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Jake required to find out the perimeter of an equilateral triangle whose sides measure x + 4 cm each. Jake realized that he could multiply 3 (x + 4) = 3x + 12 to find out the total
Martha has $20 to spend and would like to buy as several calculators as possible along with the money. The calculators that she needs to buy are $4.50 each. How much money will she
Short Cuts for solving quadratic equations
A circular pool is filling along with water. Supposing the water level will be 4 ft deep and the diameter is 20 ft, what is the volume of the water required to fill the pool? (π =
verify liouville''s theorem for y''''''-y''''-y''+y=0
Following are some examples of complex numbers. 3 + 5i √6 -10i (4/5) + 1 16i 113 The last t
A bag holds 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble is selected at random. What is the probability in which the marble chosen is blue? The probability of blue
mathematical induction theorem
Let f : R 3 → R be de?ned by: f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y
Find out the greater of two consecutive positive odd integers whose product is 143. Let x = the lesser odd integer and let x + 2 = the greater odd integer. Because product is a
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