Hi

Find the x- and y-intercepts of the line, and find the area and the perimeter of the triangle formed by the line and the axes.

 A) 3x + 5y = 15 

I have gotten both intercepts, which are, x-intercept(5,0) y-intercept (0,3).

Plot points, connect with line.   units^2

 

Hi

Note:    and i^2 = -1

 

Hi,  

a vending machine contains dimes and quarters. 

There are 339 coins all together totalling $54.15.

Question states***CENTS make sense

 25x + 10(339-x)= 5415’

      15x = 2025’

        x = 135 Quarters and 204 Dimes

and

CHECKING our Answer***

 = 3375’ + 2040’ = 5415’ or $54.15

 

Hi

4a=3-b

4a=2-b

 3-b = 2-b

  3 ≠ 2   || No solutions for this systen of equations 

 

Hi

The sum of the length l and the width w of a rectangular area is 260 meters. 

(a) Write w as a function of l.

 w = 260 - l

 (b) Write the area A as a function of l.

 A = l(260-l)

 (c) Find the dimensions that produce the greatest area. (When rectangle is a Square)

 l = 130 m

 w = 130 m

for Ex:  and 

 

 

Hi

The distance s that an object falls due to gravity varies jointly as the

 acceleration g due to gravity and the square of the time t of fall

 s = gt^2

rock falls for 2 seconds on earth

 s = 4g

gravity on the moon is 0.172 that on earth

how many seconds would be required for the rock to fall an equal distance on the moon? 

 4g = .172gt^2

 4/.172 = t^2

  4.8sec = t  (rounded to one decimal point)

 

Hi,  

 -(x-4) ≥ 4  OR  

  x-4 ≤ -4   |Note: change of the direction of the Inequality when multiplying thru by -1

    x ≤ 0

 -3x > 9     OR  

   x < -3    |Note: change of the direction of the Inequality when dviding thru by -3

 4x > 12  

  x > 3      |Multiplying or dividing thru with a positve number does NOT change the direction of the Inequality

 

Hi,  

factor: 

5x^2 + 12x = 0    |Note: the use of ^ (uppercase 6)

 

Hi,  

 

Hi,  

Mary is twice as old as Samantha. Bill is four years older than Mary. 

If Samantha is 7 years old, how old is Bill?  Mary is 14  and Bill is 18

 

Hi,  

The area of a rectangular plot 24 feet long and 16 feet wide will be doubled 

by adding an equal distanceto each side of the plot.

Question states*** Note: A = l*w

 2(24*16) = (24 + 2x)16

   48 -24 = 2x

    x = 12' the distance added to each side

and

CHECKING our Answer***

  

 

Hi,  

the cost of 21 objects was 168$.

how many objectscould be purchased for 528$

Info sets Up the Proportion:

    | Cross Multiply to solve for x

 

Hi,  

Solve using the SUBSTITUTION method: 

3x + y = 26    or y = -3x+26  (Green)   |Solving 1st EQ for y, so as to have something to 'substitute' for y in the 2nd EQ

-6x + y = -37 

-6x + (-3x+26) = -37    ||Substituting (-3x+26) for y gives the solution for x

     -9x = -63

       x = 7  and 

Ordered pair (7,5) is the solution for this system of EQuations

 

Hi,  

    |Multiplying thru by 6 so as all denominators = 1

  3x + 2x = 21

     5x = 21

      x = 4.2  

and

CHECKING our Answer***

 

 

Hi,  

x2 + 4y2 + 10x – 56y = -205   |completing the Square

 (x+5)^2 + 4(y-7)^2  = -205 + 25 + 196 = 16

   

C(-5,7) and V(-1,7),V(-9,7)  & V(-5,9), V(-5,5)



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 right and  left is:

   with C(h,k) and vertices 'a' units right and left of center  

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

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



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 

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

& Asymptote 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.

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



the vertex form of a Parabola opening right(a>0) or left(a<0),  where(h,k) is the vertex.

