What is the numeral preceding and succeeding each of the following.
a) 640 base 7
b) 1 base 2
c) 555 base 6
d) 100 base 5
e) 1 base 4
f) 405 base 6

a) and  

b) and  

c) and  

d) and  

e) and  

f) and  

Step-by-step explanation:

The logics followed in order to find them:

Base numbers work exactly the same as base 10 numbers (the ones we use on a daily basis). Take for example, in a decimal system, we have 10 digits available:

0,1,2,3,4,5,6,7,8,9.

when counting, when we get to the 9, we start over again, but writting a 1 to the left.

0,1,2,3,4,5,6,7,8,9,10,11,12....20,21,22,23....,90,91,92,93,94,95,96,97,98,99,100

when reaching 99, we have no more digits to use, so we start the count again and go from 99 to 100.

The same works with any other base number, take for example the base 7 numbet. When counting in base 7, we only have 7 digits available: (0,1,2,3,4,5,6) So when we re0_{7},ach the digit 6, we go immediately to 10, like this:

notice how it went from 6 to 10 and from 16 to 20. This is because in base 7, there is no such thing as digits from 7 to 9, so we don't have any other option to go directly to 20.

So, on part A) if we were working with decimal numbers, the  previous value for 640 would be 639, but notice that in base 7, there is no such thing as the digit 9, so the greatest digit we can use there would be 6, therefore, the previous value for the number would be . The next number would be because the 1 does exist for a base 7 system.

The same logics is followed for the rest of the problems.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc