Hi

Hi

  | Recommend cross multiplying to solve for a

 1.25a = .5*5      |* indicates completing the 'cross multiplication' process

     a = 2.5/1.25  | .5 multiplied by 5 is 2.5

     a = 2

Hi

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

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

y= 5/8x –2 has a slope m = (5/8). A line parallel to it would have a slope m =5/8

as parallel lines have slopes that are equal to one another

Hi

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

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

y= 5/8x –2 has a slope m = (5/8). A line ⊥ to it would have a slope m = -8/5

as ⊥ lines have slopes that are 'negative reciprocals' of one another

Hi

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

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

I. solve for y

4x + y= -7    |solving for y

   y = -4x - 7   Slope m = -4 and y-intercept is -7

II. Plot the y-intercept Pt(0,7)

III. using the slope of -4/1 to plot one or two more points: (-1,-3)for ex

 m = -(4/1) as y increases/decreases by 4, x value changes by 1 in the opposite direction

IV.  connecting points with a line completes the graphing

Hi

Let x represent the grams of hemoglobin in 39cm^3

Question Sets Up the Proportion***

   |cross multiply to solve for x

 10cm^3x = 1.2g*39cm^3

       x = 1.2g*39cm^3/10cm^3

       x = 4.68g

Hi

16x^3-144x^2-81x+729   |dividing by (x-9)

(x-9) (16x^2 - 81) 

(x-9)(4x-9)(4x +9)

Hi

simplifying

2w + 8w + 5   |Combining Like terms

  10w + 5

Hi

x + 22 = 46        |isolating x on one side of the equation to find the solution

x + 22 - 22 = 46  - 22  |subtracting 22 from both sides of equation

       x = 24

Hi

the second is 2 times the third

Let x and 2x represent the third and second angles respectively

question states***

72° + 2x + x = 180°

solving for x

     3x = 108°

      x = 36°, the second angle.  The third is 72°  (2*36°)



CHECKING our Anwer

  72° + 36° + 72° = 180°

Hi

x + 4 < 3   x < -1  to the Left of -1 on number Line

-4x < -12   x > 3   to the Right of 3 on number Line

these two Inequalities have NO numbers in common

Hi

3z + 7 > 2z + 3

  z > -4

 z = (-4,)

Hi

-6x > -24  OR x < 4  |dividing by negtive number reverses the direction of the Inequality

x + 6 > 5  OR x > -1

 (-1,4) is the interval notation for the solution set

On the number line, the portion of the line between -1 and 4 would represent

the solution set of these Inequalities (open circles on the -1 and 4)

Hi

angle 1 is 6 more than 3 times its supplement(angle 2), 

Let x and (3x + 6) represent ∠2 and ∠1

Questions states***(Note: sum of supplementary angles is 180°

 x + (3x + 6) = 180°

solving for x

   4x = 174°

    x = 43.5°, meausre of ∠2.  Meausre of ∠1  is 136.5°  (3*43.5°+ 6°)



CHECKING our Answer

  43.5° + 136.5° = 180°



Note: If a question is regarding 'complementary' Angles: their sum is 90°

Hi

how many different ways can 5 students be seated in a row?

 5! = 5*4*3*2*1 = 120 ways

Hi

Let x, 2x, 4x represent the number of nickels,dimes and quarters respectively

Questions states*** Cents amke sense!

 5x + 10*2x + 25*4x = 1250 CENTS

solving for x

  125x = 1250

     x = 10, the number of nickels.  There are 20 dimes and 40 quarters



CHECKING our Answer

  50 + 200 + 1000 = 1250 or $12.50

Hi

If $1000 more is invested at 9% than at 10% per year

Let x and (x+1000) represent the amount at 10% and 9% respectively

question states*** $150/mo (interst over 12months)

