

h = sqrt(12^2 - 6^2) = sqrt(108) = 6sqrt(3)

A = (1/2)b*h = (1/2)12*6sqrt(3) = 36sqrt(3)

 

Hi,

  

the surface area of a rectanglular solid is 12 inches long, 11 inches wide, and 5 inches high. 

 Surface Area = 2*12"*11" + 2*12"*5" + 2*11*5" = 494in^2

 

Hi,

The y-axis is the line of symmetry for these graphs

 

Hi,

The origin is the point of symmetry

 

Hi,

Find the circumference, in inches, of a circle with a diameter of 6.9 inches. 

   (Rounded to the nearest whole inch)

 

Hi,

What is the best classification for a triangle with sides 4, 6, and 5? 

A.) equilateral NO

B.) isosceles   NO

C.) right       NO   (16+25 ≠ 36)

D.) scalene    YES 

 

Hi,

the endpoints of a circle's diameter are 

(6, 2) and 

(0, –6)   D = sqrt(36+64) = 10, the diameter. r = 5  A = 

Note: D = 

 

Hi,

{22.12, 22.49, 22.86, 23.41,...}

Geometric with  = 22.12 and r = 1.02





   |2010 would be the 8th term

 

Hi,

find the vertex, axis of symmetry, and direction of the opening of the parabola 

Putting into vertex form

the vertex form of a parabola opening right or left,  where(h,k) is the vertex.

1. y^2=-8x 

  (-1/8)y^2 = x   Vertex (0,0), a = (-1/8)<0 opens to the left along x-axis

2. (y-8)^2=-4(x-4)

 (1/4)(y-8)^2 +4 = x  Vertex(4,8) a = (-1/4) opens left along y = 8

 

Hi,

 

Hi,

purchased 120 such boxes 

Let x and (120 -x) represent the number of boxes of pens and pencils respectively

Question states***

 17.99x + 7.49(120-x) = 1234.80

      10.50x = 1234.80 - 7.49*120

        10.5x = 336

            x = 32 boxes of pens and 88 boxes of pencils  (120-32)



CHECKING our Answer***

  32*$17.99 + 88*$7.49 = $575.68 + $659.12 = $1234.80

    

 

Hi,



Write each equation in standard form. State whether the graph of the equation is a parabola, circle,ellipse, or hyperbola.

 y = x^2 + 3x + 1 

y = (x+3/2)^2 -9/4 + 1 = 

y = (x+3/2)^2 -5/4  |Parabola opening upward with Vertex (-3/2,-5/4)

standard form is , (x-3)^2 = y + 5/4



x^2+4y^2+2x-24y+33=0

 (x+1)^2 - 1 + 4(y-3)^2 - 36 + 33 = 0

  (x+1)^2 + 4(y-3)^2 = 4

  (x+1)^2/4 + (y-3)^2 = 1 |Ellipse, C(-1,3) major axis along y = 3





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 and a and b  are the respective vertices distances from center.



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.

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.



the vertex form of a parabola opening up or down,  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 or left,  where(h,k) is the vertex.The standard form is , where  the focus is (h +p,k )

 

Hi,

solving by elimination

3r-8s=-55

8r+3s=48



    3r  -8s=-55

(64/3)r +8s=48*8/3 = 128  |multiplying the 2nd EQ thru by (8/3) to eliminate r

    (73/3)r = 73

        

         r = 3  and s = 8



CHECKING our Answer

3r-8s=-55

 9 - 64 = -55

 

Hi,

5 ill week 1, each spreading to 4 people by the end of the next week...

By the end of the tenth week of the epidemic, how many people have been

 affected by the illness?

{5,20,80,320,...}

Geometric sequence r = 4



 = a(1-r^n)/(1-r)= 5(1-4^10)/(1-4) = 1,747,625

 

Hi,

coin is tossed 4 times

P(getting HTTH in that order) = (1/2)^4

 

Hi,



slant height of 26 inches and a radius of 24 inches 

 26^2 = 24^2 + h^2

 h^2 = 26^2 - 24^2 = 100, h = 10

 V =  in^3