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To determine the value of xx such that 42x542x5 is a multiple of 9, we can sum the digits of the number and see if the result is a multiple of 9.

The number 42x542x5 can be written as 420+10x+5420+10x+5.

Now, let's consider the sum of the digits:

4+2+0+1+0+x+5=12+x4+2+0+1+0+x+5=12+x

For the entire number to be divisible by 9, the sum 12+x12+x must be a multiple of 9.

To find the value of xx, we need to find a digit such that 12+x12+x is divisible by 9.

Let's try different values of xx from 0 to 9:

• If x=0x=0, then 12+0=1212+0=12 which is not divisible by 9.
• If x=1x=1, then 12+1=1312+1=13 which is not divisible by 9.
• If x=2x=2, then 12+2=1412+2=14 which is not divisible by 9.
• If x=3x=3, then 12+3=1512+3=15 which is divisible by 9.

So, x=3x=3 is the value that makes 42x542x5 a multiple of 9.

To determine if a number is divisible by 3, you can sum its digits and check if the result is divisible by 3.

Let's sum the digits of the number 10011:

1+0+0+1+1=31+0+0+1+1=3

Since the sum of the digits (3) is divisible by 3, then 10011 is also divisible by 3.

If 3x123x12 is a multiple of 3, it means the sum of its digits is also a multiple of 3.

Let's sum the digits:

3+x+1+2=6+x3+x+1+2=6+x

For 3x123x12 to be a multiple of 3, 6+x6+x must be divisible by 3.

We know that if a number is divisible by 3, then the sum of its digits is also divisible by 3.

Let's try different values of xx from 0 to 9 and see if 6+x6+x is divisible by 3:

• If x=0x=0, then 6+0=66+0=6, which is divisible by 3.
• If x=1x=1, then 6+1=76+1=7, which is not divisible by 3.
• If x=2x=2, then 6+2=86+2=8, which is not divisible by 3.
• If x=3x=3, then 6+3=96+3=9, which is divisible by 3.
• If x=4x=4, then 6+4=106+4=10, which is not divisible by 3.
• If x=5x=5, then 6+5=116+5=11, which is not divisible by 3.
• If x=6x=6, then 6+6=126+6=12, which is divisible by 3.
• If x=7x=7, then 6+7=136+7=13, which is not divisible by 3.
• If x=8x=8, then 6+8=146+8=14, which is not divisible by 3.
• If x=9x=9, then 6+9=156+9=15, which is divisible by 3.

Therefore, the value of xx that makes 3x123x12 a multiple of 3 is x=0x=0, x=3x=3, or x=6x=6.

To determine the value of xx such that 35x35x is a multiple of 9, we can sum the digits of the number and see if the result is a multiple of 9.

The number 35x35x can be written as 350+10x350+10x.

Now, let's consider the sum of the digits:

3+5+x=8+x3+5+x=8+x

For the entire number to be divisible by 9, the sum 8+x8+x must be a multiple of 9.

To find the value of xx, we need to find a digit such that 8+x8+x is divisible by 9.

Let's try different values of xx from 0 to 9:

• If x=0x=0, then 8+0=88+0=8 which is not divisible by 9.
• If x=1x=1, then 8+1=98+1=9 which is divisible by 9.

So, x=1x=1 is the value that makes 35x35x a multiple of 9.

The usual form of the number 9×100+7×19×100+7×1 is obtained by simply evaluating the expression:

9×100+7×1=900+7=9079×100+7×1=900+7=907

So, the usual form of the expression 9×100+7×19×100+7×1 is 907.