Hi,



If the area of a parallelogram is bh, and the base is 8 and the height is 

 A = bh = 

  = 55.4 units^2  in decimal form rounded to the nearest tenth

 

Hi,

The function f(x) = x^2. Green

The graph of g(x) is f(x) translated to the left 6 units and down 5 units.  Blue

g(x) = (x+6)^2 - 5   |Using the Vertex form

 

Hi,

What is the graph of the absolute value function?

y = 2|x|  The part of the Lines y = 2x and y = -2x in the 1st and 2nd Quadrants

 

Hi,

64x^2+16y^2+320x-192y+960=0

 64(x +5/2)^2 - 64(25/4)  +  16(y+6)^2 - 16(36) +960 = 0

 64(x +5/2)^2 +  16(y+6)^2 = 16

  4(x+5/2)^2  + (y+6)^2 =1  Yes, good Work.

    This format gives the standard form

 C(-5/2,-6)   V(-3,-6)   &    V(-2,6)  and   V(-5/2,-7)  &  V(-5/2,-5)

sqrt(1-1/4) = sqrt(3/4) = ± sqrt(3)/2  F(-5/2, -6±sqrt(3)/2)  

 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

 

Hi,

 

factoring

  (a+10b)(a - 8b)

F	First terms   a^2

O	Outside terms -8ab

I	Inside terms  10ab

L	Last terms    -80b^2

 

Hi,

find the product

= 

F	First terms  (1/14)x^3

O	Outside terms (1/14)x^2

I	Inside terms  (-2/10)x

L	Last terms      -2/10

  

 

Hi,

 Opens right and left along y = 4

  C(-3,4) and V(-10,4) & V(4,4)

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 from center along y = k

 

Hi,

Recommend 1st sketching cos(x)(green) and using that pattern for 2cos(x)(blue)

 

Hi,

Find three consecutive integers, ,           

in which four times the sum of the first two is the same as six times the third

   4[ x + (x+1)] = 6(x+2)***

     4(2x+1) = 6(x+2)

     8x + 4 = 6x + 12

           2x = 8

            x = 4  Integers are 4,5,6

 CHECKING our Answer***

      4(9) = 6(6) = 36

 

Hi,

solving for w. 



factoring

       (w+5)(w-3) = 0,  w = 3  or w = -5

use FOIL to check the factoring is correct

F	First terms  w^2

O	Outside terms  -3w

I	Inside terms    5w

L	Last terms     -15

 

 

Hi,

  

  1. Find AB if possible, if not explain

 NOT possible: Matrices multiplication is possible only when the number of columns of first matrix

 is equal to the number of rows of second matrix

 2. Find BA if possible, if not explain

 Yes! Good Work!  



 2. Find 3A-4B if possible:  NOT possible matrices must be the same size to add

   or subtract them

 

Hi,



The perimeter of a rectangular garden is 290 feet. If the width of the garden is 66 feet, 

what is its length?

  P = 2W + 2L = 2·66ft + 2x = 290ft

                  132ft + 2x = 290ft

                           2x = 158ft

                            x = 79ft

CHECKING our Answer***

 2·66ft  + 2·79ft = 290ft

 

Hi,

The sum of two consecutive integersand is 10 more than the third 

   x + (x+1) = (x+2) + 10 

     2x + 1 = x + 12 

      x = 11

Integers are 11, 12, 13

CHECKING our Answer***

  11 + 12 = 23 = 13 + 10

 

Hi,

   ||Cross Multiplying to solve

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

 x^2 + x = 2x^2 -x - 15

       0 = x^2 - 2x - 15

          (x-5)(x+3) = 0   x = -3  or x = 5     

 

Hi,



 |Multiplying thru by (x-3)(x+3) so as all denominators = 1

   6(x+3) -(x-3) = 51

    5x +21 = 51

     5x = 30

      x = 6

  

 

Hi,

   ||Yes!|Multiplying thru by 60 so as all denominators = 1

   12x + 5 = 10x

     2x = -5

       x =   Good Work!

 

Hi,previously Posted

 

Hi,

 

Hi,

Add the following: 

(-3.3x^2 + 3.3x – 2.1)  

(-8.7x^2 + 9.8x + 4.2)

 -12x^2  + 13.1x + 2.1

 

Hi,

What is the least integer solution of 

  12x > -12

    x > -1,   0 would be the least integer solution

 

Hi

A canoe takes 7 hours to travel 48 km down a river and back.The rate of the current of the river is 2 kmph.

Find the rateof the canoe in still(calm) water.

 D =rt   or  D/r = t

     |Multiplying thru by (r+2)(r-2)so as all denominators = 1

   48(r-2) + 48(r+2) = 7(r+2)(r-2)

         96r = 7(r^2 - 4)

            7r^2 - 96r - 28 = 0  

             (7r+2)(r - 14) = 0  |throwing out negative solution for rate

                       r = 14 kmph is the speed of the canoe in still(calm) water.

CHECKING our Answer***

    = 3hr + 4hr = 7hr

 

Hi,

A truck weighs 28,500 lb.  The total weight limit for the truck is 64,000 lb.

 What are the possible loads  the truck can carry?

 25,500 lb + x <64,000 lb

            x < 38,500 lb

 

 

Hi,

factor this polynomial completely

 

Hi,



Thw paralellogram is a rhombus, and its asking to solve for xy. 

Note: sides of a rhombus are of equal length

3y+4 = 7y-4 

  8 = 4y      y = 2 

2x+4 = 4x+2   

   2 = 2x     x = 1 and     xy = 1·2 = 2

          

 

Hi,

system of equations: 

x + y + z = 210

x + z = 230 

  y + 230 = 210 , y = -20



x + y = 120 

x +(-20) = 120

     x = 140



CHECKING our Answer*** Note: z = 90

 140 -20 + 90 = 210

 

Hi,

Find the coefficient of  from the expression  coefficient is 20C3 = 1140

 

Hi,

In General 

A = Accumulated Amount

P= principal = 5000

r= annual rate = .045

n= periods per year = 1

t= years = 11

 

Hi,

Solve the system of equations by using the inverse of the coefficient matrix.

 -x-2y=8

 3x+4y=24 

                                  





 = 2

 

Hi,

the side of a cube is represented by 2x-1 . 

Find, in terms of x, the volume of the cube

 Volume of cube = s^3 = (2x-1)^3 = 

Note: (2x-1)(2x-1) = 4x^2 - 4x + 1

(4x^2 - 4x + 1)(2x-1)= 2x(4x^2 - 4x + 1) + 1(4x^2 - 4x + 1) gives us  

Or use      |where a = 2x and b = -1



3x-4y-16 = 0, that is a Line y = (3/4)x - 4, slope = (3/4) and (0,-4) the point

this line crosses the y-axis

 

Hi,

last week we drove to detroit at an average speed of 50 miles per hour the trip took 4 1/2 hours.

how farwas it?

 D = rt = 

 

Hi,

(425)^1/2   

(90)^1/2    

(4)^1/2     

(32/64)^1/2