Hi

( x^2-9)/(x+2) X (x^2-4)/(x-3)   |Note the use of() to clarify

Hi

In a 30-60 right triangle, where angle A=30 and side a=3, what is side b? 3



30-60-90 Triangle... sides are in the ratio: 1:sqrt(3):2

Hi

how do I find the vertex for X^2-3x-4=0? 

by completing the Square and putting into the vertex form

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

x^2 - 3x - 4 = 0

 (x-3/2)^2 - 9/4  - 4 = 0

 (x-3/2)^2 - 25/4 = 0  vertex  is Pt(3/2,-25/4)

Hi

 180° - 24° = 156°

Hi

Let x represent the number in the original group

Question states***

 160/x - 160/(x+1) = $8

Solving for x

160(x+1) - 160x = 8x(x+1)

  8x^2  + 8x -160 = 0

   x^2 + x - 20 = 0   

  (x+5)(x-4)=0   x = 4  |tossing out negative solution for count



CHECKING our Answer***

 160/4 - 160/5 = $40 - $32 = $8

Hi

cube with 6 sides having total area of 96 in^2

  96in^2/6 = 16in^2 per side  s*s = Area (side) where s(length of a side) = 4in

 Volume(cube) = s*s*s = 4in * 4in * 4in  = 64 in^3

Hi

 e^x  Green

 e^(-x) Blue

Hi

-7x+y=63 OR y = 7x+63

7x+3y= -35

7x + 3(7x+63) = -35

     28x = -224

       x = -8 and y = 7  (-56+63)



CHECKING our Answer***

using elimination method

 7x+3y= -35

-7x+ y=63

    4y = 28

     y = 7 and x = -56/7 = -8 (using 1st EQ)

Hi

-8x-25 = 27 2/3 = 83/3     |27 2/3 is the same as  83/3 

-8x-25 =  83/3  |multiplying thru by 3 so as all denominators = 1

 -24x - 75 = 83

    -24x = 158

       x = -158/24  = -79/12 

Hi

Using the quadratic formula to solve  

3x^2 -7x – 2 = 0   |Note use of ^  (uppercase 6)







4x^2 =7-2x

4x^2 + 2x - 7 = 0 

Hi

Hi

Population formulas, where x is the number of years beyond 1998

16.7e^0.0015x = 14.6e^0.0135x

 16.7/14.6 = e^(.0135x-.0015x) = e^.012x

 ln(16.7/14.6)/.012 = x

            x = 11 years (to the nearest year)

 1998 + 11  = 2009, the year the populations will be equal.

Hi

  |recommend using () for clarity. for ex:(8-x)/(9-x) = 1/(x-9) 

 

   8-x = -1

    9 = x   |Cannot have zero in the denominator.  

 There is NO solution

Hi

 2x^2 + 14x – 9 +  12x – 3  = 2x^2 + 26x - 12

   supply cost    utilities = total cost

Hi

solving by completing the square 

 p^2-5p = -4 

 (p-5/2)^2 = -4 + 25/4

 (p-5/2)^2 = 9/4

 (p-5/2) = ± 3/2

   p = 5/2 ± 3/2

  p = 4 or p = 1 



CHECKING our Answer***

 p^2-5p +4 = 0

(p-4)(p-1) = 0 

(p-4)= 0   p = 4

(p-1)=0    p = 1 

Hi

A new coat is regularly priced at $49.95. It is on sale with a discount of 10%

 sale price = $49.95 - .10*49.95 = $44.96

 Saving:  $49.95 - $44.96 = $4.99

Hi, Previously posted

graph the inequality on a plane

5x+6y ≤ 30

I. Graph the line: 5x+6y=30  Pt(0,5) and Pt(6,0) on this line.

   Plot points and connect with line.



II. shade area under/including the line

Hi

graph the inequality on a plane

5x+6y ≤ 30

I. Graph the line: 5x+6y=30  Pt(0,5) and Pt(6,0) on this line.

   Plot points and connect with line.



II. shade area under/including the line

Hi

Let x and (x+ 9cm) respresent the width and length respectively

  2(x+9) + 2x = 50cm  

       4x = 32

       x = 8cm, the width.  The length is 17cm   (8cm + 9cm)

CHECKING our Answer***

 2*17cm + 2*8cm  = 50cm

Hi

 x = 1/2 t(y-z)

 2x/t = (y-z)

 2x/t  + z = y 

Hi

rectangular lot that has a perimeter of 1350 m and a width of 275 m

  2*L + 2*275m = 1350m

     L = 400m

Hi

The length of a rectangle is 15 feet. The width is 8 feet.

  2*15ft + 2*8ft = 46ft

Hi

Let x and (x+34ft) respresent the width and length respectively

  2(x+34) + 2x = 268ft  

       4x = 200

       x = 50ft, the width.  The length is 84ft   (50ft+34ft)

CHECKING our Answer***

 2*84 + 2*50 = 268

Hi

  2L + 2*26.9cm = 134.2cm   L = 40.2cm

 Area = l*w = 26.9cm*40.2cm

Hi

length of a rectangle is 2 inches longer than the width of the rectangle

Let x and (x+2) represent the width and length respectively

  2(x+2) + 2x = 46in

      4x = 42in

       x = 10.5in, the width.  The length is 12.5in  (10.5 + 2)

CHECKING our Answer***

  2*12.5in + 2*10.5in = 25in + 21in = 46in    

Hi

Hi

 



For ex:

 

Hi

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

the graph of the quadratic 

y = -2x^2 + 3   Vertex is Pt(0,3)  

translated down 4 units  Vertex would be Pt(0,-1)

y = -2x^2 - 1

Hi

Let x, x/2, (x-8), represent the sides

Question states***

  x + x/2 + (x-8) = 42m

Solving for x

5/2x = 50m

       x = 20m   x/2 = 10m  and (x-8)= 12m

Length of sides are: 10m,12m,20m



 CHECKING our Answer***

  20m + 10m + 12m = 42m

   

Hi

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

y=2x^2-6x-14    |completing the square to put into the vertex form

y= 2(x-3/2)^2 -9/2 -14

y= 2(x-3/2)^2 -37/2  |vertex Pt(3/2,-37/2)  x = 3/2 the line of symmetry

CHECKING our Answer***

Hi

Sketch the graph of y= - sqrt(x+2)

Note: Pt(-2,0) and III and IV quadrant portions of the parabola: x = y^2 - 2