Hi,

If you drive 40mph, how far will you drive in 4 1/2 hours?

Note: D = rt

 

 

Hi,

2x^3+11x^2+17x+6   | Note IF x = -2,   ⇒  -16 + 44 - 34 + 6 = 0

(x+2) one factor , could represent one of the three dimensions of the box

 

Hi,

-3x-2y+3z= -1                0r )

 2x+5y-3z= -6

  -x+ 3y = -7                0r 

 

  4x+3y+3z= 22 

 2x+5y-3z = -6

    6x + 8y = 16



  -x+ 3y = -7         |multiplying 1st EQ by 6 and adding to 2nd EQ to eliminate x 

6x+ 8y = 16

      26y = -26

        y = -1  and x = 4  and z = 3

 

Hi,

 x+y+3z= -4                0r  

-x-y-2z= 5     

      z = 1

 2x-z=-3

 2x-1 = -3

     2x = -2

      x = -1  and y = -6       



and...

 

 

Hi,

Note: the vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex  and  x = h  is the Line of Symmetry

1. f(x)= x^2+ 4  | parabola opeing UPward, V(0,4), doesNOT cross x-axis

2. , parabola opeing UPward, V(-1/2,11.75), doesNOT cross x-axis 

 

Hi,

Billy is twice as old as his son's age ( Billy's age now being 2x)

in 10 years, the ratio of their ages will be 3:5

Question states***

   Cross Multiplying to solve for x

   5(x+10) = 3(2x+10)

   5x + 50 = 6x + 30

        20 = x, son' age NOW, Billy is NOW 40

and...in 10 years

   

 

Hi,

find all the roots: 

x^3-11x^2-25x-13=0    |Note x = -1 as root:  -1 -11 +25 -13 =  0

(x+1) a factor:

Using synthetic division

-1	1	-11	-25	-13

 	 	-1	 12	 13

 	1	-12	-13	 0

Yields:

  x^2 - 12x - 13 = 0

 (x-13)(x+1) = 0

  x = 13  or  x = -1

x^3-11x^2-25x-13=0 = (x+1)(x+1)(x-13)

Roots are:  -1, -1, 13

 

Hi,

In a circle...it would be C,S,D,B,A  WITH A + C = 6, Dahlia in the number 3 chair

 

Hi,

look it over ...

1) 

2)

3) 4b+3 |(20b^3+7b^2+22b+27

4) (2x^2-9xy+y^2) 

 + (-6x^2-6xy-y^2)

    + (x^2+xy-4y^2)

     -3x^2 - 14xy - 4y^2

5) 

6) 6x^2-5x+1=0   = ±1,  2 real roots 

7)   Denominator CANNOT = 0, underfined for x = ± 3

 

Hi,

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.

perpendicular to y= 2x-1 ( m = 2), contains (2,7)

New Line:   Note: negative reciprocal of 2

 y = (-1/2)x + b

 7 = (-1/2)·2  + b   |Using ordered pair (x,y): (2,7)  to solve for b

 8 = b

 y = (-1/2)x + 8

 

Hi,

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.

line passing through (0, 2) and perpendicular to the line y = 4x – 3, m = 4

New Line:   Note: negative reciprocal of 4

 y = (-1/4)x + b

 2 = (-1/4)·0  + b   |Using ordered pair (x,y): (0,2)  to solve for b

 2 = b

 y = (-1/4)x + 2

 

Hi,

A = {1,2,3,4,5,6} 

B = {1,2} 

C = {6, 7}

a) A ∩ B   {1,2}  

 b) A U C  {1,2,3,4,5,6,7} 

 c) B U C  {1,2,6,7} 

 d) (A U B) ∩ C  {6}

 e) A U (B U C) {1,2,3,4,5,6,7} 

 f) (A ∩ B) ∩ C  { }

 g) (A ∩ B) U C   {1,2,6,7}

 

Hi,

factor following expression

 2y + xy = y(2+x)

 

Hi,

Factorize: 

x^2-x-20=0

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

 x = 5  0r  x = -4



May check factoring Using FOIL

F	First terms x^2

O	Outside terms 4x

I	Inside terms -5x

L	Last terms  -20

 

Hi,

 x^2 + x = 6

 x^2 + x - 6 =0

by factoring

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

    x = -3  or x = 2

may check factoring Using FOIL

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

 

Hi,

Susan can clean the house in 3 hours. 

Her husband Mike can clean the house in 5 hours. 

How long will it take for both working together to clean the house? 

Question states*** PER hour is Key

    |Multiplying thru by 15x so as all denominators = 1

    5x + 3x = 15

       8x = 15

        x = 15/8 = 1.875 hr

 

Hi,

Yes.  Good work.

E(X) = 

 

Hi,

 , where t is the number of months since January 2010 (Jan 2010 t = 0, Feb t = 1, etc)

The population of butterflies in a local pasture is 60 in January 2010. a = 60

In March 2010, the population of butterflies is 80:  80 = 60b^2 , 

B. According to the model, what will the population of butterflies be in January 2011? t = 12



 C. According to the model, when will the population reach 200? 

 

 

   = t = 8.38 or in the 9th month

 

 

 

Hi,

Of the 375 people who responded

181 people watched movies on VHS tapes.

 245 people watched movies on DVDs. 

66 people watched movies both on VHS tapes and DVDs. 

i. Of those surveyed, how many watched only VHS tapes? 115

ii. Of those surveyed, how many watched only DVDs?  179

iii. Of those surveyed, how many watched VHS tapes or DVDs, but not both? 294 

iv. Of those surveyed, how many watched VHS tapes or DVDs, or both? 360

 

Hi,



 36" by 6" by 8"

 Surface Area = = 1104in^2

 

Hi,

Note:   and 

  = -1/4  as    and 



     

as 

 

Hi,

Note: 

One leg of a right triangle is 7cm shorter than the other leg.

Question states*** area is 30cm^2

        || 

      60 = x(x - 7)

    x^2 - 7x - 60 = 0

   (x - 12)(x + 5) = 0   || Tossing out negative solution for unit measure

      x = 12cm   and y = 5cm

Applying the Pythagorean Theorem: 

P = 12cm + 5cm + 13cm = 30cm

 

Hi,

Paid  = .80 0r 80%,   dress was 20% off

 

Hi,

four is greater than six times a number t.

Write as we Read:

 4 > 6t

 

Hi,







F	First terms

O	Outside terms

I	Inside terms

L	Last terms

 

Hi,

{– 33, –26, –19, – 12, ...}

Artitmetic Sequence, d = 7

 

 = -33

 = -26

 = -19

 = -12

 

Hi,

5 - digit numbers using the 4 digits: 5, 4 , 0, 8

(first digit cannot be zero) There are  = 768 of them