Hi,

Write in decimal form 

(3 x 10^1) + (4 x 10^0)



 30 + 4 = 34 

 

Hi,

 

Hi,

one number is 5 more than another

Question states*** the difference of their squares is 30

 y^2 - x^2 = 30       | y = (x+5)

(x+5)^2 - x^2 = 30    

   x^2 +10x + 25 - x^2 = 30

         10x = 5

           x = .5, the smaller number.  5.5 the large number y.



and...



  

 

Hi,

 

 

Hi,

P(-.55 < z < .55) = .4176    | Note: cannot have a  -probability

 

Hi, re TY, note highlighted.  

Please carefully follow the work, so as you may learn how to others like it.

Solve the system of equations by using the inverse of the coefficient matrix.

 x+6y=-16 

-5x+6y=8 

                                  

 = 







and...

 

Hi,

Please carefully follow the work, so as you may learn how to others like it.

Solve the system of equations by using the inverse of the coefficient matrix.

x+8y=-29 

2x+3y=-19

                                  

 = -13







and...

 

Hi,

   |Multiplying thru by x so as all denominators = 1

 

 

 

  |multiplying denominator and numerator by y

 

Hi,

Mark had 3 times more marbles than Isabella.  Isabella had 2/3 as many marbles as Jack's  marbles 

Jack    

Isabella      

Mark       2x                  

       

                x = 27, number Jack has. Isabelle has 18  and Mark 54



and...  

 

Hi,

half life problems on this site are found under:

Algebra: Exponent and logarithm as functions of power

As Decay is generally describe using:



 fnding the value of k = ln2/(half life) and using that value into the general EQ to find Q(t)

 

Hi,

my hundreds digit is 2 more than my ones digit and my tens dgit is 1 less than my hundreds digit

results all depend on what the ones digit is....

210, 321, 432, 543, 654, 765,  876, 987

 

Hi,

If You meant

   |Note;  Cannot divide by ZERO  

Domain (allowable x-values) is all real numbers such that x ≠ 7

 

Hi,





       rounded to the nearest tenth

 

Hi,

takes Kurt twice as long to earn $60  as it takes Paul to earn $40 

Let x represent Paul's time 

Question states*** 

Kurt:  or 

Paul:   or 

ratio of Kurt's pay per hour to Paul's pay per hour

 

 

Hi,

Question states*** They each drive the same amount of time:  t = D/r

Let x represent the amount of distance driven by Kelvin

       | Cross Multiplying to solve

       60x = 50(385-x)

      110x = 19250

         x = 175, distance driven by Kelvin.  t = 175/50 =3.5 hrs 

left home at 3:00 P.M. met at 6:30 P.M.



and(just checking...) Sandy's time = 210/60 = 3.5 hrs 

 

Hi

If 3,000 dollars is left in an account for 4 years, the earned interest is $84  or $84/4 = $21 per year

In 7 years:  7*$21 = $147 in interest would be earned

 

Hi,

Solve the system of equations by using the inverse of the coefficient matrix.

 x+5y = 25 

5x+5y = 45

                                  

 = -20







and...





Checking our answer using the Elimination Method:

 x+5y = 25 

5x+5y = 45   |Subtracting 1st EQ from the 2nd

  4x = 20  

   x = 5  and y = 4  as 

(x,y) Ordered pair (5,4) the solution for this system of equations

  

 

 

Hi, Previously Posted

x^2- 12x = -5

x^2 - 12x + 5 = 0

 

 

 

 

  x = 11.57  or x = .43   rounded to the nearest hundredth

 

Hi,

x^2- 12x = -5

x^2 - 12x + 5 = 0

 

 

 

 

  x = 11.57  or x = .43   rounded to the nearest hundredth

 

Hi,

3x − 5y + 2z = 2

 x − 3y + 2z = 2

5x − 11y + 6z = 6

Dependent system as D =0, as well as Dx=0, Dy= 0 and Dz = 0

or as demonstated by selecting different pairs of EQs and eliminating z for both: 

2x - 2y = 0

2x - 2y = 0    |Subtracting 2nd from 1st

     0 = 0   Dependent System

Dependent relationship in terms of z: (z-1, z-1, z)

 x = z - 1     |Eliminating y-variable using a pair of EQs

 y = z - 1     |Eliminating x-variable using a pair of EQs

 

Hi,

Solve the system by putting each of their graphs on the same graph

the point they intersect at: (-2,6) is the solution for this system



If You are having difficulty graphing each of the linear equations:

find at least 2 (x,y)points for each and connect pair of the 2 points with their

respective line 

2x+y=2   x = 0  ⇒ y = 2,  y = 0  ⇒ x = 1  (0,2) and (1,0) on this line

6x+4y=12   x = 0  ⇒ y= 3,  y = 0  ⇒ x = 2  (0,3) and (2,0) on this line

 

Hi,

 

Hi,

A manufacturer pays its assembly line workers $11.14 per hour. 

In addition, workers receive a piece work rate of $1.24 per unit produced. 

   where x is number of units produced per hour

 

Hi,

 She earns a weekly salary of $225 plus a commission of 3.5% on all her sales.

$3595 in sales  ⇒ she earns:  $225 +  .035*$3595  =  $225 + $125.83 = $350.83

 

Hi,

Find the slope of the line that passes through the pair of points 

(-3,5),

(-4,5)   m = 0/1 = 0    

  m = 0 , this is a horizontal line, y = 5

 

Hi,

Why is 

 

Hi,

x+y+z=11

2x+3y++2z=27

x+2y+2z=19

 D = 1, Dx = 3, Dy = 5, Dz = 3

 , ,  

 

Hi,

8(3x-4)=4(6x+7)

 24x - 32 = 24x + 28

    -32 ≠ 28, there is NO solution

 

Hi

has oil worth 36 a quart and oil worth 52 a quart

Let x represent number of quarts woth 52  a quart

Question states**wishes to produce 300 gallons( 4qts/gal) of oil worth 40 a quart*

   Money = Money

 52x + 36(1200 - x) = 40(1200)  

         16x = 4800

           x = 300 qts at 52   and 900 qts at  36



and 

  

 

Hi,

Mark had 3 times more marbles than Isabella.  Isabella had 2/3 as many marbles as Jack's  marbles 

Jack    3

Isabella      2

Mark       2x             6     

         Jack needs to have at least 3 marbles 

  or a multiple of 11 is the number of marbles there could have been.

 

Hi,

Find two consecutive integers,  whose product is 72.

 x(x+1) = 72

 x^2 + x - 72 = 0

(x+9)(x-8) = 0 , x = -9  or x = 8

two consecutive integers are:  -9, -8   or  8, 9

There are no  two consecutive even integers whose product is 72



Find two consecutive even integers , whose product is 168. 

 x(x+2) = 168

 x^2 + 2x - 168 = 0 

(x+14)(x-12) = 0. x = -14   or x = 12

two consecutive even integers are:  -14, -12   or 12, 14