Hi,

Complete the square for the parabola 

y=3x^2+5x+17 = 3(x+5/3)^2 - 25/3 + 17 = 3(x+5/3)^2 + 26/3 

 

Hi,

 A square's side  is increased by 2 yards,

 which corresponds to an *increase in the area by 36 square yards.

How many yards is the side of the initial square?

  (x+2)^2 - x^2 = 36yd^2

   x^2 + 4x + 4 - x^2 = 36

      4x = 32

       x = 8yds 

CHECKING our Answer***

 100- 64 = 36 

 

Hi,

A father is NOW 5 times as old as his son...yrs old NOW . 

In 18 years, the father will be twice as old as his son.

   5x + 18 = 2(x+18)

    3x = 18

     x = 6yr, son's age NOW.  Father is 30 years old at the present.

 

Hi,

May be accomplished much like any divsion Problem

           3x^2 + (-5x) +   4

        __________________________

2x + 3 | 6x^3 - x^2 -  7x - 9

        - (6x^3 + 9x^2)

       ---------------

                -10x^2 - 7x

             - (-10x^2 - 15x))

                --------------

                         8x - 9

                      - (8x  +12)

                          --------

                               -21

 

Hi,

The Diagonal of a rectangular room is 13ft long. one wall measures 7ft longer than the adjacent wall. 

 13^2 = x^2 + (x+7)^2

 169 = 2x^2 + 14x + 49

  2x^2 + 14x - 120 = 0

  x^2 + 7x - 60 = 0

factoring:

 (x-5)(x+12) = 0

   x = 5  throwing out negative solution for unit measure

 Dimensions of the room are 5ft by 12ft

 

Hi,

A square is made up of section A and section B. 

Section A is 500 sq. ft. and section B is 750 sq. ft. 

What percent of the square is section A?

  500/1250 = .40    or 40%

 

Hi,



(x³ + 2x² - 3x + 2) ÷ (x + 1) 

Using synthetic Division:

-1	1	2	-3	2

		-1	-1	4

	1	1	-4	6

   x^2 + x - 4   R = 6

 

Hi,

Assuming highlighted

(1/16x^4+6/7x^3++7) + (-9/16x^4+3/8x^2-7)

  

  

 

Hi,

 x^2+y^2+16x+18y=-129

 (x+8)^2 -64  + (y+9) - 81 = -129

   C( -8,-9) r = 4

 

Hi, In 3 steps...

(x^2+7) (x^3-5x-4) = x^2(x^3-5x-4) + 7(x^3-5x-4)

                              = x^5-5x^3-4x^2 + 7x^3-35x-28

                              = x^5+2x^3-4x^2 -35x-28

 

 

Hi,

4x-5=6x+11

  -16 = 4x    ||Isolating variable on side of the EQ

   -4 = x

 

Hi,

What is the hypotenuse of the right triangle if it's legs are 11 and 60 units

 

 

Hi,

 

Hi,

The height of a triangle is 6 m more than twice the length of the base.

The area of the triangle is 28 m^2 = L*H

  x(2x+6) =28

  2x^2 + 6x -28 = 0

   x^2 + 3x -14 = 0

 

   = (-3 +8.06)/2 = 2.5 rounded to 1 decimal point (throwing out neg solution for unit measure

length = 2.5m, height is 11m

 

Hi, Re TY, Note: completed the exercise by demonstrating using the 1st  derivative.

The equation is y=(x+2)^2+k where k is a constant.

a)Find k when its tangent at x=1 passes through (0,0). 

y=(x+2)^2+k , y' = 2(x+2), x=1, m = 6, tangent line is y = 6x, Tangent at(1,6)

6 = (1+2)^2 + k, k = 

b)Find k when the quadratic is tangent to y= -x^2, k = -2 (see 2nd graph)

 Taking 1st derivatives of both:  2(x+2) = -2x, x = -1, tangent at (-1,-1)

 -1 = (-1+2)^2 + k, k = -2

 

Hi,

In General 

A = Accumulated Amount

P= principal = 6000

r= annual rate = .03

n= periods per year = 1

t= years = 



 log3/log(1.03) = t

 

