Answer: (D) 
Explanation:
Just a note on writing down these expressions: I recommend using parentheses whenever you can to avoid misinterpretation. An expression 1/x-1/y / 1/x+1/y could be interpreted by someone as 1/x-(1/y / 1/x)+1/y, which is a different thing.
<span>Ayesha's right. There's a good trick for knowing if a number is a multiple of nine called "casting out nines." We just add up the digits, then add up the digits of the sum, and so on. If the result is nine the original number is a multiple of nine. We can stop early if we recognize if a number along the way is or isn't a multiple of nine. The same trick works with multiples of three; we have one if we end with 3, 6 or 9.
So </span>
<span>has a sum of digits 31 whose sum of digits is 4, so this isn't a multiple of nine. It will give a remainder of 4 when divided by 9; let's check.
</span>
<span>
</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1. So we see multiplying by 10 doesn't change the remainder. So
has the same remainder as
.
When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder. Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
<span>
It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:
</span>
The equation to model the above scenario is 
+22x - 23 = 0
The perimeter of the expanded rectangle is 48 units
<h3>What is a rectangle?</h3>
A rectangle is a quadrilateral with its 4 angles 90°
Analysis:
First rectangle:
length = 10 + x
width = x
Second rectangle:
length = x + 14
width = x + 8
Area of expanded rectangle = 135 square unit
(x+8)(x+14) = 135
+ 8x + 14x + 112 = 135
+ 8x + 14x -23 = 0
+ 22x -23 = 0
+ 23x - x - 23 = 0
(x-1)(x+23) = 0
Therefore x = 1
Expanded length = 1+14 = 15
Expanded width = 1+8 = 9
Perimeter = 2(9+15) = 48 units
Learn more about Rectangles: brainly.com/question/25292087
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9514 1404 393
Answer:
3 cm
Step-by-step explanation:
The largest possible square will have a dimension that is the greatest common factor of 12 and 15. That number is 3.
The largest square is 3 cm.
__
The paper will be cut into 5 squares lengthwise and 4 squares across.
Answer:
x=5
Step-by-step explanation:
You first have to distribute. So multiply the 3 with whats inside the parenthesis. So 3 times 2x is 6x. And 3 times -3 is -9. That means that so far you have 6x-9. Now on the other side you have 4x+1. So you move the 9 over to the other side by doing the opposite of it. Meaning +9. So you add 9 to 1 giving you 10. Now you have, 6x=4x+10. Just subtract 4x from 6x, which gives you 2x. Lastly, you divide the 10 by 2x because division is the opposite of multiplication
