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Fill in the circles with the numbers 1, 2, 3, 4, 5, 6 and 7. Each number can be used once without repetitions. The sum of the digits inside the circles at the four vertices of the square on the left is 15 and the sum of the digits inside the circles at the vertices of the regular pentagon on the right is 24. How many possible arrangements are there?
Suppose the 6 digit number 18abc2 can be divided evenly by both 17 and 31. Find the largest possible value for a+b+c
the sum of the digits of a two-digit number is 11. when you reverse its digits you decrease the number by 9 . Find the number
let p(x) be a real polynomial of degree 2015. suppose that P(n) =n/n+1 for all n=0;1;2;...;2015
The value of P(2016) is .........
n lines are drawn on a piece of paper to divide it into 172 regions. Find the smallest possible value of n
A certain number of fifty-cent coins is to from an equilateral triangle. The same number of fifty-cent coins can also be used to from a square. The number of fiftty-cent coins on each side of the square is 6 fewer than the number of fifty-cent coins on each side of the equilateral traingle. How many fifty-cent coins are there altogether?
Find the number of 3-digit positive numbers that have product of digits equals to 21.
1. Two bisector BD and CE of the triangle ABC intersect at O. Suppose that BD.CE 2BO.OC . Denote by H the point in BC such that .OH⊥BC . Prove that AB.AC 2HB.HC 2. Given a trapezoid ABCD with the based edges BC3cm , DA6cm ( AD//BC ). Then the length of the line EF ( Ein AB,Fin CD and EF // AD ) through the intersection point M of AC and BD is ............... ? 3. Let ABC be an equilateral triangle and a point M inside the triangle such that MA^2MB^2+MC^2 . Draw an equilateral triangle ACD whe...
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1. Two bisector BD and CE of the triangle ABC intersect at O. Suppose that BD.CE = 2BO.OC . Denote by H the point in BC such that .\(OH⊥BC\) . Prove that AB.AC = 2HB.HC
2. Given a trapezoid ABCD with the based edges BC=3cm , DA=6cm ( AD//BC ). Then the length of the line EF ( \(E\in AB,F\in CD\) and EF // AD ) through the intersection point M of AC and BD is ............... ?
3. Let ABC be an equilateral triangle and a point M inside the triangle such that \(MA^2=MB^2+MC^2\) . Draw an equilateral triangle ACD where \(D\ne B\) . Let the point N inside \(\Delta ACD\) such that AMN is an equilateral triangle. Determine \(\widehat{BMC}\) ?
4. Given an isosceles triangle ABC at A. Draw ray Cx being perpendicular to CA, BE perpendicular to Cx \(\left(E\in Cx\right)\) . Let M be the midpoint of BE, and D be the intersection point of AM and Cx. Prove that \(BD⊥BC\)
1,A circular cynlinder with a volume 81 pi.if the perimeter of the base is 6 pi,the height is ?2,The total surface area of 2 indentical blocks which together with the volume is 1,458 units is ?3,If one side of 6-inch ruler will be marked in inches,how many points will be in the edge including 0 and 6 inch mark?4,Two sides of the O and P pointer that started from a vertical position as shown.Pointer O turns back the clock with a speed of 5 degrees per second and pointer P rotate clockwise at9 deg...
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1,A circular cynlinder with a volume 81 pi.if the perimeter of the base is 6 pi,the height is ?
2,The total surface area of 2 indentical blocks which together with the volume is 1,458 units is ?
3,If one side of 6-inch ruler will be marked in inches,how many points will be in the edge including 0 and 6 inch mark?
4,Two sides of the O and P pointer that started from a vertical position as shown.Pointer O turns back the clock with a speed of 5 degrees per second and pointer P rotate clockwise at9 degrees per second.How many complete revolutions will be made when completing 335 P O complete revolution?
5,In a certain game of 50 questions,the final score calculated by subtracting tiwce the number of wrong answer from the total number of correct answers.if a player has tried all questions and get a final score of 35 ,the number of wrong answers,he has to be ...