Hi,

graph the equation by plotting points

y=x-5  

y = 0 -5

0 = x -5

Pt(0,-5) and Pt(5,0) on this line

Plotting points and connecting with a Line

 

Hi,

graph the equation by plotting points

y=x+2   

y = 0 + 2

0 = x + 2

Pt(0,2) and Pt(-2,0) on this line

Plotting points and connecting with a Line

 

Hi,

 



(x+2)(x^3 + 4x^2 + 9x + 36) = (x+2)(x+4)(x^2+9) = (x+2)(x+4)(x-3i)(x+3i)

 

Hi, 

Find the coordinates of the turning point of the curve 

  |Turning point is the Vertex of the Parabola

  y = -[x^2 - 4x] + 6

  y = -[(x-2)^2 - 4] + 6

  y = -(x-2)^2 + 10  V(2,10), the turning point

       a = -1 -1<0, Parabola opens downward, turning point is a maximum

 

Hi,

Find the coordinates of the turning point of the curve 

  |Turning point is the Vertex of the Parabola

  y = -[x^2 - 4x] + 6

  y = -[(x-2)^2 - 4] + 6

  y = -(x-2)^2 + 10  V(2,10), the turning point

       a = -1 -1<0, Parabola opens downward

 

Hi,

"Factor out" the greatest common factor from the expression 

 15x^5-9x^4

 (5x-3)

 

Hi,

How many different groups of six balls can be drawn 

from a barrel containing balls numbered 1-36? (A group of 36)

  36C6 = 36! /(6!30!) = 1,947,792 different groups

 

Hi,

How many different 5 card hands can be dealt from a 52-card deck?

  52C5 = 52!/(5!(52-5))! = 52!/5!47! = 2,598,960 different hands

 

Hi,

-4x^2-40x-100 = -4(x^2 + 10x + 25) = -4(x+5)(x+5) = -4(x+5)^2

                               

                                    F	First terms x^2

                                    O	Outside terms 5x

                                    I	Inside terms  5x

                                    L	Last terms    25

 

 

Hi,

Carpeting will cost $7.00 a square yard.

1st room is 24 yds x 30 yds.  A = 720yd^2  C = 720/7 = $102.86

2nd room is 7 yds x 12 yd.    A = 84yd^2   C = 84/7 = $12.00

 

Hi,

if two people comple a job in 40 minutes and it takes one to do it in 70 mins.

 how long does it take the other?

Per minute the Equalizer

 1/70 + 1/x = 1/40  |Multiplying thru by 40*70*x so as all denominators = 1

 40x + 40*70 = 70x

        2800 = 30x

       x = 93 1/3 min

 

Hi,





length is 10 yards less than three times the width

Let x and ( 3x-10) represent the width and length respectively

Question states***

 2(3x-10) + 2x = 92yd

Solving for x 

        8x = 112yd

         x = 14yd, the width.  The length is 32yd    (42-10)

CHECKING our Answer***

  64yd + 28yd  = 92yd

 

Hi,

  |Cross Multiplying to solve

    (x+2)(x+1) = 20

    x^2 + 3x + 2 = 20

    x^2 + 3x - 18 = 0

factoring

   (x+6)(x-3) = 0

   (x+6)=0   x= -6  Extraneous solution(CANNOT divide by zero)

   (x-3) = 0   x =   AND 5/5 = 4/4 = 1 (checking out answer)



the 2nd is completed in a similar manner

 

Hi,

triangle with sides 12.5 cm, 30 cm and 32.5 cm

 (12.5)^2 + 30^2 = 156.25 + 900 = 1056.25 = (32.5)^2 !!!

Applying the Pytahgorean Theorem shows it is a right triangle

 

Hi,

$55,000 original investment earns 'simple interest' for 3 years..

earns ($65,000-$55,000) = $10,000 in interest.

'simple interest'

I = P*r*t

10,000 = 55,000*r*3

 10/3*55 = r

    .0606 = r  Interest rate is 6.06%

 

Hi,

 

Hi,

Rewrite the following in the form Ax+By=C 

Process: 

1) all denominators = 1

2) removing parenthesis

3) doing allowable operations to achieve standard from:



1.) y =4x+9   |4x -y = -9

2.) y =4/7x-5/7 

    7y = 4x - 5     |4x-7y = 5

3.) y =3(x-4)+5  | 3x - y = 7

4.) y = 2/5(x-5)+10 

    5y = 2(x-5) + 50   |2x-5y = -40

5.) y = 7x-5+4(x-1)/2 

    2y = 14x-10 + 4(x-1)

         18x - 2y = 14 

 

Hi,

Let s and c represent the rate of the sailboat(still water) and the rate of

the currecnt respectively

Question states*** Note D = r/t OR r = D/t

 s+c = 20mi/4hr = 5mph

 s-c = 20mi/5hr = 4mph

  2s = 9mph

   s = 4.5mph  and c = .5mph   (5mph- 4.5mph = .5mph) 

 

Hi,

Five thousand tickets were sold. 