Hi,

Please help me graph 

2x^2+6x+5=0     ||Recommend completing Square

y = 2(x+3/2)^2 - 9/2 + 5

y = 2(x+3/2)^2 +1/2  Parabola Opening Upward as 2>0, V(-3/2,1/2)

Axis of symmetry x = -3/2

 

Hi,

a person has deposited rs 25,000 in an investment which yields 14% simple interest annually.

do these amounts (principal+interest) form an arithmatic progression? 

if so, determine the amount of inverstment after 20 years

In General 

A = Accumulated Amount

P= principal =  25,000

r= annual rate = .14

n= periods per year = 1

t= years = 20

= $343,587.25

 

Hi,

a man travels in a motorized boat at the rate of 15 kph from his barrio to the city and comes back at the rate of 12 kph. 

if his total time of travel is 3 hrs. find the distance from the barrio to the city

 D = rt   OR    D/r = t

     |Multiplying thru by 60 so as all denominators = 1

   4x + 5x = 180

    9x = 180

     x = 20mi, the distance from the barrio to the city

 

Hi,

    ||Isolate the radical

  ||Square both sides of the EQ

    3x+6 = (x+14)^2/16

   48x + 96 = x^2 + 28x + 196

        x^2 -20x + 100 = 0

    (x-10)(x-10) = 0

            x = 10

   

 

Hi,

How much demineralized water do you add to 36% HCl to make 1 m3 of 15% HCl.

   water = water

  

          .36x = .21

             x = .583 C^3 water needs to be added

 

Hi,

Please help me solve 2x^2+6x+5=0 

Note:  Using the Quadratic formula is ALWAYS a sure thing:

 

 

 

 

Hi,

John bought a number of notepads for $70. $70/x per pad Four of the notepads got spoiled. 

He sold the remaining notepads at $3 more per pad than he paid, and made a total profit of $10. 

How many notepads did John buy?

  ****

   |||Multiplying thru by x so as all denominators = 1

  70(x-4) + 3x(x-4) = 80x

   3x^2 + 58x -200 = 80x

   3x^2 -22x  - 280 = 0





   x = 14, throwing out the negative solution for count

CHECKING our Answer***  70/14 = $5 pd for the notepads originally

  10· $8 - $70 = $10  

 

Hi

in a scale drawing of a city the distance of 45 kilometers is represented by a line sector 3 inches long .

on the same drawing what distance is represented by a line sector 2 inches long

    ||Cross Multiplying to solve

    3x = 90

     x = 30Km

 

Hi,

Find three consecutive odd integers, , 

such that 3 times the second minus the third is 11 more than the first?

 3(x+2) - (x+4) = x+11

 3x + 6 -x-4 = x + 11

    2x + 2 = x + 11

     x = 9 

  9, 11 , 13

CHECKING our Answer***

3·11 - 13 = 20

 

Hi,





The perimeter of a rectangle is 44 meters the length is 10 meters more than twice the width.

 P = 2L + 2W = 2(2x+10) + 2x = 44m

   2(2x+10) + 2x = 44m

    6x = 24m

     x = 4m, the width.  The length is 18m

 

Hi,

a two-tailed test is conducted at the 5% significance level.  

What is the right tail percentile required to reject the null hypothesis?  

 2.5% 

 

Hi,

In how many ways can 40 contestants in a spelling bee finish first through third?

Order Important:  40P3 = 40!/37! = 59,280 ways

 

Hi,

If i have a total of 16 coins using only nickles and quarters to equal $3, how many quarters will i have?

Note:  CENTS makes sense

 25x + 5(16-x) = 300¢

      20x = 220

        x = 11, number of quarters.  There are 5 nickels



CHECKING our Answer***

25*11 + 5*5 = 300¢ or $3.00

 

Hi,

The mean time taken by all participants to run a road race was found to be 220 minutes with SD= 20min

Using the 68 – 95 – 99.7 Rule, find the percentage of runners who ran this race:

a. In less than 180 minutes (2 SD) (1-.95)/2 = 2.5%

 b. In more than 220 minutes  50%

 c. In between 160 and 280 minutes (3 SD)  99.7%

 d. In at least 240 minutes    84%

 e. In no more than 200 minutes    16%  

 

Hi,

sum of the series S28 for -143+(-134)+(-125)+(-116)+..

Arithmetic Series, d = 9