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professor190 [17]
3 years ago
7

Line m passes through point (–2, –1) and is perpendicular to the graph of y = –23x + 6. Line n is parallel to line m and passes

through point (4, –3). Which is the equation of line n in slope-intercept form?
Mathematics
1 answer:
Ilya [14]3 years ago
5 0

\huge\boxed{y=\frac{1}{23}x-\frac{73}{23}}

First, find the slope perpendicular to -23. We can do this by finding the opposite reciprocal.

Multiply the slope by -1 and write the result as a fraction.

-23*-1=23=\frac{23}{1}

Flip the numerator and the denominator.

\frac{23}{1}\longrightarrow\frac{1}{23}

This is the slope of line m. Since lines m and n are perpendicular, this is also the slope of line n.

Write the formula for point-slope form.

y-y_1=m(x-x_1)

Substitute in the values for line n.

y-(-3)=\frac{1}{23}(x-4)

Simplify the negative subtraction.

y+3=\frac{1}{23}(x-4)

Distribute the \frac{1}{23} to the (x-4).

y+3=\frac{1}{23}x-\frac{4}{23}

Subtract 3 — which is equivalent to \frac{69}{23} — from both sides.

\boxed{y=\frac{1}{23}x-\frac{73}{23}}

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Greg has collected 4,385 pennies and Hannah has collected 3,899 pennies. How many times as great as the value of 3 in 4,385 is t
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Read 2 more answers
B. What are the second and third terms of this arithmetic sequence? 80, 페, 페, 125,...........
nataly862011 [7]

The 2nd and 3rd term of an AP is found to be (a₂ = 95) and (a₃ = 110).

<h3>What is the sequence of AP arithmetic progression?</h3>

In Arithmetic Progression, the difference between the two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come across a few key concepts in AP that had been labeled as:

  • The first term (a)
  • Common difference (d)
  • Term nth (an)
  • The total of first n terms (Sn)

As shown below, the AP can also be referred to in terms of common differences.

  • The following is the procedure for evaluating an AP's n-th term:  an = a + (n − 1) × d
  • The arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].
  • Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ......      = an - an-1.

Now, the given sequence is; 80, _, _, 125.

The series comprises of four given terms.

Let the first term be 'a₁' = 180.

The second term be 'a₂'.

The third term be 'a₃'.

And, the fourth term is 'a₄' = 125.

Use the nth term formula to find the common difference 'd'.

n-th term:  an = a + (n − 1) × d

a₄ = a + (n - 1)d

125 = 80 + (4 - 1)d

45 = 3d

d = 15

Thus, the common difference is 15.

The second term is calculated as;

a₂ = a₁ + d

a₂ = 80 + 15

a₂ = 95.

The third term is estimated as;

a₃ = a₂ + d

a₃ = 95 = 15

a₃ = 110

Therefore, the 2nd and third term of an AP is computed as 95 and 110.

To know more about Arithmetic Sequence, here

brainly.com/question/24989563

#SPJ4

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