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MaRussiya [10]
3 years ago
5

1. Find the equation of a line that passes through the point (4,1) and is perpendicular to the

Mathematics
1 answer:
slava [35]3 years ago
7 0

Answer:

  x - 4y = 0 . . . in standard form

  y = (1/4)x . . . in slope-intercept form

Step-by-step explanation:

The slope of the given line is ...

  m = (y2 -y1)/(x2 -x1) = (9 -(-7))/(-1 -3) = 16/-4 = -4

The slope of the perpendicular line is the negative reciprocal of this:

  desired slope = -1/m = -1/-4 = 1/4

This can be used in the point-slope form of the equation of a line:

  y -h = m(x -k) . . . . . line with slope m through point (h, k)

Your perpendicular line has a slope of 1/4 and goes through point (4, 1), so its equation can be written as ...

  y -1 = (1/4)(x -4)

  y = (1/4)x -1 +1

  y = (1/4)x

In standard form, this is ...

  4y = x

  x -4y = 0

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Find the equation of the line through point (5,1) and perpendicular to 5x−y=−3. Use a forward slash (i.e. "/") for fractions (e.
IRINA_888 [86]
Y = -1/5x + 2

A line perpendicular to another line has an opposite reciprocal slope. What opposite means is that you flip the sign (from - to + or from + to -) and reciprocal means that you flip the numerator and denominator (so if line A is perpendicular to line B and line As slope is -3, line Bs slope would be 1/3).

First find the slope of 5x - y = -3
Add y to both sides
5x = y - 3
Add 3 to both sides
y = 5x + 3

So the slope of the line is 5. That means the slope of of the perpendicular line is -1/5.

Plug the slope of the perpendicular line and the point (5, 1) into point slope form to solve the equation

y - y1 = m(x - x1)
y - 1 = -1/5(x - 5)
y - 1 = -1/5x + 1
y = -1/5x + 2
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2 years ago
A rectangular living room has an area of 425 ft.² the width of the room is 17 feet
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What are you trying to find? If it’s the length, just divide 425 by 17, which is 35 ft!
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3 years ago
Belinda Weedman's company pays 70%
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Saeed wants to have his birthday at an amusement park with a few of his friends but he can't spend no more then $80. The amuseme
OLEGan [10]

Answer:

T=35X6.50

Step-by-step explanation:

4 0
3 years ago
The Food and Drug Administration (FDA) produces a quarterly report called Total Diet Study. The FDA’s report covers more than 20
pav-90 [236]

Using the normal approximation to the binomial, it is found that:

  • The mean of X is of 52 samples.
  • The standard deviation of X is of 4.2661 samples.
  • 0.0017 = 0.17% probability that less than half without any traces of pesticide.

--------------------------------

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, with mean given by:  

E(X) = np

And standard deviation of:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution  

Z-score formula is used, which, in a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • Each z-score has an associated p-value, which measures the percentile of measure X.

--------------------------------

  • 65% of samples had no pesticide, thus p = 0.65
  • 80 samples, thus n = 80

The mean of X is of:

E(X) = np = 0.65(80) = 52

The standard deviation of X is of:

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{80(0.65)(0.35)} = 4.2661

Using the approximation and continuity correction, the probability is P(X < 40 - 0.5) = P(X < 39.5), which is the p-value of Z when X = 39.5. Thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{39.5 - 52}{4.2661}

Z = -2.93

Z = -2.93 has a p-value of 0.0017, thus:

0.0017 = 0.17% probability that less than half without any traces of pesticide.

A similar problem is given at brainly.com/question/24261244

8 0
2 years ago
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