Let x and (5000-x)represent the number of $6 tickets and $3 tickets respectively

Question states***

 $6x + $3(5000-x) = $18,000

Solving for x

     3x = 3000

      x = 1000, number of $6 tickets.  4000 $3 tickets sold

      

CHECKING our Answer***

 $6*1000 + $3*4000 = $6000 +  $12,000 = $18,000

 

Hi,

find the greatest common factor of 20a^3b, 16a^2, and 36ab^3

 the greatest common factor is 4ab

 

Hi,

A city council with nine members must appoint a three person subcommittee. 

How many subcommittees are possible? 9C3 = 84 possible subcommittees

 

Hi,

6 types of green balls, 8 types of blue balls and 5 types of red balls. 

If Roberto's mom allows him to get one of each color, how many options does Roberto have?

 6C1*8C1*5C1 = 6*8*5 = 240 options

 

Hi,

A city council with nine members must elect a four person executive committee   consisting of a mayor,deputy mayor, secretary, and treasurer.

How many executive committees are posssible?(order important) 

9P4 = 9!/(9-4)! = 9!/5! = 3024 ways

 

Hi,previously posted

Proceed by placing the "all three" of 23

then: 34-23=11  41-23 = 18   27-23 = 4

then: 114 -11-23-18=62, 44-11-23-4=6 and 54-18-23-4=9 to complete



(a) How many grew only tomatoes? 62

(b) How many grew both tomatoes and zucchini, but not cucumbers? 18

(c) How many grew only zucchini? 9

(d) How many grew none of these three or only cucumbers? 17+6 = 23

(e) How many vegetable gardeners were surveyed? 114 + 6 + 4 + 9 + 17 = 150

Hi, 

180 people 

74 people watched movies on VHS tapes (Event A)

123 people watched movies on DVDs (Event B)

27 people watched movies both on VHS tapes and DVDs 



i. Of these surveyed, how many watched only VHS tapes? 47

ii. Of these surveyed, how many watched only DVDs? 96

iii. Of those surveyed, how many watched VHS tapes or DVDs, but not both? 143

iv. Of those surveyed, how many watched VHS tapes or DVDs, or both? 170

 

Hi,

standard deck of cards has 12 face cards and four Aces (Aces are not face cards). 

A. P(drawing the King of Hearts given it’s a face card.) 1/12

B. P(rolling a sum of 3 on two fair six sided dice) 2/36 = 1/18

C. P(rolling a sum of 5 on two fair six sided dice) = 4/36 = 1/9

D. P(drawing a queen given it’s a face card) = 4/12 = 1/3

E. P(rolling a sum of 4 on two fair six sided dice = 3/36 = 1/12



___1_2_3__4__5__6

1|_2_3_4__5__6__7

2|_3_4_5__6__7__8

3|_4_5_6__7__8__9

4|_5_6_7__8__9_10

5|_6_7_8__9_10_11

6|_7_8_9_10_11_12

 

Hi,

Median:  1/2(n+1) = 15.5 (starred term)

find 1st quartile, Q1 = 71

find 3rd quartile, Q3 = 89

98 97 96 95 94 93 91 88 87 84 83 83	82 81 *	

81 80 78 77 76 74 72 69 66 63 62 61  60 59

 

Hi,

Determine if this study is  or observational:

Biologists "restrict the amount of sunlight received" by a group of plants 

to study the growth patterns over a period of 6 months.  

 

Hi,

Determine if this data is  or quantitative:

Brown eyes

 

Hi,

Determine if this is an example of a  or a parameter:

Caloric intake 

 

Hi,

Proceed by placing the "all three" of 23

then: 34-23=11  41-23 = 18   27-23 = 4

then: 114 -11-23-18=62, 44-11-23-4=6 and 54-18-23-4=9 to complete



(a) How many grew only tomatoes? 62

(b) How many grew both tomatoes and zucchini, but not cucumbers? 18

(c) How many grew only zucchini? 9

(d) How many grew none of these three or only cucumbers? 17+6 = 23

(e) How many vegetable gardeners were surveyed? 114 + 6 + 4 + 9 + 17 = 150