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julia-pushkina [17]
2 years ago
12

Suppose that the division N/5 leaves a remainder of 4, and the division N/2 leaves a remainder of 1, what is the ones digit on N

?
Mathematics
1 answer:
Tju [1.3M]2 years ago
7 0

Since <em>N</em>/2 leaves a remainder, <em>N</em> must be odd and ends with 1, 3, 5, 7, or 9.

<em>N</em>/5 also leaves a remainder, so <em>N</em> is not divisible by 5, so it does not end in 5.

The only correct choice is then 9, since

1 = 0•5 + 1 and 1 = 0•2 + 1

3 = 0•5 + 3 and 3 = 1•2 + 1

7 = 1•5 + 2 and 7 = 3•2 + 1

9 = 1•5 + <u>4</u> and 9 = 4•2 + <u>1</u>

<u />

Alternatively, the given information is equivalent to saying

N\equiv 4\pmod5\\\\N\equiv1\pmod2

Then you can use the Chinese remainder theorem to find <em>N</em>.

You might be interested in
Which choice below shows the following numbers in order from least to greatest?
vfiekz [6]

Answer:

1/3, \sqrt{4}, π, \sqrt{16}, 8

Step-by-step explanation:

Simplifying or rounding complicated numbers to integers can help us order them.

  • Integer - an integer is any whole number, including zero, that can be negative or positive.

Simplifying Numbers

Numbers like 1/3 and 8 don't need to be simplified because they are commonly used and understood.

Both 4 and 16 are perfect squares. So, to simplify these numbers we can just solve.

  • \sqrt{4} = 2
  • \sqrt{16} = 4

There is no way to "solve" pi, but we can round it to an easier number. Technically, pi is irrational, so there is no way to write out the whole number. However, in this case, we can just round to the nearest whole number.

  • π ≈ 3

This means, in the order they appear, the simplified numbers are 2, 8, 4, 1/3, and 3.

Ordering the Numbers

From this point, they should be easy to order.

  • 1/3 is the smallest because it is the only number less than 1.
  • \sqrt{4} is next because it is equal to 2
  • π is third since it is only slightly above 3
  • \sqrt{16} is fourth since it is equal to 4
  • 8 is the largest number on the list.
5 0
2 years ago
What tool is used to draw circles
aleksklad [387]

Answer:

Pair of compasses.

Step-by-step explanation:

These are used to inscribe circles/arcs.

Compasses are used in maths, navigation,e.t.c.

Hope it helps.

3 0
3 years ago
Arthur's dog, Shep, had to go on a diet. After three months of dieting, Shep had lost 16% of his weight, which was 24 pounds. Ho
lidiya [134]

Answer: 150 pounds

Step-by-step explanation:

Let her initial weight be represented by x.

Since Shep had lost 16% of his weight, which was 24 pounds. Shep weight before he was put on a diet would be:

16% × x = 24

0.16 × x = 24

0.16x = 24

x = 24/0.16

x = 150 pounds

5 0
2 years ago
Which equation best matches the graph shown below ?
zubka84 [21]
Answer is too right
You know the y intercept is -4 so it’s gotta be on of the top 2. Then I plugged in x=1 and it’s just shy of 6 for the one in the top right which matches the graph.
5 0
3 years ago
Dana draws a triangle with one angle that has a measure of 40∘.
OLEGan [10]

Answer:

140°

Step-by-step explanation:

<u>Given:</u>

Dana draws a triangle with one angle that has a measure of 40∘.

<u>Question asked:</u>

What is the measure of the angle’s adjacent exterior angle?

Solution:

<u>As we know:</u>

<u><em>Sum of the adjacent interior and exterior angles is 180°.</em></u>

Interior angle = 40°

Adjacent exterior angle = ?

Interior angle + Adjacent exterior angle = 180°

40° + Adjacent exterior angle = 180°

<u>By subtracting both sides by 40°</u>

40° - 40° + Adjacent exterior angle = 180° - 40°

Adjacent exterior angle = 140°

Therefore, the measure of the angle’s adjacent exterior angle will be 140°.

4 0
2 years ago
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