Hi

7 is 175% of what no 

1.75x = 7

    x = 7/1.75 = 4

 

Hi

x-intercept a^2 and y-intercept ab

(a^2,0)

(0, ab)  m = -ab/a^2 = -b/a

y = (-b/a)x + ab

y/b = -x/a + a

x/a + y/b = a

 

Hi

20% of 110  is   = 22

 

Hi

 ⇒ 64^(1/3) = 4 

 

Hi

If P(z > c) = 0.1093, find c.

P(z ≤ c) = 1- 0.1093 = .8907,  c = .81345

 

Hi

find the roots of 

g(x)=6-(x-2)^2 

     6-(x-2)^2 = 0

     (x-2)^2 = 6

        

g(x)= -(x-2)^2  + 6  parabola Opening Downward, V(2,6)

 

Hi

3x - 2y = 6  ||(x,y) ordered pairs (0,-3) & (2,0) on this Line: Plot Pts, connect with line

2x + y = 4   ||(x,y) ordered pairs (0,4) & (2,0) on this Line: Plot Pts, connect with line

 

Hi

Good Work.

 

Hi

NOte:  7^3 = 343

 

Hi

f(x) = ((x+2)(x-3))/((x+1)(x-2))

y-intercept at 3 

 

Hi



A rectangle's length is 3 more than three times its width

 finding the Dimensions is to find the length and width

  2L + 2W = 110cm

   L + W = 55cm       

 3W +3 + W = 55cm

      4W = 52cm

       W = 13cm   and L = 42cm    and   

 A = L•W = 13cm•42cm = 546cm^2 

 

Hi

 

Hi

h(t)= -16t^2 +5t+5 

h(t)=  -16(x- 5/32)^2 + 25/64 + 5

h(t)=  -16(x- 5/32)^2 + 5.3906  ||Parabola opening Downward  V(5/32, 5.3906)

How long did it take for the ball to reach its maximum height?  5/32 sec

How many seconds passed before the ball hit the ground? h(t) = 0

 -16t^2 +5t+5 = 0





          t = .7381 sec passed before the ball hit the ground

 

Hi

10x^2yz^3 - 6x^2y^2z - 4xy^3z^2 

  || Dividing: subtract Exponents

 

 

 

Hi

Original price is $60. 

Percent discount is 15%  (Paying 85% )

 .85 • $60 = $51

 

Hi

 In General 

A = Accumulated Amount 19713.77

P= principal = 

r= annual rate = .07

n= periods per year = 4

t= years = 6







 $19,713.77/1.5164 = P = $13,000.01

 

Hi

find two consecutive even integers whose sum is 442.

  x + (x+2) = 442

      2x = 440

       x = 220

two consecutive even integers are:  220, 222

 

Hi

find the smallest of three consecutive even integers whose sum is 99.

Not possible for even integers to have a sum of 99

 

Hi

21/28÷5/28÷49/28    ||Multiplying by the reciprocals...





       

 

Hi

How many pounds of each kind must he use to make 70 pounds that can be sold for 1.50 per pound?

 has tea worth $1.20 a pound and tea worth $1.90 a pound.

Mixing algebraically

 1.90x + 1.20(70-x) = 1.50 • 70

           .70x = .30• 70

                x = 30lb of the $1.90  and 40lb of the $1.20

and

 

Hi

David emptied his pockets and found that he had 30 coins worth $4.80. 

He only had quarters and dimes.

CENTS makes sense

 25x + 10(30-x) = 480¢ 

      15x = 180

        x = 12, the number of Quarters.  18 Dimes

 

Hi

 D = rt    0r  r = D/t

 r - c  = 14  

 r + c =  28  

  2r = 42

   r = 21mph  and c = 7mph   

 

Hi

how to make 91 cents with 8 coins

91

-1     1 Penny

-50    2 Quarters 

-30    3 Dimes   

-10    2 Nickels

 

Hi

5(2x-8)-2=5(x-3)+3

10x-40-2=5x-15+3    Yes.  Good work.

10x-42= 5x - 12     || Adding -5x and 42 to both Sides of the Eq to combine Like Terms

   5x = 30

    x = 6

 

Hi

using standard form:  y = ax^2 + bx + c

y= -x^2+2    || a = -1 , b = 0  and c = 2

x -intercepts  (when y = 0)

 -x^2 + 2 = 0

   x^2 = 2

   x = ± sqrt(2)

 

Hi

-30x^3-9x^2-3x = -3x(10x^2 - 3x - 1) = -3x(5x + 1)(2x-1)

Check factoring of (10x^2 - 3x - 1) Using FOIL

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

 

Hi

f(x)=2x^2+20x+52 =2x^2+20x + 50  -50 +52 = 2(x+5)^2 - 50 + 52 = 2(x+5)^2 + 2 ,  V(-5,2)

the vertex form of a Parabola opening up(a>0) or down(a<0):  

where(h,k) is the vertex  

 

Hi

A = 64y^2-25z^2 = (8y-5z)(8y+5z)  ||Factors representing one possible set of dimensions

 

Hi

h= -16t^2+80t+48 = 0   (object hitting the ground)

 -16t^2+80t+48 = 0

 16t^2-80t-48 = 0

 t^2-5t-3 = 0



 ||Positive value only for unit measure

0r

 -16(t-5/2)^2 + 100 + 48 = 0

 -16(t-5/2)^2 + 148 = 0

     t = 5/2 ± sqrt(148/16)

     t = 5/2 ± sqrt(37)/2