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

 

Hi,  

What is the length of the minor axis of the ellipse given by the equation     

||length of the minor axis = 2*5 = 10 

 

Hi,  

Solve each system by graphing

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

2x+y=8  Points (0,8) and (4,0) on this line

Plot points and connect with respective lines.

Lines parallel.  NO solution for this system of equations

 

Hi,  

x^2+ 2x – 48   | Note use of ^ (uppercase 6)

factoring:  

(x+8)(x-6)     | watch Your signs while factoring... Outside terms and Inside terms = 2x

F	First terms  x^2

O	Outside terms -6x

I	Inside terms   8x

L	Last terms    -48

  

 

Hi,  

Find the sum of the first 32 terms of the following sequence: 

{-10, -2, 6 . . .}  arithmetic sequence d = 8 

 

Hi,  ·

The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0

y = (x+3)(x-3)(x-4), zeros are x = -3,3,4

y = (x+3)(x-3)(x-4) = (x^2-9)(x-4)= x^3 -4x^2-9x + 36   y-intercept is (0,36)

 

Hi,  

Find all the zeros of the equation: 

-4x^4 - 44x^2 + 3600 = 0    | Let X = x^2

-4X^2 - 44X + 3600 = 0

  X^2 + 11X - 900 = 0





  X = 25 OR X = -36

  x^2 = 25,  x= ±5   Zeros

  x^2 = -36  x = ±6i

 

Hi,  ·

three quarters of the sum of two numbers is 6,while one half of their difference is 1

Let x and y represent these numbers

Question states***











   x + y = 8

  x - y = 2

      2x = 10

       x = 5   and 

     

 

Hi,  ·

How to graph the following:

y = -5    Horizontal Line (Green)

x = 1     Vertical Line (blue)

 

Hi,

 Divide -3x^3 - 2x^2 - x - 2 by x – 2   |Note use of ^ (uppercase 6)

Using Synthetic Division:

2	-3	-2	-1	-2

		-6	-16	-34

	-3	-8	-17	-36

   = -3x^2 - 8x - 17   R = -36 

 

Hi,  



As to 512 being 8^3 ... some just know that...

others arrives at that by experimenting dividing 512 by logical selections.. like an 6 or 8

  ******





********

 

Hi,  

-6x+2y=14   | Multiplying (-3x+y = 7) by 2 to eliminate the y variable

 4x-2y=3 

    -2x = 17,  x = -17/2   and 

 Ordered pair (-17/2, -37/2) is the solution for this sytem of equations



 -4x+6y= -14   | Multiplying (2x-3y = 7) by -2 to eliminate the x variable

  4x-5y= 3

       y = -11  and  

 Ordered pair (-13, -11) is the solution for this sytem of equations

 

Hi

What is the equation of y = x^3 with the given transformations? 

horizontal translation right 10 units and vertical translation down 12 units

y = (x-10)^3 -12

Might recommend downloading the FREE graph software at 

http://www.padowan.dk.com  to use in 'checking' Your answers. Picture is worth a 1000 words!

 

Hi,  

 In General 

A = Accumulated Amount $4,300

P= principal = $3,800

r= annual rate = .

n= periods per year = 4

t= years = 2





 log(43/38) =8 log(1 + r/4)

      .0067 = log(1 + r/4)

    10^(.0067) = 1 + r/4    | Solve for r 

 

Hi,  

·The base of an equilateral triangle with side 2a lies along the y-axis such that mid-point of the base is the at the origin.

Note below when a = 1, then  is the distance along the x-axis

Vertices of the Triangle described: (0,a), (0,-a), (a,0)

 

Hi, 

 a man and a boy complete work together in 24 days.*** 

if for the last 6 days man alone does the work then it is completed in 26 days,

 how long will the boy takes to complete the work?

Let x and y represent one's day work by the man and boy respectively

Question states***

  or y = 1/24-x

     , x = 1/32   

 and  would take the boy 96 days alone

CHECKING our Answer***

 

    

 

Hi

A commitee of 6 members is formed out of 7 men and 5 women.

how many commitees can be formed so that at least 1 woman is always on the commitee?

  12C6 - 7C6*5C0