1.Given the quadrilateral ABCD with two diagonals perpendicular and AB = 8cm, BC = 7cm, AD = 4cm. Evaluate CD.
2.Given three consecutive even natural numbers, which have the product of last two numbers is 80 greater than the product of first two numbers.
Find the largest number.
Answer: The largest number is
Find the values of a,b and c such that
\(\left(ax^2+bx+c\right)\left(x-1\right)=-5x^3+4x^2+3x-2\).
Answer: The values of a,b and c are ......... , respectively.
(used " ; " between the numbers)
The lengths of three sides of a triangle are all primes, and the perimeter of the triangle is 17. Find the sum of all possible value(s) of the second longest side.
Given three consecutive even natural numbers, which have the product of last two numbers is 80 greater than the product of first two numbers.
Find the largest number.
Answer: The largest number is ............. .
The lengths of three sides of a triangle are all primes, and the perimeter of the triangle is 4343. Find the sum of all possible value(s) of the longest side.
The sum of 2018 and a 3-digit number is a square number. Find the smallest possible value of the 3- digit numbers
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?
A factory has male and female workers in the ratio of 3 : 5. Some female workers but no male workers resigned. 5 more workers are then employed. The ratio of male to female workers is now 4 : 3 while the number of female workers is 15. Find possible original numbers of female workers.
Suppose n is a positive integer and 3 arbitrary numbers are choosen from the set {1, 2, 3, . . . , 3n+ 1} with their sum equal to 3n + 1. What is the largest possible product of those 3 numbers?
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