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## Answers by Amarjeet K.

Let width be x so length = 2x -65   perimeter = 2x + 2(2x-65) = 830 solve for x   2x + 4x - 130 = 830 6x = 960 x = 960/6 = 160   so width = 160 and length = 2x160 -65 = 255 :)

Let one number be x so other number must be x-3/4   x + x - 3/4 = 9  1/4 = 37/4   solve for x   2x = 37/4 + 3/4 = 40/4   x = 40/(2x4) = 40/8 = 5   so one number is 5 and other number is 5-3/4 = 4  1/4 :)...

Let amount Kevin kept for himself = x   x + x/2  + x/4 = 735000   solve for x   7x/4 = 735000 x=420000   Kevin got = \$420,000 Daughter got = 420000/2 = \$210,000 Father got = 420000/4 = \$105,000

Top soil required = 50 x 40 x 0.5 = 1000 cubic feet = 1000/27 cubic yard   Option 1 Bags required = 1000/3 = 333.33 ~ 334 bags cost = 334 x 2.25 = \$751.50   Option 2   Cost = (18 x 1000/27) +50 = \$716.67   Option 1 is less expensive...

Let amount invested in 6% account = X So amount invested in 9% account = X + 2000   Interest earned by 6% account = X x 6/100 x 1 = 6x /100 Interest earned by 9% account = (X+2000) x 9/100 x 1 = 9x/100 + 180   as per question   6x/100...

Let number of T shirts bough6t = x   15x + 6 = 111   solve for x   15x = 111 - 6   x = 105/15 x= 7 :)

πr2h = 1.84 ft3 /min  - as long as flow rate is constant and independent of height of water in the pool.   3.14 x 152ft2 x h = 1.84  ft3 /min calculate h :)

distance between two points whose coordinates are x1y1 and x2y2  ü√(y2-y1)2 + (x2-x1)2   In this case a and b are on x axis and their y coordinates are 0. Plug in values x2 = b and x1=a   Distance = b-a   also we know absolute value of b-a is...

Distance travelled = ∫ (0.3t2 + 8t)dt   Integrate from t = 0 to 4   Distance travelled = 0.3t3/3   + 8t2/2   Distance travelled = (0.3 x 43/3   + 8 x 42/2) - 0 Distance travelled = 70.4 units :)

3x + 5x + 9x = 136 17x = 136 x = 136/7   length of all the pieces are: 3 x 136/7, 5 x 136/7,  9 x 136/7   :)

Assume sister read x books so sagar read x+5   x + x + 5 = 23 2x = 18 x = 9   sister read 9 books sagar read 9+5 = 14 books :)

120 + 1.5x = 150 + 1x   Time of make pies on Monday = 120 minutes Time to make pie on Tuesday - 150 minutes x = number of potatoes   Solve for x   0.5x = 30 x = 60 :)

Volume of sphere, V = 4/3 Π r3   Rate of change of volume with respect to time = dV/dt   Differentiate expression of V with respect to time(per week)   dV/dt = 4/3  x   Π   x   3r2 = 4Πr2dr/dt   radius r...

Function of instantaneous height with respect to time instantanious distance = 6 + ut - 1/2 gt2   u = initial velocity = 20 ft/sec g = acceleration due to gravity t = time   Fucntion of final velocity with respect to time   Final velocity...

1 mole of NaCl will have 6.023 x 1023 atoms   8.56 x 1033 moles will have 6.023 x 1023 x 8.56 x 1033 = 51.55688 x 1056 atoms   :)

Math help!!! (answer)

Assume Bert started with x money   spent on notebook = 4.75   Remaining money = x-4.75   spent on text book = 1/2 (x - 4.75)   remaining money = (x - 4.75) - 1/2(x - 4.75) = 1/2(x - 4.75)   spend on sheet music = 4   remaining...

Math help!!!! (answer)

Second plan will fetch him = .25 + .5 + 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.75   second plan would be most profitable.   :)

Find slopes of both lines. If product of the slopes is -1 then the line are perpendicular.   Slope of line AB = (9-6)/(-4 -1) = -3/5   Slope of line CD = (1-9)/(3-9) = 8/6=4/3   Products of two slopes is not -1 so lines are not perpendicular :)

Assume 100 beans in the soup   Lentils = 36/100  x 100 = 36   Green = 33.33/100   x 36 = 12   If green lentils are removed left beans = 100 - 12 = 88   Left beans = 88/100  x 100 = 88% of original beans   x = 8...

Amount = principal ( 1+ r)n   Amount = 1200 ( 1+ 4.5/100)55-19   = 5852.85

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