rust8y

F and E are the midpoints of the sides AB and AC of a triangle ABC. X and Y are points on the side BC such that EX and FY are parallel. Show that the parallelogram EFYX has half the area of the triangle ABC.

0 is definitely in the bottom row. Where is its position and what are the digits in the bottom row?

This 2x5 grid is filled with digits which are all different. the 4 digit number B is a multiple of the 4 digit number A. All but one of the 2 digit down numbers are primes. No 2-digit and 4-digit number starts with 0. In which square must 0 be placed? Explain why this is the only possible square. Complete the grid and explain at each step why you placed each digit in a particular position.

This 2x5 grid is filled with digits which are all different. the 4 digit number B is a multiple of the 4 digit number A. All but one of the 2 digit down numbers are primes. No 2-digit and 4-digit number starts with 0. In which square must 0 be placed? Explain why this is the only possible square. Complete the grid and explain at each step why you placed each digit in a particular position.

(Q2) Still stuck. Show that a number which has 0 and 9 as fenders has at least four more fenders. I've worked out (Q3). The smallest 10-fender is less than 700. I've found 630 but cannot explain why it is the smallest.

Someone please help...I'm stuck on these problems. The fenders (factor enders) of 156 are 1, 2, 3, 4, 6, 8, 9 and that 156 is a 7-fender (that is, it has seven fenders) {1},{2, 12, 52},{3,13},{4},{6, 26, 156},{78},{39} Q1 Find a 1-fender which is composite. Is the answer {1, 11, 121} Q2 Show that a number which has 0 and 9 as fenders has at least four more fenders. Q3 The smallest 10-fender is less than 700. Find it and explain why it is the smallest. Another 7-fender is 460 - its set of fenders is {0, 1, 2, 3, 4, 5, 6}, which is different from the set of fenders of 156. Q4 Find three 9-fenders less than 1000 with different sets of fenders.

The integers 1,2,3,...,100 are written on the board. What is the smallest number of these integers that can be wiped off so that the product of the remaining integers ends in 2?

(i) how many odd six-digit palindromic numbers are there? (ii) how many odd seven-digit palindromic numbers are there in which every digit appears at most twice?

i'm having difficulty working out this question find all possible values of d when a certain positive integer N is divided by a positive integer d, the remainder is 7. if 2N + 3 is divided by d the remainder is 1 any help to get me started.........

In an experiment, we were told to make some casein by mixing vinegar with low cream milk. What is casein and the purpose of adding the vinegar?

Two cars on Crete left the towns of Knossos and Phaistos at the same time to drive to the other town, passing each other at Gortyns and both travelling at different constant speeds. The car from Knossos travels 20 km/h faster than the car from Phaistos. The distance from Knossos to Gortyns is 10 km more than the distance from Phaistos to Gortyns. The car from Phaistos completed the journey from Gortyns to Knossos in 35 minutes. Find the distance from Knossos to Phaistos.

(a) Find all positive integers N such that the product 2005 x N has exactly 6 divisors. (b) Find all composite integers M such that the product 2005 x M has exactly 8 divisors.