Hi,

Line:

y=5/7x-12   |||Multiplying thru by 7 so as all denominators = 1

7y = 5x - 84

 5x - 7y = 84  ||The Line in standard form

 

Hi,

A woman on a bicycle traveled at a constant speed and moved 150 kilometers in 6 hours.

 

 

Hi,

y = -6.9x + 5.1 

10y =-69x + 51

 69x + 10y = 51   ||Line in standard form

 

Hi,

line perpendicular to y = 1/3x+5  through (2, 1) 

 m = -3

y= -3x + b

1 = -3*2 + b    ||Using (x,y)ordered pair(2,1) to solve for b

7 = b

 y = -3x + 7

 

Hi,

Write the equation in slope-intercept form:  y = mx + b

-11x + 9y = -12 ⇒   y = (11/9)x - 12/9    y-intercept is -12/9= -4/3

 

Hi,

Dawn starts running 5 minutes after Julia does.

Julia runs at an average speed of 8 ft/s : 480ft/min 

Dawn runs at an average speed of 9 ft/s :  540ft/min

how many minutes after Dawn starts running will she catch up with Julia

Translate into an equation: Note: Distance the same for both.  D= rt

 Dawn D = Julia D

  540*x = 480(x+5)

    (60ftpm) x = 2400ft 

      x = 40min  

 

Hi,

2/3 and 5/8  are they proportional?

check the cross products:

&   16  ≠  15, they are NOT proportional

 

Hi,

f(1+sqrt2+sqrt3) = f(4.1463)

f(4.1463)= 2x^4-8x^3-5x^2+26x-28 = 14.702

 

Hi,

a metallurgist has one alloy containing 20% copper and another containing 70% copper. These can be blended to get a mixture between 20 and 70%. 

Create a model to determine how many pounds of each alloy to mix to achieve 

a given weight and copper percentage: 

calculate the mixture needed for 50lbs of 40% copper.

      

                   .50x = .20*50

                      x = 20lbs 70%  and 30lbs 20%

 

Hi,

 

Hi,

 2L + 2W = 228      || Mulitplying 1st EQ by -2 and adding to 2nd

 7L + 4W = 690

     3L = 234

      L = 78'   and W = 36'

 

Hi,

 3 Appetizers

 4 Entrées

 3 Desserts

How many meals can be created if you choose one item from each of the following categories?

 

  

 

Hi,



Denominator x(x^2 - 4)  CANNOT = 0

this happens IF x = -2, 0, 2 

Therefore Domain is  All real numbers except -2, 0, and 2

 

Hi,

A boat travels at an average speed 15km/h in still water. The boat travels 12km downstream 

in the same time as it travels 8km upstream.

  

     | Cross Multiply to solve for c

      4(15-c) = 40

        15-c = 10,  c = 5kmph

 

Hi,

What is the fourth term in the expression of 

(3x-2)^2 = 9x^2 -12x + 4    ||this expression has three terms (n=2, n+1 = 3)

 

Hi,

Not clear what this is...IF  Purple

f(x)=- 1 -2

 x+1 

Below: y = 1/x Green,   f = -1/x Blue

 

Hi,

 

Hi,  Standard Forms are the quidelines

Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center. (a variable positioned to correspond with major axis)

 a and b  are the respective vertices distances from center

 and ±are the foci distances from center: a > b

(x-3)^2/9 + (y+3)^2/16= 1 C(3,-3), V(0,-3)& V(6,-3), V(3,1) &(3,-7), 

F(3, -3 + sqrt(7)) and F(3,-3-sqrt(7))







Standard Form of an Equation of an Hyperbola opening up and down is:

   with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis

Foci units units up and down from center, along x = h

& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a

 

Hi, Standard form is the quideline

Standard Form of an Equation of a Circle is  

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

x^2 + (y-4)^2= 64 center(0,4) radius = 8

 (x+3)^2 + (y+6)^2 = 49 center(-3,-6) radius = 7  eccentricity = 0



·	At eccentricity = 0 we get a circle

·	For 0 < eccentricity < 1 we get an ellipse  

·	for eccentricity = 1 we get a parabola

·	for eccentricity > 1 we get a hyperbola   

·	for infinite eccentricity we get a line

 

Hi,

Lea had $134, and Drew had $180. After both of them spent an equal amount of money shopping, 

Drew had 3 times as much money as Lea.

 Translate into an equation:

   ||Yes, good work.

        2x =  = 222

         x = $111

and..

 

Hi,

A sales person earns $80 for every computer he sells. 

He earns an additional $250 for every 10 computers he sells that month.

Earnings = 80x + 250(x/10) = 2340

                     105x = 2340

                        x = 22.3   At least 23. 

 

Hi,

a study indicates that 4% of american teenagers have tattoos. 

if you randomly sample 30 teenagers  

what is the probability at most 3 teenagers will have tattoos?

bionomial Probability distribution: P = nCx , p = .04, q = .96  and n = 30 

P (x ≤ 3) = P(x=0)+ P(x=1)+  P(x=2) +  P(x=3) = .9694

 

Hi,

how many license plates can be made consisting of 3 letters and 4 numbers, where the numbers and letters cannot be replaced

 

 

Hi,

A regular polygon has 34 sides. whats the size of each interior angle?

 

 

Hi,

a club has 100 members, and 40% of the members have brown hair. 

Of those with brown hair, 30% are boys. 

 

Hi,

The width of a rectangular box is 3 times its height 

and its length is 2 more than its height.

its volume is 288 cubic

Translate into an equation: 

 lwh = 288 in^3

(x+2)(3x)x = 288

  3x^3 + 6x^2 = 288

  3x^3 + 6x^2 - 288 = 0

   x^3 + 2x^2 -96 = 0   x = 4, one solution

  using Synthetic Divsion

4	1	2	0	-96

 	 	4	24	96

 	1	6	24	0

results in:  x^2 + 6x + 24  with imaginary roots

height is 4in, length 6in and width is 12in

 

Hi,

total of 36 coins.

Karla has $4.60 in nickels and quarters.

 Translate into an equation: CENTS makes sense

 25x + 5(36-x) = 460¢

     20x = 280

       x = 14, number of quarters.  There are 22 nickels

and...

 

 

Hi,

if the probability of an event is .46

what is the probability of the complement? 1 - .46 = .54

 

Hi,

Important that you learn how to do these:

 

6x-2y=-4     ||Substitute for y and find x ( then y = 5x)



 ||Substitute for x and find y (then  x = 8-2y)

4x-y=5 



-7x+y=32    || Multiply 1st EQ by -3 and add to eliminate y (you'll find x =-3

2x+3y=27



2x+y=5      || Multiply 1st EQ by 3 and add to eliminate y  (you'll find x =1/2

4x-3y=-10 



4x+2y=7  

x-5y=10     || Multiply 2nd EQ by -4 and add to eliminate x (you'll find y = -3/2

 

Hi,

f(x) = x^2 + 2

f(1/4) = 

 

Hi,