Answers:
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Explanation:
7+6 = 13. Divide this over 5 to get 13/5 = 2 remainder 3. The quotient 2 is something we don't care about. <u>We only worry about the remainder</u>. Therefore 7+6 = 3 (mod 5)
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2+1 = 3 (mod 5) for similar reasoning as above. 3/5 = 0 remainder 3.
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20 = 9 (mod 11) since 20/11 = 1 remainder 9. Imagine you had 20 cookies and 11 friends. Each friend would get 1 whole cookie (quotient) and there could be 9 left over (remainder).
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35/11 = 3 remainder 2
Or you could use repeated subtraction like so to find the remainder
35-11 = 24
24-11 = 13
13-11 = 2
The last result (2) is smaller than 11, so we stop here and this is the remainder.
Therefore, 35 = 2 (mod 11)
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Here's another way to think of it. Consider you have $35 in your pocket. Let's say a store is selling trinkets for $11 each. We can pose these key questions:
- What is the most number of trinkets you can buy?
- If you buy that max amount, how much will you have left over?
The answer to the first question is 3 trinkets because 3*11 = 33 dollars is under the budget of $35. The amount left over is 35-33 = 2 dollars which is the remainder. It's not larger than 11, so we cannot buy any more trinkets at this point.
X=23 First, you have to subtract 12 by 12 to cancel it out. Next, you have to do the same thing to 20.05. 20.05 minus 12 is 8.05. All you have left is .35x. To get rid of the this you have to divide .35x by .35. Now all you have left is x. Finally you have to do the same thing to 8.05. 8.05 divided by .35 is 23. So, x=23
Answer:
700.4 cm
Step-by-step explanation:
Use a proportion.
Let x be the vertical distance for the 700 cm pipe.
1 cm is to 30 cm as x cm is to 700 cm
1/30 = x/700
30x = 1 * 700
30x = 700
3x = 70
x = 70/3
Now we need l. We have a right triangle with legs measuring 70/3 cm and 700 cm, and we are looking for the hypotenuse l.
a^2 + b^2 = c^2
(70/3)^2 + 700^2 = c^2
c^2 = 4900/9 + 490000
c = 700.4
l = 700.4 cm
Answer:
Step-by-step explanation:
→ Minus the z² terms
→ Minus the whole numbers
→ Add the z terms
11z
