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mrs_skeptik [129]
3 years ago
10

What is the equation of the line that is perpendicular to y= -3x + 1 and passes through (2,3)?

Mathematics
2 answers:
umka2103 [35]3 years ago
6 0

Answer:

  y = 1/3(x -2) +3

Step-by-step explanation:

The slope of the given line is the coefficient of x, -3. The slope of the perpendicular line will be the negative reciprocal of that: -1/-3 = 1/3. The line through a point (h, k) with slope m can be written in point-slope form as ...

  y = m(x -h) +k

For m=1/3, (h, k) = (2,3), the equation of the line is ...

  y = (1/3)(x -2) +3

Aleonysh [2.5K]3 years ago
3 0

Answer:

\large\boxed{y=\dfrac{1}{3}x+2\dfrac{1}{3}}

Step-by-step explanation:

\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=-3x+1\to m_1=-3.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-3}=\dfrac{1}{3}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{3}x+b.\\\\\text{The line passes through }(2,\ 3).

\text{Put the coordinates of the point to the equation.}\ x=2,\ y=3:\\\\3=\dfrac{1}{3}(2)+b\\\\3=\dfrac{2}{3}+b\qquad\text{subtract}\ \dfrac{2}{3}\ \text{from both sides}\\\\b=2\dfrac{1}{3}

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No copy and paste answers.
miss Akunina [59]

Answer:

  2.5 miles

Step-by-step explanation:

The relation between time, speed, and distance is ...

  distance = speed × time

We can define t to be Stanley's swimming time. Then t+0.5 was his running time, and 2(t+0.5) was his biking time. His total distance covered is ...

  64 = 9(t +0.5) +16(2(t +0.5)) +2.5(t)

  64 = 43.5t +20.5 . . . . . . . simplify

  43.5 = 43.5t . . . . . . . . . subtract 20.5

  t = 1 . . . . . . . . . . . . . . divide by the coefficient of t

Stanley swam for 1 hour, so the distance he covered while swimming was ...

  (2.5 mi/h)(1 h) = 2.5 mi

Stanley covered 2.5 miles while swimming.

_____

<em>Additional comment</em>

Stanley ran for 1.5 hours, covering 9×1.5 = 13.5 miles. He biked for 3 hours, covering 16×3 = 48 miles. His total distance was 2.5 +13.5 +48 = 64 miles, as given.

6 0
2 years ago
) in how many ways can 5 ice cream toppings be chosen from 12 available toppings
grandymaker [24]
12*11*10"9*8 whatever that turns out to be lol
3 0
3 years ago
Read 2 more answers
A rain storm came through Clifton park and it was accumulating 2/3 inches of rain/hour. How many inches of rain would fall in 6
nlexa [21]

4 inches of rain would fall in 6 hours

<h3><u>Solution:</u></h3>

Given that, A rain storm came through Clifton park  

And it was accumulating \frac{2}{3} inches of rain/hour

So amount of rain accumulated in 1 hour = \frac{2}{3}

Thus amount of rain accumulated in six hours is calculated by multiplying the amount of water accumulating per hour and 6

Amount of water accumulated in 6 hours = Amount of water accumulated in 1 hour \times 6

\text { Amount of water accumaulated in 6 hours }=\frac{2}{3} \times 6=4

<em><u>Another way:</u></em>

Let "n" be the amount of rain accumulated in 6 hours

1 hour ⇒ \frac{2}{3} rain accumulated

6 hours ⇒ "n"

By cross multiplication, we get

6 \times \frac{2}{3} = 1 \times n\\\\n = \frac{2}{3} \times 6 = 4

Hence, 4 inches of rain would fall in 6 hours.

4 0
3 years ago
Erin had 55 stuffed bears. She took out her favorite 7 bears and then equally divided the other bears among her 3 sisters. Erin'
Pavel [41]

Answer:

27 stuffed bears

Step-by-step explanation:

Erin: 55   Su: 15

Erin: 55-7=48 ( 7 will be kept for herself)

Erin and her sisters: 48/4= 12

Each sister besides Erin and Su have 12

Su: 15+12=27

Thus, Su will have 27 stuffed bears

3 0
3 years ago
Read 2 more answers
What is the equation of a parabola with vertex (0, 0) and directrix x = -3.
miv72 [106K]

Answer:

{y}^{2}= 12x

Step-by-step explanation:

The standard equation of a parabola with vertex at the origin and and directix x=-p is of the form

{y}^{2} =  4{p}x

Where p is simplify the distance from the origin to the directrix.

That is

p =  3

{y}^{2}  = 4 \times 3x

This simplifies to

{y}^{2}= 12x

3 0
3 years ago
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