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  

Hi

From a standard deck of cards, first two cards are drawn from the deck without replacement.

P(both are Jacks) = 4/52*3/51

Note: w/o replacement, on 2nd card, there are 3 Jacks left out of the 51 cards left

Hi

Solving system by substition method  ('manipulated'...never heard it put quite that way :)

4x+y=8  Or y = (-4x-8)

2x=3y+11

2x =3(-4x-8) + 11

2x = -12x - 24 + 11

14x = -13

  x = -13/14  and y = -4*-13/14 - 8 = 52/14 - 112/14 = -60/14 = -30/7

  y = -30/7

CHECKING our Answer***

  2x  =  3y+11

 -13/7 = -90/7 + 77/7 = -13/7

Hi

nazia is twice old as kanwal

Let x and 2x represent as Kanwal and Nazia's ages NOW respectively

Question states*** 10years ago...

 2x-10 = 4(x-10)

Solving for x

    30 = 2x

    x = 15, Kania age Now.  Nazia is 30.  (2*15)

  

CHECKING our Answer***

   20 = 4*5

Hi

Standard Form of an Equation of an Ellipse is   where Pt(h,k) is the center and 

vertices are determined by distance of a and b from center

 C(-1,1): a = 5  and b = 2

 

Hi

-0.3x^2 + 0.1x = -0.02  |multiplying thru by -100

 30x^2 - 10x - 2 = 0

 15x^2 - 5x - 1 = 0

Hi

h(t) = -9.8t^2 – 10t + 210, where t is in seconds, and height is in meters

when it hits the ground: h(t) = 0

 -9.8t^2 – 10t + 210 = 0   |multiplying thru by -10

  98t + 100t - 2100 = 0

  49t^2 + 50t - 1050 = 0

  |tossing out negative solution for time

  t = 4.15  (rounded to the nearest hundredth's place)

Hi

Completing the square:

- 1/5x^2 - 1/2x + 2 = 0  |Multiplying thru by -10 so as all denominators= 1

   2x^2 + 5x  -20 = 0

  2(x^2 + 5/2) - 20 = 0

  2[x + 5/4)^2 -25/16] - 20 = 0

  2(x+5/4)^2 - 25/8 - 160/8 = 0

  2(x+5/4)^2 - 185/8 = 0

Hi

y+4x=-5

y+5x=3

Sets Up for a simple elimination:

 -y-4x = 5  |mulitplying 1st Eq thru with -1 to eliminate y

  y+5x= 3

    x = 8

    x = 8 and y = -37  (y +5x=3;  y = -5*8 + 3)

CHECKING our Answer***

 y + 4x = -5

-37 +32 = -5

Hi

simplifying:

 (3/4-2/3) + (1/2+1/3)

 1*(3/4-2/3) + 1*(1/2+1/3)

 3/4 -2 /3 + 1/2 + 1/3  |using the common denominator of 12 for each term:

 9/12 - 8/12 + 6/12 + 4/12

  (9 - 8 + 6 + 4)/12 =  11/12

Hi

Decide whether or not the ordered pair Pt(3,2) is a solution of the system.

 2x+y=4    | 6 + 2  ≠ 4

 4x+2y=8   |12 + 4  ≠ 4

 NO this ordered pair is NOT the solution for this system of 2 linear equations

 NOte: These linear equations represent the SAME line:  y = -2x + 4

Hi

The numerator of a certain fraction is 7 less than its denominator.

Let x and (x-7)represent the denominator and numerator respectively

Question states***

 [(x-7)-4] / (x+1) = 1/3

Solving for x

    |cross multiplying to solve for x

       3(x-11) = (x+1)

         2x = 34

          x = 17, the denominator. The numerator is 10.  (17-7)

   Fraction is 10/17



CHECKING our Answer***

   6/18 = 1/3

Hi









  3^5 = 3x

   81 = x

 

Hi

number  whose ten’s digit is h and whose units digit is k

algebraically, number would be :  10h + k

Hi

Note: nCx =  and nPx = 

A club has 15 students. 

a)How many different 3-member committees could the club form: 15C3

  15C3 = 15*14*13/2*3 = 2730/6 = 455

b) How many different 6-member committees could the club form:15C6

  15C6 = 15*14*13*12*11*10/2*3*4*5*6=3603600/144 =  5005

c)In how many ways can a club president,vice-president and a secretary be chosen?

