Hi,

An airplane flight took 2 hrs. to travel 780 miles with the headwind 

and the return trip with the tailwind only takes 1.5 hrs. 

Let p and w  represent the speed of the plane in still air and the speed of the wind respectively

Question states*** Note: D = rt or  t = D/r

 2 = 780/(p-w)  ⇒ (p-w) = 780/2 = 390  ⇒ p = 

 1.5 = 780/(p+w)    

p+w = 780/1.5= 520   

 + w = 520

       2w = 130  

        w = 65mph   and p = 455mph    || p = 

and****Checking our Answer

 

 

Hi,

Three numbers have the  

The second number is 23 greater than the first number

  and the third is 32 greater than the second number.

Question states***



                3x = 447 - 78

                3x = 369

                 x = 123, the 1st number. The 2nd number is 146 and 3rd is 178

and****

 123 + 146 + 178 = 447

 

Hi,

how much liquid will fit into a container thatis 320 cubic yards capacity ?

Note: 1 yd^3 = 201.97 Gal(US)

 

 

Hi,

An investor invested a total of 1500 in two mutual funds. 

One fund earned 7% profit while the other earned 2% profit. 

total profit was $95

Question states***

  .07x + .02(1500-x) = $95

      .05x = 95 - 30

      .05x = 65

         x = 65/.05 = $1300, invested at 7%.    $200 invested at 2%

and****

 

 

Hi,

when the cost of a car is multiplied by 0.06 the result is 1780.

  .06x = 1780

    x = 1780/.06

 

Hi, Previously Posted

Write the equation of the line which passes through (2, –3) and is perpendicular to y = 4x + 7  ( m = 4/1)

New Line: m = -1/4 (negative reciprocal of 4/1)

 y = (-1/4)x + b

-3 = (-1/4)2 + b

 -5/2 = b

 y = (-1/4)x -7/2    or   x + 4y = -14

 

Hi,

A piece of wire 35/3 inches long is to be divided into two parts such that one part is 2/3 that of the other length

Question states***

      |Multiplying thru by 3 so as all denominators = 1

   3x + 2x = 35in

      5x = 35in

       x = 7in, the shorter piece is  or 4 2/3in

and*****

   

 

Hi,

Note:  

how many diagonals are there in 80 sides? 

how many sides are there in 152 diagonals?

 

   304 = n^2 - 3n

     n^2 - 3n - 304 = 0





 

    n = 19   (tossing out negative solution for n)

 

Hi,

If  and 

2a+7b+8c=3870

 2a + 2a + 2a = 3870

 3(2a) = 3870

   2a = 1290

 

Hi,



the perimeter of a lot is 86 ft.. the length is 19 ft. greater than the width.



  , 

   

 (w + 19ft) + w = 43ft

    2w = 24ft

     w = 12ft  and  l = 31ft

 

 

Hi,

1 = 31                    ||| 1 + 2 = 11 (2 = -20) ⇒ 1 = 31

2 = -20               ||| 4 + 2 = 80 (4=100)  ⇒  2 = -20

3 = 3              |||  3+4 = 103   ⇒ 4 = 100  and 3 = 3

4 = 100

5

 1 + 3 =  31 + 3 = 34

 

Hi, Previously Posted

Write the equation of the line which passes through (–4, 2) and is parallel to y = –x + 6 ( m = -1)

New Line: Parallel..same slope

 y = -x + b

 2 = -(-4) + b

 -2 = b

 y = -x -2

 

Hi,

if 5 is added to a number and the sum is tripled, 

the result is 21 more than the number.

Question states***

 3(x+5) = x+ 21

 3x + 15 = x + 21

    2x = 6

     x = 3

****and...

 

Hi,

A box contains 10 chips. Seven of the chips are perfect, but the remaining three have some imperfection. 

In a random drawing of 4 chips without replacement, what is the probability that all the chips are perfect?

 In a random drawing of 4 chips with replacement, what is the probability that none of the chips are perfect? 0

 In a random drawing of 4 chips without replacement, what is the probability that none of the chips are perfect? 0

 

Hi,

Write the equation of the line that is perpendicular to the x-axis and passing through the point (5,1).

line is x = 5

 

Hi,

the smallest of three consecutives integers,, 

is added to twice the largest, the result so obtained is 15 less than four timess the middle integer.

