Hi,

-6a^5+48a^4+12a = -6a(a^4-8a^3-2) 

 

Hi,

ratio of two areas of the circles A and B is 4





    

 ratio of the radii of A and B is 2/1

 

Hi,

A team gained 13 yards on one play ,lost 5 yards on another, 

and gained 18 yards on the last play of the first half. 

NET 26 yds gained on these three plays

total gain for the first half: 218yd + 26yd = 244yd

 

Hi,

5(x-2)^2=125

(x-2)^2= 25

 x-2 = ± 5

  x = 2 ± 5,  x = 7 OR x = -3

 

Hi,

what is the measure of each angle in a regular 1000gon?

 sum of angles = 180°(n-2)= 998* 180° = 179,640°

measure of each angle = 179,640°/1000 = 179.65°

 

Hi,

what is the sum of angles in a 516gon

 sum of angles = 180°(n-2)= 514* 180° = 92,520°

 

Hi,

Deteremine the number of diagonals of a regular 79-gon.

Number of diagonals = n(n-3)2 = 79*76/2 = 3002

 

Hi,

Let x represent Mike's age...then

David is(x+5)

sheila is (x+6)

nancy is (x+9)

claire is (x+10)

Question states***

 x + (x+5)+(x+6)+(x+9)+(x+10) = 120

  5x +30 = 120

     5x = 90

      x = 18, Mike's age. David 23, Sheila 24, Nancy 27 and Claire 28

CHECKING our Answer***

 18 + 23 + 24 + 27 + 28 = 120

 

Hi,

A 21 inch square TV is on sale at the local electronics store.

Let x represent the length of the side of the screen

Using the Pythagorean theorem:

  x^2 + x^2 = 21^2

   2x^2 = 441

    x^2 = 220.5

      x = sqrt(220.5) =  14.85in

 

Hi,

What is the midpoint of the line segment that runs between (-3, 1) and (1, 5)?

Note: Midpoint Pt(x,y):  ( , )

(-3, 1) and 

 (1, 5)  midpoint is (-2,3)

 

Hi,

N=2x^2+4x+1 , where N, in thousands, have a computer x years after 1990. 

Solve in what year were there 97 thousand households with computers 

 97 = 2x^2 + 4x  1

 2x^2 + 4x - 96 = 0

 x^2 + 2x - 48 = 0

factoring

(x+8)(x-6)= 0

   x = 6 |tossing out negative solution for number of years.

 1990 + 6 = 1996, the year there were 97 thousand households with computers 



 2*6^2 + 4*6 + 1 = 72 + 24 + 1 = 97  |checking our answer

 

Hi,

Find the slope of the line that contains: 

(-7, -5) and 

(-4, -6)  m = -1/3

Using the point-slope formula, 

 

Hi,

If I am understanding your question properly

 tan 59 = x/10cm, x = 10cm*tan 59 = 16.6428cm

 

Hi,

V =   |sweeping the base up thru the Ht to find volume

 

Hi,

the sum of two number is 3

Let x and (3-x) represent the numbers

Question states***

 x^2 + (3-x)^2 = 12

 x^2 + 9 -6x + x^2 = 12

 2x^2 - 6x -3 = 0

  

  

product of these numbers:

  

  (36 -60)/16 = -24/16 = -3/2

 

Hi,

Note: 

B and E refer to standard 52 card deck/12 face cards and 4 aces. (52-16)= 36 

Probability of:

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

B. drawing a black seven,given it's not a face card of an Ace = 2/36 = 1/18

C. rolling a sum of 11 on two fair six sided dice = 2/36 = 1/18

D. rolling a sum of 7 on two fair six sided dice = 6/36 = 1/6

E. drawing a three, given it's not a face card or an Ace = 4/36 = 1/9



___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,

Line perpendicular to the line:

