Hi, Yes! You are exactly corect

Solving by the elimination method 

5r - 8s = -3

8r + 5s = 102 



25/8r - 5s = -3*5/8   |multiplying 1st EQ by 5/8

 8r   + 5s = 102 

  89/8 r = -15/8 + 102

    89r  = -15 + 816

    89r = 801

      r = 9   and s = (5r+3)8 = 48/8=6

Hi

0.15x = 31.97-x     |adding x to both sides to combine Like terms

0.15x + x = 31.97

  1.15x = 31.97 

      x = 27.8

 

As You know, we really don't 'get rid' of the x... We combine Like terms!

Hi

(3,135)

(0,120   m = 15/3  OR increase of 15 every 3 years.



Predicting 150 of weekly domestic violence arrest in 2009

Hi

As to checking the answer: 

Note:

  1) (x-1) is a factor as when x=1, then f(1)= 1+2+3-6= 0



  (x^3+2x^2+3x-6)/(x-1)= x^2 + 3x + 6  

  2) checking the result of the division could be done by showing:

      (x-1)(x^2 + 3x + 6) =  x^3+2x^2+3x-6



          x^2 + (3x) +   6

        __________________________

x - 1 | x^3  +2x^2   +3x   -6      

      - (x^3 -x^2)

       ---------------

               3x^2 + 3x

             - (3x^2 -3x))

                --------------

                      6x - 6

                   - (6x - 6)

                          --------

                            0

Hi

the x and y intercepts 

x + 5y = 10

Yes! (10,0) and (0,2) is correct:

Hi

 x^4-4x^3+4x-1 = 0    |If x=1 then 1-4+4-1 = 0 (x-1) a factor

dividing the above by (x-1)

x^3 - 3x^2 - 3x + 1    |If x= -1 then -1-3+3+1 = 0 (x+1) a factor

dividing the above by (x+1)

x^2 - 4x + 1









all the REAL zeros of the function:

 {-3.7321,-1, -.2679, 1 }

 

Hi

   |Squaring both sides of the Equation

    x-2 = x^2 - 8x + 16

   x^2 -9x + 18 = 0

factoring

 (x-3)(x-6) = 0 Note:SUM of the outside terms(-6x) and the inside terms(-3x) = -9x

 (x-3)= 0    x = 3  |Tossing out: sqrt(1) ≠ -1

 (x-6) = 0   x = 6

It is always recommended to 'check out' the solutions found in the original EQ

Hi

is 32 a perfect square? NO 

A number  p  is called a perfect square if and only if 

there exists a whole number n  for which p = n^2 

As to 32, there is no whole number such that 32 = n^2

Hi

If these are corresponding sides of similar triangles:

    |Cross Multiplying 

   20x = 72

     x = 72/20 = 18/5 = 3 3/5

Hi

 300km/6hr = 50kmph

Hi

Note 1 ton = 2000lb and 1 yd^2 = 27 ft^2

0.54 tons/yd^3 =  .54*2000lb/27ft^3 = 40lb/ft^3

Hi

 Note: x^2*x^3 = x^(2+3) OR x^(1+4)

Hi

Using the point-slope formula, 

(4, 2) and 

(5, -2)   m = 4/-1 = -4

 Always important to watch the signs.

Line  y = -4x  for example slants to the left

Line  y = 4x slants to the right

Hi

How do you find the perimeter of triangle ABC on the Pythagorean theorem?

The pythagorean Theorem States:  a^2 + b^2 = c^2

that allows one to find a third side given the other two sides ...

which allows for finding the P = a + b + c

for example: if a = 3 and b = 4, the c = 

 and therefore,   P = 3 + 4 + 5 = 12 units

Hi

Note: Diagonals of a Rectangle are equal to each other:

  3y/5 = 3(y-4)

   3y = 15(y-4)

   3y = 15y - 60

   60 = 12y

     y = 5    Diagonals are both 3 units  

Hi

area(triangle) = (1/2)b*h = (1/2)9cm*12cm = 54 cm^2



 

Hi

Hi

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

Standard Form of an Equation of a Circle is 

where Pt(h,k) is the center and r is the radius

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.

Hi

Ellipse:

4x^2 + 8y^2 = 32 



 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.

