Hi,previouslyy Posted

 In General 

A = Accumulated Amount

P= principal =  5000

r= annual rate = .04

n= periods per year = 1

t= years =5

 

Hi,re TY, at 28, the age wll be fractional...unusual for age problems..but interesting

steven is 13 years older than his sister sarah age

Together they are 25 years old. 

How old is Steven and how old is Sarah?

Question states*** believe You meant 25 

 Sarah   Steven

  x  +  (x +13) = 25

      2x =  12

       x = 6, sarah's age and Steven is 19

 Sarah   Steven

  x  +  (x +13) = 28

         2x = 15

          x = 15/2, Sarah 7 1/2 yrs old and Steven 20 1/2 years old

      

 

Hi,

 In General 

A = Accumulated Amount

P= principal =  5000

r= annual rate = .04

n= periods per year = 1

t= years =5

 

Hi,

(x-5)/9 ≤ - 2     \Note:  using parenthesis makes it very clear

 x-5  ≤ -18

   x ≤ -13

 {x : x ≤ -13 }

 

Hi,

find the vertex, line of symmetry, min or max and graph. 

f(x)= -2x^2+2x+1        |Completing square y = ax^2 + bx + c   ⇒ y = a(x -(-b/2a)^2) - a(-b/2a)^2 + c

f(x)= -2(x-1/2)^2 + 1/2 +1

  V(1/2,3/2,maximum   -2<0, parabola opens downward along x =.5



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)



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 )

 

Hi,

  ⇒  and y = 2

 

Hi,

 y = mx + b

 y = 2x ,  slope m = 2

 

Hi,

f (x)= sqrt(x)  Green (nice to keep in mind what this looks like)

f(x) = sqrt(x+6) is shifted 6 units to the left.  Blue

 

Hi,

Number such as 32, true it is are not a perfect square...

But...it may have a perfect square as one of its factors, which allows for simplyfying it:

for ex:

 

 

  

 

Hi,

Note:   

 

Hi,

Mary Lou has 2 more nickels thanpennies, 

and she has 30 coins all together

Question states***

Pennies +  Nickels = 30 coins

   x    +  (x+ 2)  = 30   Solve for x (the number of pennies)

 

Hi,

what is the length of the transverse axis of the hyperbola defined by the equation 

(y+3)^2/7^2- (x+3)^2/3^2=1  

length of the transverse axis = 14, the distance between the vertices along x = -3





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 

 

Hi

a positive number is 5 times another number   

if 21 is added to both the numbers:     

then one of the number becomes twice the other new no. what are the nos.

Question states*** Note: as x is a positive number...5x is larger that x

     5x + 21 = 2(x+21)

         x = 7, the smaller number.  larger number is 35

and

CHECKING our Answer*** 

    35+21 = 56 = 2(7+21) = 2*28

 

Hi

find three consecutive integers  ,   ,  

for which the sum of the squares is 65 more than three times the square of the smallest intege

  x^2 + (x+1)^2 +(x+2)^2 = 3x^2 +65

Expand, Solve for x, List the 3 Integers. 

 

Hi,

write the equation of the line with slope = 4/5 and containing the point (3,7)

 y = mx + b

 y = (4/5)x + b

   |  using pt(3,7) to find b

    7 = 12/5 +b

   35/5-12/5 = b = 23/5

 y = (4/5)x + 23/5

 

Hi,

What is the slope of the line passing through the points 

b–1, – 4g and 

b–7, – 4g    m = 0/6 = 0

 

Hi,

how do i graph this?   

I. find 2 points (x,y) on this line 

II. Plot points on graph

III. then connect those points with a line

2x - 3y = 6 

x = 0  ⇒   Pt(0, -2) on this Line

y = 0  ⇒   Pt(3, 0) on this Line

Plotting these points and connecting with a line

 

Hi,

  Note: 

 

Hi,

Note:Standard Form of an Equation of a Circle is   

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

 

    C(0,0)     

 

Hi,

Note: Standard Form of an Equation of a Circle is  

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



Write an equation of the line tangent to the given circle at the given point.

 (-4,6)  || Center of the circle is (0,0)

(-4,6)

(0,0) m = 6/-4 Green Line has slope m = -3/2, 

the Line Tangent at (-4,6) would be perpendicular to the Green with m = 2/3

 y = (2/3)x + b

 6 = -8/3 + b,  

  26/3 = b ,     y = (2/3)x + 26/3

 

Hi,

Note: D = 

what is the distance between 

(-4,-12) and 

(11,-6)     D = 

 

 

Hi,

 = (3x - y + 4z)(3x - y + 4z)

                 = 3x(3x - y + 4z)-y(3x - y + 4z)+4z(3x - y + 4z)

                 = 9x^2 - 3xy +12xz - 3xy + y^2 - 4yz + 12xz - 4yz + 16z^2

Yes Good work!   = 9x^2 + y^2 + 16z^2 - 6xy + 24xz - 8yz 

 

Hi,

4 times my daughters age... today 

7 years earlier i was 11 times her age

Question states*** 7 years earlier...

 mother

   4x  -7 = 11(x-7)

       70 = 7x

        x = 10, daughters age now.  Mother is 40

and

CHECKING our Answer*** 7 years earlier...

      

 

Hi

Note: 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

Write the equation of the ellipse with the given characteristics and center at (0,0).

 Vertex: (4,0)

 Co-Vertex: (0,2)

 

 

 

Hi,

A student scored 67, 81, and 98 on three algebra tests.

What must he scoreon the fourth test in order to have an average grade of at least 85?

Question states***

  (67+81+98+x)/4  ≥ 85

  67+81+98+x ≥ 340    solve for x

 

Hi,

Find the range for the measurement of the third side of a triangle, x, 

given the measures of the two sides: 3.8 ft and 9.2 ft.

 3.8t + 9.2ft = 13ft, 

 3rd side < 13ft   || Note:  sum of two sides must be greater than the 3rd side

 

Hi

Monica can type a proposal in 3 hours. while jose can type the same proposal in 5 hrs. 

How longwould it take them to type the proposal if they work together?

Question states*** PER hr KEY

  1/3 + 1/5 = 1/x      |Multiplying thru by 15x so as all denominators = 1

     5x + 3x = 15    Solve for x

 

Hi,

Jose is 27 years older than his son age    

10 years from now, he will be twice as old as his son. 

How old is each now?

Question states***  10yrs from now...

 father

 (x + 27) + 10 = 2(x + 10)

       x + 37 = 2x + 20,  

                x = 17, son's age.  Father is 44.  (17+27)

and..

CHECKING our Answer***10yrs from now...

   54 = 2*27

 

Hi,

Note:Standard Form of an Equation of a Circle is   

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

 =12    C(0,0)     

 

Hi,

Note:Standard Form of an Equation of a Circle is   

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



  C(0,0)   

 

Hi,

A small swimming pool can be filled with water by 2 pipes in 3 hours. 

If the larger pipe alone takes 8 hours less than the smaller pipe hrsto fill the  pool

find the time in which it will be filled by each pipe operating singly

Question states***PER hr Key

  |Multiplying thru by 3x(x-8) so as all denominators = 1

  3(x-8) + 3x = x(x-8)

  3x - 24 + 3x = x^2 - 8x

            x^2 -14x + 24 = 0

            (x - 12)(x - 2) = 0

                   x = 12hr  (throwing out illogical solution x = 2)

  Smaller Pipe takes 12hr and the larger Pipe 4hrs to fill the pool by itself