Hi,



horizontal asymtope:  y = 1

 

Hi,

2x-y+z=-4    ||  z=5 

-2x+3y-z=-10 ||   z=5 

 

2x - y = -9       

-2x + 3y = -5    || Adding to eliminate x

     2y = -14

      y = -7  and x = -8    

 

Hi,

How many quarts of pure alcohol must be added to 10 quarts of a 15% alcohol solution 

to obtain a mixture which is 25% alcohol? 

Translatethe 'Mixing' into an equation***expressing ALL in terms of alcohol

    || Solve for x

          .75x = .10·10

             x = 1.3 qt

 

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.

Doesn't get simpler than that:

y = 3x+2   Yes.  m = 3 and the y=intercept is 2   Green

y= -4x+2    m = -4  and the y=intercept is 2      Blue

 

Hi,

A) how many students were taking math but neither English nor chemistry NONE

 B)how many were taking math and chemistry but not English 10

 C) how many were taking English and chemistry but not math 10

 

Hi,



As to least to greatest when u have negatives decimals and fractions:

Might recommend this Number Line Site (Numbers least to greatest read from left to right)

number line

 

Hi,

In a class of 32 are 22 boys what is the percentage ?

 = 68.75%

 

Hi,

Re TY: have You posted Your 2 other?

On checking with 100 families, it was found that 83 subscribe to time, 55 to Newsweek, and 10 to neither. 

How many subscribe to both? 100- 10 = 90.   83+55 - 90 = 48 to both

 

Hi,

How many liters of a 14 percent Alcohol Solution must be mixed with 20 liters of a 50 percent Alcohol solution 

to get a 20 percent alchohol solution. 

Translate into an equation: 

   

   ||| Solve for x

 

Hi,

What is the solutions of x and y for the equations 

x+y=1    

2x-y=-2   ||Adding to eliminating y

 3x = -1

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

 

Hi,

x+5y-4z=-10

2x-y+5z=-9    ||eliminating z

 13x + 21 y = -86

2x-y+5z=-9

2x-10y-5z=0   ||eliminating z

 4x - 11y = -9 

 13x + 21 y = -86

   21x = -105,  x = -5   and y = -1  and z = 0

 

Hi,

find the average rate of change of f(x)= -3x^2 + 4

a- From -2 to 0 

 b- From 3 to 5 

 c- From -2 to 1

 

Hi,

y=√x  Green

1- Reflected about the x-axis (flipped) 

 2- Shift up 7 units 

 3- Shift left 4 units 

 y =   Blue

 

Hi,

f(x)=x³+x, find the average rate of change of f from 1 to x: 

f(x) - f(1)/(x-1) = 

Note:x^3 + x - 2 ,  x = 1 a root 0r (x-1) a factor 

using Synthetic Divsion

1	1	0	1	-2

 	 	1	1	2

 	1	1	2	0

generates the factor

  x^2 + x + 2

 

Hi,

 

Hi,

With fraction subtractions, it is the same as with whole number subtraction...

sometimes You have to 'borrow' ...

   No need to borrow on this one





Borrowing '1' from the 7 is the same as Borrowing  and 

 

Hi,

y = x^3 - 10.5x^2 + 30x +20

y' = 3x^2 - 21x + 30

When Slope = 0, maxima and minina pts are achieved at x.

 3x^2 - 21x + 30 = 0

  x^2 - 7x + 10 = 0

 (x-2)(x-5) = 0  x = 2 or x = 5

f(2) = 46   maxima

f(5) = 32.5 minima

 

 

Hi,

Use the distributive property to rewrite the expression. 

(c+3)2 = 

 

Hi,

y=2x+9

y=7x+8

 2x+9 = 7x+8

   1 = 5x

   1/5 = x  and 

 

Hi,

F(x) = (x-1)^2(2x+3)^3

F'(x) = 

Will Let You finish Up

 

Hi,

Re TY: 

just substitute the x-value given into the EQ y = (x+1)to find the y-value...

y = x+7   (1,_) x = 1, y = 8, Point is (1,8)



y = x+7   ||Note (0,_) represents an ordered pair (x,y)

Question is asking "What is y when x = 0 "

y = 0 + 7  

y = 7  ,  Ordered pair (x,y) is (0,7)

 

Hi,

is this what You meant



IF so...

          

            6 = a

 

Hi,

Re TY, Yes, you certainly had the right idea!



Yes. Consider when the denominator is zero

  3x^2 + x = 0

 x(3x+ 1) = 0   

 x = 0

Or (3x+ 1) = 0  

 x = 0  Or  x = -1/3  makes the denominator zero and make 4x/3x^2+x undefined

 

Hi,





Take a look and finish Up

 

Hi,







 

 

Hi,

A painter can paint a certain house in 12 hours by herself: 

In 5hrs  done.   of the house remaining to complete

helper 15 hours to do the same job himself:

   = 9/60  of the house per hour together

 = 35/9 hr   remaining time together

 

Hi,

eight divided into a number y  

Same as:  y divided by 8  

 

Hi,

74% 'of' 38 is 

 

Hi,

Re TY.  Thank You for calling attention to the typo. 

Andy can paint a room in 4 hours, Betty in 6 hours and Chuck in 8 hours. 

Betty and Chuck work together for 1 hour  0r did  = 7/24 of the room

 17/24 left:   together do 13/24 of room per hour

  = 1.3 hours Andy worked (rounded to the nearest tenth)

 

Hi, Previously Posted

One number is 3 less than a second number 

Twice the second number is  5 less than 3 times the first.

Translating 2nd statement into an equation: 

    2x = 3y - 5     |||  From 1st statement

     2x = 3(x-3) - 5

    2x = 3x - 9 - 5

     14 = x  and y = 11

and...