Center is (0,0)

Vertices:  (sqrt(8),0) and (-sqrt(8),0)  AND (0,2) and (0-2)

foci: (2,0) and (-2,0)    c = 

length of major axis is : 2sqrt(8)

length of minor axis is : 2*2 = 4

Hi

Area(parallelogram) = b*h = 2x*5x = 250cm^2

 10x^2 = 250 cm^2

   x^2 = 25

   x = 5cm   (tossing out negative solution for a measure)

 Base is 10cm and Height is 25cm



CHECKING our Answer***

 10cm*25cm = 250 cm^2

Hi

Note Prime Numbers between 1 and 100

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

 how do you express 96 as the product of only prime numbers?

   2*2*2*3*2*2 = 

Hi

The cost in millions of dollars for a company to manufacture x thousand

 automobiles is given by the function C(x)=4x^2-24x+81.

Find the number of autromobiles that must be produced to minimize cost.

4x^2-24x+81   |parabola opening upward. completing the square to find the vertex

c(x)= 4[(x-3)^2 -9] + 81

c(x)= 4(x-3)^2 - 36 + 81

c(x)= 4(x-3)^2 + 45  Vertex(3,45)   x= 3  OR 3000 automobiles

Hi

The height of the arrow is given by the function h(t)=-16t^2+64t+34, 

where t is the time in seconds. What is the maximum height of the arrow?

-16t^2+64t+34    |parbola opening downward, completing the square to find vertex

h(t)=-16t^2+64t+34,

h(t)=-16(t-2)^2 + 64 +34

h(t)=-16(t-2)^2 + 98   |Vertex(2,98)

  98ft is the maximum height of the arrow

Hi

Let x, (x+2) and (x+4) represent the consecutive odd Integers respectively

Question states***

 x + (x+4) = 5(x+2) - 69

Solving for x

   2x + 4 = 5x - 59

        63 = 3x

        21 = x   The consecutive odd Integers are 21,23,25

CHECKING our Answer***

  46 = 5*23 - 69 = 115-69  = 46

Hi

factoring

a^2+7a+12=0

(a+4)(a+3)= 0

Note:SUM of the inner product(4a) and the outer product(3a) = 7a

(a+4)=0    a = -4

(a+3)= 0   a = -3



CHECKING our Answer*** SUBSTITUTING our Answers back into the original Equation

a^2+7a+12=0

16 -28 + 12 = 0  |checking a = -4

9  -21 + 12 = 0  |checking a = -3

Hi

Sales tax = .08*25,000 = $2000

       DP = .15*25,000 = $3750   with tax $5750

 OR .23*25,000 = $5750

Hi

Note: the idea solving using substitution is for that to result

in an equation with ONE unknown.



2x+4y=12    OR  x = 6-2y    |solving for x

4x+16y=8   |Substituting that into the 2nd EQ

4(6-2y)+16y = 8    |now we have an EQ with ONE unknown

solving for y

 24 - 8y + 16y = 8

       8y = -16

        y = -2    and x = 10   (6- 2*-2)



CHECKING our Answer***

 4x+16y=8 

 40 -32=8

Hi, 

would like to accomplish eliminating the y-terms in one step:

solve the system of equations using the addition method.

 2x-(1/5)y=-5

 3x-(5/2)y=-37/2



 -25x +(5/2)y = 125/2  |Mulitplying 1st EQ by -25/2 Note: = -25x

  3x  -(5/2)y = -37/2

       -22x = 88/2 = 44

         x = -2  and y = (2x+5)5 = 5

Ordered pair (-2,5) the solution for this system



CHECKING our Answer***

 3x -(5/2)y= -37/2

 -6 - 25/2 =  -12/2 - 25/2 = -37/2

Hi

Note:  To combine(add) must be 'Like' terms: 

In this case to the same 'power of ten' 

(which can be done by moving the decimal point)



(8.28x10^6)+(6.17x10^5)= (82.8x10^5)+(6.17x10^5)= 88.97x10^5 = 8.897x10^6

OR

 (8.28x10^6)+(6.17x10^5)= (8.28x10^6)+(.617x10^6)= 8.897x10^6

Hi

6 teams are involved in a round robin tournament			

each team plays every other team once and only once	

how many games in all are played? 15 

Example: 5 Rounds : 3 games each round.

	1	2	3	4	5	6

1		II	III	IV	V	I

2			IV	V	I	III

3				I	II	V

4					III	II

5						IV

6