Find the slope of a line passing though the given points (1,4) (3,2)

Very quickly pleasee!!! What is the remainder when 3 to the power of 2020 is divided by 30

Misha Larkins [42]

<h3>Answer: 21</h3>

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Explanation:

Let's see if we can find a pattern where we divide powers of 3 over 30

In other words, let's see if we can find a pattern for (3^n)/30 where n is a natural number {1,2,3,4,...}

We only care about the remainders so ignore the quotients.

This is the pattern of remainders:

3^1 = 3. When divided over 30, we get remainder 3.
3^2 = 9. When divided over 30, we get remainder 9.
3^3 = 27. When divided over 30, we get remainder 27.
3^4 = 81. When divided over 30, we get remainder 21.
3^5 = 243. When divided over 30, we get remainder 3.
3^6 = 729. When divided over 30, we get remainder 9.

We see the pattern repeating again after we get to remainder 3 a second time. The pattern of remainders is {3, 9, 27, 21} which repeats forever.

The length of this cycle is 4. So what we do is divide the exponent by 4 to see what the remainder is. For instance, both 1 and 5 lead the same remainder when we divide by 4. This tells us 3^1 and 3^5 lead to the same remainder as shown in the pattern above.

Similarly, 3^2 and 3^6 lead to the same remainder. These items are spaced exactly four units apart, which is the length of the cycle.

For the exponent 2020, we get 2020/4 = 505 remainder 0

Having a remainder 0 is the same as having remainder 4, when dividing by 4.

So we'll be looking in the fourth slot of the cycle {3,9,27,21} to see the answer is 21.

Dividing 3^2020 over 30 leads to a remainder of 21.

6 0

3 years ago

Answer for brainlist & extra points! i can see if your answer is correct or not :)

ioda

Answer:

The equation simplifies to n = 7.

Step-by-step explanation:

Hey there! We have an algebraic equation with the variable <em>n</em>. We want to solve for n. Therefore, we need to simplify the expression as much as we can.

To do this, we're going to notice we have two like terms in the equation:

71
1

These two terms can be combined to make one term. In order to do this, we're going to check which side of the equation has two terms.

Left side → 1 term
Right side → 2 terms

We are going to then check the sign of the constant. As a reminder, constants are numbers without a variable attached to them.

We see our constant is 1 on the right side and it is positive due to it being added to 10<em>n</em>. Therefore, we are going to do the opposite and subtract it from 71.

71 - 1 = 70

This leaves us with a more simplified equation: 70 = 10n.

To make things easier, we're going to use the commutative property and switch the terms around. This will give us 10n = 70. It is easier to operate when our variable term is on the left side.

Now, we need to get our variable by itself. A coefficient is multiplying the variable by that value, so to reverse that, we must divide.

In addition to that, what we do on one side of the equation must be done on the other side of the equation.

$\displaystyle \frac{10n}{10} = \frac{70}{10}$

This simplifies to n = 7, which is our final answer.

8 0

2 years ago

Read 2 more answers

the sum of 2 consecutive integers is less than 55.the pair of integers sum are 26 and 27. true or false?

son4ous [18]

X + x + 1 < 55
2x + 1 < 55
Subtract 1 from both sides
2x < 54
Divide both sides by 2
x < 27
The integer less than 27 is 26.
26 + 27 < 55. True

6 0

3 years ago

The Department of Education wishes to estimate the proportion of all college students who have a job off-campus. It surveyed 160

NeX [460]

Answer: 2. All college students

Step-by-step explanation:

A population is a large group of individuals that have some common feature by the researcher's point of interest.

Herero , the Department of Education wishes to estimate the proportion of all college students who have a job off-campus.

So , he need data of all students to compute the exact proportion.

But instead of that he surveyed 1600 randomly selected students which determine the sample.

Sample just gives the estimate of the parameter.

Hence, the population of interest to the Department of education is " All college students" .

7 0

3 years ago

What do all of these number have in common <br>3,5,7,11,13

kondor19780726 [428]

All the numbers are Odd.

6 0

3 years ago

Read 2 more answers