Question states***

  x + 2(x+2) = 4(x+1) - 15

    3x + 4 = 4x + 4 - 15

         15 = x

The three consecutives integers are 15, 16, 17

and

 

 

Hi,

A box contains 10 chips. Seven of the chips are perfect, but the remaining three have some imperfection.

In a random drawing of 4 chips with replacement, what is the probability that none of the chips are perfect? 0

 In a random drawing of 4 chips without replacement, what is the probability that none of the chips are perfect? 0

 

Hi,

Write the equation of the line which passes through (–4, 2) and is parallel to y = –x + 6 ( m = -1)

New Line: Parallel..same slope

 y = -x + b

 2 = -(-4) + b

 -2 = b

 y = -x -2

 

Hi,

Write the equation of the line which passes through (2, 1) and is perpendicular to x = –2 (vertical line)

 Line is y = 1 (horizontal line)

 

Hi,

Write the equation of the line which passes through (2, –3) and is perpendicular to y = 4x + 7  ( m = 4/1)

New Line: m = -1/4 (negative reciprocal of 4/1)

 y = (-1/4)x + b

-3 = (-1/4)2 + b

 -5/2 = b

 y = (-1/4)x -7/2    or   x + 4y = -14

 

Hi,

x-2y=5

x-2y=2

  5 ≠ 2,  there is NO solution for this system

in slope-intercept method...

x-2y=5   

x-2y=2     Slopes equal, lines parallel (can never intersect)

 

Hi,

Electric current (i) flowing in a circuit is inversely proportional to resistance (R).

 The current flow is 2 amps. When the resistance is 3 ohms:   , 2 = k/3, k = 6

(1) the resistance when the current flow is 5 and 6 amps.respectly. 6/5 ohms = R,  6/6 ohms = R

 (2) the current flow in a circuit when the resistance is 4 and 6 ohms respectly. i = 6/4 amps, i = 6/6 amps

 

Hi,

One number is five more than twice another number 

The two numbers add to 29.

Question states***

  x + (2x+5) = 29

     3x = 24

      x = 8, the samller number. Larger is 21.  

and...

 

Hi,

six times the denominator of a fraction is two less than eight times the numerator 

and ten times the numerator equals 20 less than ten times the denominator.

Let n and d represent the numerator and denominator respectively

Question states***

  6d = 8n-2

 10n = 10d-20  , 

 6d = 8 - 2

  18 = 2d

   d = 9  and n = 7

the reciprocal of the fraction is  9/7

   

 

 

Hi,

if one half of an integer is added to one fifth the next consecutive integer

 the sum is 17.

Question states***

   |Multiplying thru by 10 so as all denominators = 1

   5x + 2(x+1) = 170

      7x ++2 = 170

          7x = 168

           x = 24, the smalller, the larger consecutive integer is 25

and

CHECKING our Answer***

 

 

Hi,

one numbers is two more than the other number

their product is 5 times the smaller number .find the numbers.

Question states***

 x(x+2) = 5x

 x^2 + 2x - 5x = 0

 x^2 - 3x = 0

 x(x-3) = 0

    x = 3  or x = 0 

and...

 CHECKING our Answer***

  and 

 

Hi,

1.What number will you get if you subtract the sum of 567 and 234 from their sum?

 2.A number is 350 more than the quotient of 63 and 7. 

 3.Divide the sum of 35 and 21 by 7 and multiply the result by 6. 

 4.What number will you get if you multiply the difference of 14 and 8 by the quotient of 40 and 5? 

 5.Add the product of 9 and 7 to the difference between 64 and 60.What will be the result? 

 

Hi,

If I raise the rent of my apartment from $2700 dollars to $3000 dollars is that an 11% increase? 3000/2700 = 1.11 0r 11% increase



If I raise it from $2700 to $3200 would that be a 20% increase? 3200/2700 = 1.185 or 18.5% increase

 

Hi,

f(x)=3x-4 and p(x)= 1/x -2

(f+p)(x) = 3x + 1/x - 6

(f+p)(2) = 

 

Hi,

of the following,which is greater than 1/2 = 5/10 = 7/14 = 11/22

2/5 = 4/10

4/7 = 8/14 ****

5/11 = 10/22

 

Hi,

An employer interviews  8 people for 4 technical support positions in a company, and 3 of the 8 people are men. 

If all 8 are qualified, in how many ways can the employer fill the technical support positions if exactly 2 are men

 3C2*5C2= 3*10 = 30 ways