Find the distance between y=3x+6 and y=3x−2. Round your answer to the nearest tenth.

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

6 0

Answer:

Step-by-step explanation:

These lines are parallel since they both have the slope of 3. Then it becomes a matter of seeing how far their y-intercepts are from one another. That is the distance between them, and will be the distance between them for the entire length of each line since parallel lines remain the same distance apart forever. The first line has a y-intercept of 6 and the second line has a y-intercept of -2. From 6 to 0 is 6, then add another 2 units to get a grand total of 8 units apart. Since distance is a measure of length and length will never be negative, we are not subtracting here. We are simply counting the number of units between each y-intercept. And it doesn't have to be the y-intercept. Every point on the first line is 8 units above every point on the second line.

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Find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20

Vsevolod [243]

Answer:

The sum of the first 20 terms is -1440.

Step-by-step explanation:

We want to find the sum of the first 20 terms of the arithmetic sequence:

4, -4, -12, -20...

The sum of an arithmetic sequence is given by:

$\displaystyle S=\frac{k}{2}(a+x_k)$

Where k is the number of terms, a is the initial term, and x_k is the last term.

Since we want to find the sum of the first 20 terms, k = 20.

Our initial term a is 4.

Our last term is also the 20th term as we want the sum of the first 20 terms.

To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Where a is the initial term, d is the common difference, and n is the nth term.

Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:

$x_n=4-8(n-1)$