I'm very confused!
find all natural number solutions for each congruence.

1. y + 3 ≡ 2 mod 4

2. 3 - y ≡ 5 mod 9

1. y = 4n -1

2. y = 9n -2

Step-by-step explanation:

1. For some integer n, numbers that are congruent to 2 mod 4 are ... 4n+2. Then you have ...

y + 3 = 4n +2 . . . . next, subtract 3 from both sides

y = 4n -1 . . . . values of y are natural numbers for all natural numbers n

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2. Similarly, ...

3 - y = 9n +5

3 - 9n - 5 = y . . . . . add y-9n-5

-9n -2 = y . . . . . . . . collect terms

For every integer n, there is also an integer -n. For our purpose, we're only interested in those values of n that make -9n be positive. Rather than require n be negative so -9n is positive, we can require n be positive and use the expression 9n for the multiple of 9.

We want y a natural number, so we can write this as ...

y = 9n -2 . . . . for natural numbers n

y=x+9

?

step-by-step explanation:

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have