Hi



D =  = -48



D[x]= = -144



D[y]=  = -48



D[z] ==-96

 

  x = 3 and y = 1 and z = 2

Hi

Let x and (x+2) represent the two consecutive odd integers 

Question states***

 x(x+2) = 7055

Solving for x

 x^2 + 2x - 7055 = 0

factoring

(x+85)(x-83)=0 |Note:SUM of the inner product(85x) and the outer product(-83x) = 2x

(x+85)=0  x = -85 |the two consecutive odd integers being -85,-83

(x-83)=0  x = 83  |the two consecutive odd integers being 83,85



CHECKING our Answer(s)***

 -85*-83 = 83*85 = 7055

Hi

Ellipses:

1) 4x^2+5y^2-24x-20y+36=0

   4(x^2-6x) + 5(y^2-4y) +36 = 0   |completing squares

   4[(x-3)^2 -9] + 5[(y-2)^2 -4] + 36 = 0

   4(x-3)^2 -36 + 5(y-2)^2 -20 + 36 = 0

   4(x-3)^2 + 5(y-2)^2  = 20

    

C(3,2) V(3,4)&V(3,0) and V(3+sqrt(5),2)&V(3-sqrt(5),2)

    sqrt(5-4)= 1    f(4,2) and f(2,2)  





2) x^2+3y^2+2x-24y+46=0            |completing squares

   (x+1)^2 -1 +3[(y-4)^2 -16] + 46 = 0

   (x+1)^2 +3(y-4)^2 -49 + 46 = 0

        

 C(-1,4) V(-1,5)&V(-1,3) and V(-1+sqrt(3),4)&V(-1-sqrt(3),4)

  sqrt(3-1)=sqrt(2)       f(-1 +sqrt(2),4) and f(-1-sqrt(2),4)  

Hi

writing the equation in   ax^2 + bx + c = 0 form.

roots of quadratic equation are -7 and -5

 (x+7)(x+5) = 0

x^2 + 12x + 35 = 0   |Yes! You have completed the instructions!

Hi

Mark is 8 years younger than Jerry

Let x and (x-8) represent Jerry and Mark's ages respectively

Question states*** In 10yrs...

 (x-8) + 10 = 1/2(x+10)+10

Solving for x

 (x-8) + 10 = 1/2*x + 5 +10

   x/2 = 13

   x = 26yr, Mark's age NOW.  'Jerry' is now 18yr.  (26-8)



CHECKING our Answer***

      28 = 1/2(36) + 10 = 18 + 10

Hi

Finding the solution set in a +bi form:

6x^2 + 4x +1 =0

 a=6, b=4 and c=1  |Yes!



x = -b  ± sqrt(b^2-4ac)]/12   |Yes! Finish substituting for b, b^2 and 4ac

x = -4 ± sqrt(16-24)]/12

x = -4 ± sqrt(-8)]/12

x = -4 ± sqrt(-1*4*2)]/12    |sqrt(-1) = i

x = -4 ± 2isqrt(2)]/12

x = -1/3 ± (1/6)isqrt(2)

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

 

Hi

(42,20)

(52,10)  m = -10/10 = -1

  p = -x + b  |using ordered pair (42,20) to solve for x

 20 = -42 + b

 62 = b

  p = -x + 62

Hi

Solving using the quadratic formula:

2x^2-11x-2=0

 

 

Hi







 = 20/20 = 1

Hi

D = r*t

Let x represent the submarines speed.

Question states*** 280mi apart after traveling opposite directions

 11hr*x + 25mph*9hr =  280mi   |note:submarine left Hawaii two hours before an aircraft carrier

Solving for x

    11hrx = 55mi

      x = 5mph, the submarine's speed



CHECKING our Answer***

 55mi + 225mi = 280mi

Hi

Let x represent the number

Question states***

 7*(-x) = 3x-50

Solving for x

   50 = 10x

    x = 5

CHECKING our Answer***

 -35 = 15-50 = 35

Hi

Finding the discriminant: b^2 - 4ac  (ax^2 + bx + c = 0)

4x^2-8x+9=0 

 8^2 - 4*4*9 = 64 -144 = -80  

 Two imaginary roots

Hi

solving***

2x^2+x = 3

2x^2 + x-3 = 0

factoring

(2x+3)(x-1)=0 |Note:SUM of the inner product(3x) and the outer product(-2x) =x

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

 (x-1)=0   x = 1



CHECKING our Answer(s)***

2*9/4 -3/2 = 18/4 - 6/4 = 12/4 = 0

  2 + 1 = 3

  

Hi

add each number up to 150.

'If' it is whole numbers from 1 to 150 you wish to add:



 = 75*151 = 11,325

Hi

finding the roots using the quadratic formula

3y^2– 2y + 12 = 0

 

 

 

    x = -.5 + 2isqrt(35)/6

    x = -.5 - 2isqrt(35)/6

Sum of the roots = -1

Product: .25 + 4*35/36 

Note i^2 = -1

Hi

one part is more than twice as much as the first part

Let x and 2x represent the parts

Question states***

 x + 2x = 46

Solving for x

   3x = 46

    x = 46/3.  the parts are 46/3 and 92/3

CHECKING our Answer***

 46/3 + 92/3 = 138/3 = 46

Hi

Factoring

30c^2+19c-63 

(5c+9)(6c-7) |Note:SUM of the inner product(54c) and the outer product(-35c) = 19c

Hi

D = r*t  

 80mph*t + 54mpn*t = 938mi

  t = 938mi/134mph

  t = 7hrs



CHECKING our Answer***

 80mph*7hr + 54mpn*7hr = 560mi + 378mi = 938mi

Hi

 |multiplying thru by 2 so as all denominators= 1

  5x + 6 = 12

    5x = 6

     x =6/5 OR 1 1/5

Hi

 

6p^2+5p+10=0 

 

 

may list as follows to meet requirements there may be for Your classroom     

  

Hi

Solving by substitution

x-y=3  OR y = x-3

2x+y=6

2x +(x-3) = 6

  3x = 9

   x = 3 and y = 0  (3-3)



CHECKING our Answer***

 2x + y = 6

  6 + 0 = 6

Hi

Using the point-slope formula, 

(0,5) AND 

(1,3)   m = 2/-1 = -2

 



y = -2x + b  |using ordered pair Pt(0,5) to solve for b

5 = b

 y = -2x+5

Hi

2x^2-3x=20

2x^2-3x-20=0





  x = (3 ± 13)/4

  x = 4

  x = -10/4 = -5/2



CHECKING our Answer***

 (x-4)(x+5/2) = 0

 

 2x^2 -3x-20 = 0

Hi

length of a 'rectangle' is 6 more than its witdth

Let x and (x+6) represent the width and length respectively

Question states***

 x(x+6) = 72 cm^2    |Area of a rectangle is w*l

Solving for x

 x^2 + 6x - 72 = 0

factoring

 (x+12)(x-6) = 0

 (x+12) = 0  x = -12  |tossing out negative solution for a measure

 (x -6) = 0   x = 6cm, the width.  The length is 12cm  (6cm+6)



CHECKING our Answer***

 6cm*12cm = 72 cm^2

   



 

Hi

how many different ways can a city health department inspector visit 

3 restraurants in a city 0f 11 restraurants

  11C3 where nCx = 

   11*10*9/2*3 = 165 ways

Hi

*Note:  

On an exam with a mean of M=82, you obtain a score of X=86  

a. Would you prefer a standard deviation of s=2 or s=10?  s = 2

   z = 4/2 = 2  OR z= 4/10 = .4

b. If your score were X=78, would you prefer s=2 or s=10?  s = 10

  z =  -4/2 = -2  OR z = -4/10 = -.4

c. If one scores below the mean, one wants the SD to be larger. 

If one scores above the mean , one would wish the SD to be smaller. 

That is: it will reflect a better position as to placement on the curve.



  

Hi

total sales at restrarant A were 350,000 more than restrarant B total sales

Let x  and (x + 350,00)represent the sales at A and B

Question states***

 x + (x+350,000) = 600,000,000

Solving for x

       2x = 5,650,000

       x = 2,825,000 at one store and 3,175,000 at the other (2,825,000+350,000)

CHECKING our Answer***

 2,825,000 + 3,175,000 = 6,000,000,000

Hi

250 km from karachi to nawabshah and 120 km from kotri to karachi.

What percentage of distance from karachi to nawabshah is the distance from karachi to kotri

  120/250 = .48 OR 48%

 distance from karachi to kotri is 48% of the distance from karachi to nawabshah

Hi

Let x and (x-92)represent the rates each of the jets are traveling

Question states*** D= r*t

   9x + 9(x-92) = 10,602mi

Solving for x

        18x = 10602+ 825

        18x = 11430

          x = 635mph.  The other jet traveling at 543mph.  (635-92)



CHECKING our Answer***

  9hr*635mph + 9hr*543mph = 10,602mi

Hi

 Averaged 78 pts on first 5 tests for a total of 390 Pts on these tests.

Let x represent score on his 6th test.

Question states***

  (390+x)/6 = 80

Solving for x

    x = 480 -390

    x = 90



CHECKING our Answer***

 480/6 = 80

Hi

How much 'less' is the sum of all odd digits 'between' 24 and 308 

than the sum of all even digits 'between' 23 and 307?



  306 = 26 + (n-1)2

  306 = 26 + 2n - 2

   282 = 2n

    n = 141



  

 = 23,406    |sum of evens



305 = 25 + 2n-2

 141 = n

 141/2(50 + 280) = 141/2*330 = 23,265  |sum of odds



    23,406 - 23,265 = 141