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Sveta_85 [38]
3 years ago
10

Find the point-slope equation for the line that passes through the points (3,27) and (-8,-61). Use the first point in your equat

ion.
Mathematics
1 answer:
Llana [10]3 years ago
5 0

Answer:

\huge\boxed{y-27=8(x-3)}

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

where

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (3, 27) and (-8, -61).

Calculate the slope <em>m</em>:

m=\dfrac{-61-27}{-8-3}=\dfrac{-88}{-11}=8

Susbtitute to the equation of a line:

y-27=8(x-3)

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If it took 28 minutes to run 4 miles, then at that rate, how long would it take to run 20 miles?
SSSSS [86.1K]

Answer:

140 minutes

Step-by-step explanation:

After 28 mins you've gone 4 miles, assuming this rate is constant and you dont slow down or speed up, in order to get to 20 miles you will have run 5x as much (20/4 = 5), thus 5x the amount of time (28x5).

20/4 = 5

5x28 = 140

8 0
3 years ago
Read 2 more answers
It takes a machine 15 hour to assemble a toy.
solniwko [45]
12 toys. Dividing 15 by 60 equals 4 so 4 tots in a hour. Then multiple the 4 toys an hour by 3 hours.
8 0
3 years ago
A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021
egoroff_w [7]

The sum of the given series can be found by simplification of the number

of terms in the series.

  • A is approximately <u>2020.022</u>

Reasons:

The given sequence is presented as follows;

A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021

Therefore;

  • \displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

  • \displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}

Therefore, for the last term we have;

  • \displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

\displaystyle \frac{A}{2}  = \mathbf{ 1011 \cdot  \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460}  \right)}

\displaystyle \frac{A}{2}  = 1011 \cdot  \left(1 - \frac{1}{2} +\frac{1}{2} -  \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022}  \right)

Which gives;

\displaystyle \frac{A}{2}  = 1011 \cdot  \left(1 - \frac{1}{2022}  \right)

\displaystyle  A = 2 \times 1011 \cdot  \left(1 - \frac{1}{2022}  \right) = \frac{1032231}{511} \approx \mathbf{2020.022}

  • A ≈ <u>2020.022</u>

Learn more about the sum of a series here:

brainly.com/question/190295

8 0
2 years ago
Read 2 more answers
Please help with an explanation!
Artist 52 [7]

Answer:

6 weeks

Step-by-step explanation:

Easier way to solve: If she takes 7 quizzes each week, 7 times something (amount of weeks) equals 42.

7 X <u>6</u> = 42

Solving with algebra: We know that hanna takes six quizzes a week and takes a total of 42 quizzes, therefore the unknown (x) is the amount of weeks she takes the quizzes.

Amount of weeks X amount of tests per weeks = 42 quizzes

<em>x </em>X 7 = 42

42/7 = 6

3 0
2 years ago
Read 2 more answers
Find the 96th term of the arithmetic sequence <br> -3, -14, -25, ...
lana [24]

Answer:

-1059

Step-by-step explanation:

Katelyn, this is super easy to understand.

Anyways, to find the 96th term of the sequence, first subtract -14 and -3. You may be thinking it is -17, but it is not. -17 is only if you are subtracting -14 and 3.

(-14) - (-3) = -14 + 3 = -11.

That means the difference between each number is -11.

Now all you have to do is take the -11 and multiply it by 96, which is -1056. Then, add the -1056 to -3, which is -1059. That should be your answer.

Your school may have taught you a different way, but this is my way.

4 0
3 years ago
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