 -2x+y=9  OR y = 2x+ 9 slope m = 2

New Line: y = mx + b

 y = (-1/2)x + b   |Has a slope that is the negative reciprocal of m = 2

 y = (-1/2)x + b  |Using Pt(-2,-5) to solve for b

-5 = (-1/2)*-2 + b

 -6 = b 

Equation of the new Line is y = (-1/2)x - 6

 

Hi,

{2,4,36,__,150,180,...}



Note:   = 1^2*2 (n+1)

  = 2^2 * (n-1)

  = 3^2*(n+1)

etc





   = 16*(4-1) = 15*3 = 48

 

Hi,

  12x^2+7x-12 

factoring   

(4x -3 )(3x + 4)   If x =  3/4 or x = -4/3 then (4x -3 )(3x + 4) = 0

F	First terms  12x^2

O	Outside terms  +16x

I	Inside terms   -9x

L	Last terms  -12







  

 

Hi,



find the length and width of rectangle ABCD. P=140cm and length is 4x.

ASSUMING... x is the width

  2(4x) + 2*x = 140cm

       4x + x  = 70cm

         5x = 70

          x = 14cm, the width, the length is 56cm  (4*14cm)



CHECKING our Answer***

   2*14cm + 2*56cm = 28cm + 112cm = 140cm

 

Hi,

6x^2+24x-72 = 6(x^2 + 4x - 12) = 4(x +6)(x-2)

                          F	First terms  x^2

                          O	Outside terms  -2x

                          I	Inside terms   +6x

                          L	Last terms   -12

Above is 'factoring'

If it were a questin of solving then 6x^2 + 24x - 72 = 0

In that case: 4(x+6)(x-2) = 0  and x = -6 OR x = 2

 

Hi,

Which of the following points lie in the solution set to the following system of inequalities? 

y < -3x + 3

y < x + 2

Graphing y = -3x+3 (green) and y = x+2(Blue)

Points in the solution set?

ALL would lie in the area BELOW(left of) the Green AND BELOW the Blue Line

 

Hi,

Graphing

 x+2y=10  Pt(0,5) and Pt(10,0) on the Green Line below 

-x+4y=-8  Pt(0,-2) and Pt( 8,0) on the Blue Line below

Plot points and connect these points with the corresponding Lines

 

Hi,

 Average = (100 + 100 + 87 + 97)/4 = 384/4 = 96 average

 

Hi,

A circle has a diameter AB wher A is the point (6,4) and B is the point (-2,2)

 (6,4)

 (-2,2  

diameter length = sqrt(8^2 + 2^2) = sqrt(68) |D = 

  r = 1/2sqr5t(68) = sqrt(17) 

Standard Form of an Equation of a Circle is 

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



 (6,4)

 (-2,2  C = (2, 3) Midpoint Pt(x,y):  ( , )









 

 

Hi,

Recommend taking it a step at a time:

 

Hi,

Solve the system of linear equations using any method.

2x + y = 5   OR y = -2x+5

4x + 3y = 11

4x + 3(-2x+5) = 11

    -2x = -4

      x = 2  and y = 1  (-2*2 + 5 = 1)

The system has one and only one solution (2, 1). 

 

Hi,

Given the system of linear equations: 

y = 2x + 5   OR 2x - y = -5 

-2x + y = 7



 2x  - y = -5

-2x  + y = 7

     0 ≠  2   The system has NO solutions

 

Hi,

 =  

  =  a1(b2c3-c2b3) - b1(a2c3-c2a3) + c1(a2b3-b2a3) 

             = -4[1*2-(-1*-3)] - [-3(5*2-(-3*7)] + 3[5*-1 - (1*7)]

             = 4  + 93 - 36 = 61 

 

Hi,

 

 =  = -3*-7 - (4*-8)= 53

 

Hi,

find the roots of the quadratic equation 

2x^2-5x+3=0 = (2x-3)(x-1) = 0   x = 3/2 or x = 1

checking our factoring using FOIL

       F	First terms   2x^2

       O	Outside terms  -2x

       I	Inside terms   -3x

       L	Last terms    3