Hi,

combining Like Terms

3a - 3b + 4a

 

 

Hi,

Factoring

8x^2-30x+7

(4x - 1)(2x - 7)

check Factoring using FOIL

F	First terms  8x^2

O	Outside terms -28x

I	Inside terms  -2x    |Sum of outside terms + inside terms  = -30x

L	Last terms   7

 

Hi,

old combine, crop can be harvested in 60 hours,

new combine can do the same job in 20 hours.

How many hours would it take to harvest the crop with both combines operating?

PER hour KEY

 1/60 + 1/20 = 1/x  |Multiplying thru by 60x so as all denominators = 1

  x  + 3x = 60

     4x = 60

      x = 15hrs it would take with both combines operating

 

Hi,

find the original price of a pair of shoes if the sale price is $56 after a 60% discount

 P - .60P = $56

 P(1-.60) = $56

   P = $56/.40

 

Hi,



Denominator CANNOT be ZERO

 x ≠ 5  and x ≠ -3

Check Factoring Using FOIL

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

 

Hi,

2x+5y=34

x+2y=14     |||Multiplying 2nd EQ by -2, 2nd and adding to the 1st EQ to eliminate  x

   y = 6  and x = 2   



and...

 

Hi,

3 digit number

hundreds digits is 4 more than the units digit and the tens digit is twice the hundreds digit.

units digit   x   

hundreds digits  (x+4) 

tens digit 2(x+4) 

Question states***sum of the digits is 12

(x+4) + 2(x+4) + x = 12

        4x +12 = 12

          4x = 0

           x = 0



Number is 480

 

Hi,

x^3+125=0

 x^3 = -125



    x = -5



and 

 

Hi,

John is 4 times as old as Bill, and Bill is 1.5 times as old as Sam's age 

Sam  x

Bill 1.5x

John 4(1.5x)  0r 6x

Question states***the sum of their ages is 102

 x + 1.5x + 6x = 102

    8.5x = 102

       x = 102/8.5 = 12, Sam's age



and...

 

Hi,

If you meant

  | Cross Multiplying to solve

  2(4y+5) = 3(y-10)

  8y + 10 = 3y - 30

     5y = -40

      y = -8



and...

 

 

Hi,

$50 flat fee for birthday party rental and $5.50 for each person.  

Question states***Carma has no more than $200 to spend on her birthday party.

 $50 + $5.50x ≤ $200

           x ≤ $150/$5.50

           x ≤ 27.27  

How many people can Carma Invite to her party without exceeding her limit. 



and...

 = $198.50

 

Hi,

Isolating 'x' on one side of the Inequality sign*****

4-2x > 7-3x

  x > 3

Isolating 'x' on one side of the Inequality sign, allows us to Read the values allowed for x

 x > 3



and...

  for example...

     -4 > -5  

 

Hi,

Note: Interval Notation

• [ ] a square bracket includes end value listed, 

• ( ) a round bracket does not  Note: round bracket is used for ∞ or −∞

"x  ≤ -3 is equivalent to [-3,oo)? NO

"x  ≤ -3 is equivalent to (−∞,-3] 

 

Hi,

Note: Interval Notation

• [ ] a square bracket includes end value listed, 

• ( ) a round bracket does not  Note: round bracket is used for ∞ or −∞

"x  ≥ 5 is equivalent to [5,oo)? Yes

 

Hi,

Note: Pt(x,y) shown Pt(-3,3)  ||| x = -3  and y = 3 which is Pt(-3,3)

In the graph  f(x) = f(-3) =  , which is the y-value of the Ordered pair(x,y)

 

Hi,

x^3-3x^2+1

Note where the graph changes directions at the blue high point (0,1)

and at the red low point (2,-3)

relative maxima is f(0) = 1  and relative minima is f(2) = -3

 

Hi,

A ship travels 9 miles in 45 minutes. What is its speed in mph?

45/60 = 3/4 hrs

 

Hi,

f(x)=3x+2 

f(-5)= 

 

Hi,

f(x) = 5x + 7 from x1 = -1 to x2 = 0 (moving one unit to the right on the x-axis)

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. slope m =

Find the average rate of change of the function f(x) from x1 to x2. 

 

Hi,

y1=8x+4(7+x) 

y2=3(x-3)+10 and 

y1=y2

 8x + 28 + 4x = 3x-9 + 10

      12x + 28 = 3x + 1

      9x = -27

       x = -3

and...

 

 

Hi,

Find the intercepts of the circle 

(x+1)2 + (y-4)2=9 = 3^2   |Radius of 3

NO x-intercepts, when x = 0, y = 4 ± sqrt(8), (0,1.17) and (0, 6.83)

 

Hi,

6x+2(x-10) > 8x-7 

 6x + 2x - 20 > 8x - 7

   8x - 20 > 8x - 7

      -20 > -7   False Statement...There is NO solution

 

Hi,

y1=3x    || y1 exceeds y2 by 2

y2= (2x-1) 

Question states***

  

  = 2x -1

     x = 1

y1 = 3

y2 = 1

 

Hi,

discount card cost 1500 yen ... 1500/50 = 30 buckets, break even point 



 At least 31 buckets would have to be puchased in order to pay less, overall, with the discount card option 

 

Hi,

an isosceles triangle has two angles whose measures are equal.

If the third angle of the triangle measures 65 degrees 

what are the measures of the other two equal angles?

 65° + 2x = 180°    | sum of all angles of a Trinagle  = 180°

      2x = 115°

       x = 57.5° 

 

Hi,

The difference between two numbers  and   is 67? 

Three times the smaller number plus five times the larger number is 239.

Question states***

  y -  x = 67

 5y + 3x = 239    | multiplying 1st Eq by 3 and addinf to the 2nd to eliminate x

   8y = 239 + 201

   8y = 440

    y = 55   amd x  = -12   

and...

 

Hi,

2x^2+2y^2-8x+12y+2=0

2(x-2)^2 + 2(y+3)^2 = -2 + 8 + 18



See below descriptions of various conics                         

Standard Form of an Equation of a Circle is  

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



 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



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



Standard Form of an Equation of an Hyperbola opening right and  left is:

   with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis

Foci are  units right and left of center along y = k

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



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

The standard form is , where  the focus is (h,k + p)

and  length of  the  latus rectum is 4p.



the vertex form of a Parabola opening right(a>0) or left(a<0), 

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

The standard form is , where  the focus is (h +p,k )

and  length of  the  latus rectum is 4p.

 

Hi,

 SD = 

x	m	(x-µ)	(x-µ)^2	

20.2	30	-9.80	96.040	

22.4	30	-7.60	57.760	

30	30	0.00	0.000	

37.6	30	7.60	57.760	

39.8	30	9.80	96.040	

150			307.600	sum

30.00		sum/4	76.900	Variance

 

Hi,

Find the equation of the line that passes through the point (3,-6) and is parallel to the line 

3x+y-10=0    0r   y = -3x + 10

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. m = -3

parallel Lines have identical slopes

New Line

 y = -3x + b    | Using Ordered pair(x,y), Pt(3,-6) to solve for b



   3= b

 y = -3x +3    0r    3x + y = 3

 

Hi,

Find an equation of a line that has an x intercept of 6 ,Pt(6,0)

and a y intercept of 4 , Pt(0,4)

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.

(6,0)

(0,4) m = -4/6 = -2/3   || 

Line:

 y = (-2/3)x + b  || Using (x,y) Ordered Pair Pt(0,4) to solve for b



   4 = b

 y = (-2/3)x + 4