 15P3 = 15*14*13 = 2730 

Hi

The sum of two numbers is S

Let n and (S-n) represent the one and the other number.

Represent algebraically 3 times the other number: 3(S-n)

Hi 

 where Pt(h,k) is a center  with vertices 'b' units up and down from center.



intercepts: (0,3) and (0,-3)

the foci: sqrt(4+9) = sqrt(13)= 3.6056

the asymptotes: y = ± b/a    | y = 3/2x and y = -3/2x

Hi

f(x)=1/4(x+2)^2+1

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

the vertex: Pt(-2,1)

the line of symmetry: x = -2 

and the maximum or minimum value of f(x): 

f(-2) = 1 is a minimun  |parabola opens upward as a = (1/4)>0





f(x)= -22x^2+2x+6 OR f(x) = -22(x- 1/11)^2 + 64/11 |completing the square

Hi

Ordered pairs:{(6,-1), (-3,2), (0,5), (-2,2)}

Domain {6,-3,0,-2}

Function?  NO,  as ALL domain values do not have an unique range value

Hi

 

          r = 12/4 = 3



CHECKING our Answer***

 

Hi

1) 3(x+8)< x+4 | 2x < -20 OR x < -10

2)  OR  = (5/9)*-23° = -12.7778°C

3) not clear from the presentation what the Inequality is

4) same as first queston

Hi

As important as correctly using the quadratic formula is starting with the

correct quadratic equation to apply it to:

-x^2+6x-21=0    |Must multiply ALL terms by -1 to proceed in tha fashion

 x^2 - 6x + 21 = 0











x^2+6x-21=0   |If... this were the correct quadratic (using as an example)

-6+-sqrt(120)/(2)

-6+-sqrt(4*30)/(2)

-6+-2sqrt(30)/(2)

-3+-sqrt(30)   |important to take the 'sqrt(4)out front'









   

Hi





log2 9+ log2 a = log2 13

log2 9+ log2 a - log2 13 = 0

log2 9a/13 = 0



  2^0= 9a/13

   1 = 9a/13

  13/9 = a

Hi

Note: discounted 30% is the same as paying 70% of the value

 Let x represent the original cost

  .70*x = $16

      x = $16/.70 = $22.86

CHECKING our Answer***

  $22.86 - .30*$22.86 = $22.86 - $6.86 = $16

Hi

IF: 16x^2-24x-9=0  

THEN: 





[24 ± 24sqrt(2)]/(32)  = 3/4 ± (3/4)sqrt(2)



However, in this question: (4x-3)(4x-3)=0  | 16x^2-24x+9=0 



 x = 3/4 

Hi

*Note: 

 z = 25/15 = 1.6667

 P( z > 1.6667) = .0478

Hi

 OR 

  = 6.0015 cm

Hi

2 open pipes fill a tank together in 6min. one pipe alone fills a tank in 9min.

 find time for second pipe alone.

Let x represent the time for second pipe alone

Question states*** per min the Equalizer

   1/9 + 1/x = 1/6

Solving for x by mulitplying thru with 54x, so as all denominators= 1

   6x + 54 = 9x

       54 = 3x

        x = 18min, the time for second pipe alone

CHECKING our Answer***

 2/18 + 1/18 = 3/18 = 1/6

Hi

Attendance at a concert was 480

Let x and (480-x) represent the number of adults and children respectively

Question states***Sets up the Proportion

     |cross multiplying to solve for x

Solving for x

   3x = 5(480-x)

   8x = 2400

     x = 300, # if adults attending.  The # of children was 180.  (480-120)



CHECKING our Answer***

  300/180 = 5/3

Hi

Trevor launched a rocket in the soccer field, landing 22 feet above the ground in a tree

if the rocket and trevor are 25 feet apart, find distance between trevor and the tree

Let x represent distance between trevor and the tree

 Using the Pythagorean Theorem

  x^2 = 25^2 - 22^2

  x = sqrt(141)= 11.8743 ft

  

Hi

Let x represent how many are not necturines

Question states***

   (1/3)168 = x or 56 are not necturines