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Snowcat [4.5K]
3 years ago
5

Four Representations: Equations, Tables, Words,

Mathematics
1 answer:
andrey2020 [161]3 years ago
5 0

1) C

2) Graph 1

3) a= 3

4) b= 0

Youre welcome :)

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Why does multiple of 3 add up digits trick work?
kherson [118]
You must be referring to the quick way to determine whether a given integer is divisible by 3; that is, 3 divides an integer x whenever the digits of x sum to a multiple of 3.

Suppose x has n\ge1 digits. We can expand it as a sum of the numbers in any given digits place by the corresponding power of 10. For example, if x=2148, we can write

2148=2\times10^3+1\times10^2+4\times10^1+8\times10^0

More generally, if

x=d_{n-1}d_{n-2}\ldots d_1d_0

(where d_i denotes the numeral in the 10^i-th's place), then we have the expansion

x=d_{n-1}10^{n-1}+d_{n-2}10^{n-2}+\cdots+d_110^1+d_0

Notice that for any integer k, we have

10^k-1=\underbrace{99\ldots99}_{k\text{ 9s}}

which is clearly divisible by 3. So from each power of 10 in the expansion of x, we can add and subtract 1, then rearrange the terms of the sum:

x=d_{n-1}10^{n-1}+\cdots+d_110^1+d_0
x=d_{n-1}(10^{n-1}-1+1)+\cdots+d_1(10^1-1+1)+d_0
x=d_{n-1}(10^{n-1}-1)+\cdots+d_1(10^1-1)+(d_{n-1}+\cdots+d_1+d_0)

We know 10^k-1 is divisible by 3, which means the remainder upon dividing x by 3 is just the sum of the digits of x. If this remainder is divisible by 3, then so must be the original number, x.

Back to our previous example: if x=2148, then we have the expansion

2148=2\times10^3+10^2+4\times10+8
2148=2(999+1)+(99+1)+4(9+1)+8
2148=2\times999+99+4\times9+(2+1+4+8)

Dividing through by 3, we get a remainder of 2+1+4+8=15, which is divisible by 3, and so 2148 must also be a multiple of 3.

In case for some reason you're not convinced 15 is a multiple of 3, you can apply the same trick:

15=10+5
15=9+1+5

Dividing through by 3 leaves a remainder of 1+5=6, which is also a multiple of 3, so that 15 must be, too.
7 0
3 years ago
Id just like the awnser please.
rewona [7]

Answer:

A. 32/.0333333 = 1

   20/ .066666]

   8/.1

   -4/.3

    b. 125

3 0
2 years ago
Bishaar's height is measured at 4.75 feet tall. Express Bishaar's height in meters. Round your answer to the nearest hundredth m
LuckyWell [14K]
To make the conversion, the first thing you should know is that
 1m = 3.28ft
 Then, doing the conversion we have
 (4.75ft / 3.28ft) * (1m) = 1.448170732m
 nearest hundredth
 1.45m
 anwser
 Bishaar's height is1.45m
6 0
3 years ago
If 0 lies in the quadrant IV. What can be the value of cos 0?
Andru [333]

Answer:

Positive one

Step-by-step explanation:

The angle 0 does not lie in any of the four quadrants, it lands directly in between quadrants I and IV. The value of cos 0 is always 1.

4 0
3 years ago
The number of runs scored by the home team at a baseball game is represented by ( x + 10). The number of runs scored by the visi
Zinaida [17]

Maria participates in a sports activity and runs the following amount__________45m

Cual es la respuesta???????

7 0
2 years ago
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