 .10x + .09(x+1000) = $1800

solving for x

   .19x + 90 = 1800

       .19x = 1710

          x = $9000, amount invested at 10%.  10,000 at 9%



CHECKING our Answer***

   $900 + $900 = $1800

Hi

sum of the two rates was $130 per hour

Let x and (130 - x) represent  the $/hr of the 15hr and 5hr mechanics respectively

Questions states***

 x*15hr + (130-x)5hr = $1500

solving for x

  15x -5x + 650 = 1500

           10x = 850

             x = $85 for one mechanic.  the other $45  ($130 - $85)



CHECKING our Answer

 15*$85 + 5*$45 = $1500

Hi

'sum of a and 9'

Write as we Read***

  a + 9

Hi

Let x represent the days it would take with both computers working on it

Question states***per day the Equalizer

 1/8 + 1/5 = 1/x  |mulitplying each term by 40x so as all denominators = 1

 5x + 8x = 40

    13x = 40

      x = 40/13 = 3.0769 days with both computers working on it

Hi

cos330° = 

sin330° = -1/2





thought You might find this (cosx,sinx) summary helpful

Hi

each of the two longer sides of the triangle is three times as long as the shortest side

Let x, 3x and 3x represent the length of the sides

Question states***

  x + 3x + 3x = 84cm

solving for x

     7x = 84cm

      x = 12cm, the shortest side, the other two sides are 36cm and 36cm



CHECKING our Answer

  12cm + 36cm + 36cm = 84cm

Hi

Let x represent the nember

Write as we Read***

 (2/3)x = 3x+ 7

solving for x

   -7 =  7/3x

   -3 = x



CHECKING our Answer***

 (2/3)*-3 = -6/3 = -2 =  3*-3 + 7 

Hi

Three years ago I was six times as old as you

Let x and 6x represent Amanda's and her grandmother's ages '3 years ago'

Question states*** 6 years after that time...

 6x + 6 = 4(x + 6)

solving for x

 6x + 6 = 4x + 24

    2x = 18

     x = 9, Amanda's age 3 year ago. Her grandmother was then 54.

NOW, the grandmother is 57



CHECKING our Answer*** (Amanda is NOW 12)

57 + 3 = 4(12 + 3) = 60



  

Hi

width is half the height

Let x and x/2 represent height and width respectively

Question states***

 x(x/2) = 50 ft^2

solving for x

 x^2/2 = 50 ft^2

  x^2 = 100 ft^2

    x = ± 10  |Tossing out negative solution for length

    x = 10ft, the height of the wall.  the width is 5ft  ((1/2)*10ft)

Hi

B=1000e^(kt)

Question states

4134/1000 = e^4k

 4.134 = e^4k

ln(4.134) = 1.4192

 1.4192 = 4k

   .3548 = k

Hi



  |factoring the numerator

 Note:SUM of the inner product(-.5x) and the outer product(-16x) = (-33/2)x

  2(x -.5) OR  2x + 1

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.  

y = -3x + b  |Using ordered pair Pt(4,-1) to solve for b

-1 = -3*4 + b

11 = b

y = -3x + 11

Hi

1 hr = 3600 sec or week 13 would be ~ 1hr of  homework

Let n represent the number of weeks

1,2,4,8,16,32,64,128,256,512,1024,2048,4096...

a[n] = 2^(n – 1)

a[36] = 2^35 = 34,359,738,368 sec = 9,544,371.7689 hr

Hi

A= p(1+r/n) ^nt 

A/p = 2 = (1+r) ^10

      1.0718 = (1+r)

       .0718 = r

A = $4500(1.0718)^50

A = $144,178.38

Hi

Let x and (30-x) represent the amount of the $5 and $3.50/lb candies respectively

Question states***

Mixing to form 30lbs of $4.50/lb

 5x + 3.50(30-x) = 4.50*30

          1.5x = 1*30lb

             x = 1*30lb/1.5

             x = 20lb, the amount of the chocolate hearts

                 10lb of the candy kisses



CHECKING our Answer

  5*20 + 10*3.50 = 100 + 35 = 4.50*30 =