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garri49 [273]
2 years ago
7

Look at the figure below:

Mathematics
1 answer:
labwork [276]2 years ago
7 0
The answer to this question is 10 units
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A four-digit number N leaves a remainder of 10 when divided by 21, a remainder of 11 when divided by 23, and a remainder of 12 w
aksik [14]

Answer:

  16

Step-by-step explanation:

There may be a formal way to solve simultaneous Diophantine equations, but I don't know what it is. So, I addressed this by solving them 2 at a time.

First of all, we want to find a relation between integers p and q such that ...

  21p+10 = 23q +11

  21p -23q = 1 . . . . . . subtract 23q+10

Using the extended Euclidean algorithm or trial and error or astute observation, we find that (p, q) = (11, 10) is a solution to this equation. Then we can write p and q as ...

  • p = 23n+11
  • q = 21n+10

for some integer n.

Then our original numbers become ...

  21p+10 = 21(23n+11)+10 = 483n +241 . . . . for some integer n

For this to be a 4-digit number, we must have n such that

  1000 ≤ 483n +241 ≤ 9999

  1.6 < n < 20.2

__

Modulo 25, the number (483n+241) is ...

  8n +16

and we want that value to be 12:

  (8n +16) mod 25 = 12

  (8n +4) mod 25 = 0 . . . . . subtract 12

  4(2n+1) mod 25 = 0 . . . .  factor out 4

For this to be true, we must have 2n+1 be a multiple of 25. The only value of n that is in the required interval [2, 20] is n=12.

__

When n=12, 483n+241 = 6037. The sum of digits of 6037 is 16.

3 0
3 years ago
What is the slope of the line that passes through the points (3,3) and (-3,-1).
ArbitrLikvidat [17]

Answer:

2/3

Step-by-step explanation:

-1 - 3 = - 4

-3 - 3 = - 6

-4/-6 = 2/3

6 0
2 years ago
Read 2 more answers
On a map, 2 inches represents an actual distance of 64 miles. Towns A and B are 608 miles apart. Find the distance between the t
Lelu [443]

Answer: The distance in the map is 19 inches.

Step-by-step explanation:

On the map. 2 inches represent an actual distance of 64 miles.

The actual distance between town A and town B is equal to 608 miles, we need to divide this distance into groups of 64 miles.

N = 608/64 = 9.5

And each one of those 9.5 groups is represented with 2 inches in the map, then the distance in the map is:

d = 9.5*2 inches = 19 inches.

6 0
3 years ago
Read 2 more answers
Help ASAP, WILL MARK BRAINLIEST!!<br> please look at image before answering!
Ivahew [28]

Answer:

To know what the ratio for the cos of theta, we actually have to see the adjacent and hypotenuse values. cos=adjacent/hypotenuse.

Step-by-step explanation:

3 0
3 years ago
PLZ HELP I’LL GIVE BRAINLIEST
son4ous [18]
I’m not sure if this is right but im guessing c.
8 0
3 years ago
Read 2 more answers
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