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makkiz [27]
2 years ago
11

Write an equation in standard form for the line that passes through the point (2,-3) and is perpendicular to the line y + 4 = -2

/3(x-12)
Mathematics
1 answer:
sineoko [7]2 years ago
5 0

For this case we have that by definition, the standard form of a linear equation is given by:

ax + by = c

By definition, if two lines are perpendicular then the product of their slopes is -1. That is to say:

m_ {1} * m_ {2} = - 1

We have the following point-slope equation of a line:

y+4 = -\frac {2} {3}(x-12)

The slope is:

m_ {1} = - \frac {2} {3}

We find the slope m_ {2}of a perpendicular line:

m_ {2} = \frac {-1}{m_ {1}}\\m_ {2} = \frac {-1} {-\frac {2} {3}}\\m_ {2} = \frac{3} {2}

Thus, the equation is of the form:

y-y_ {0} = \frac {3} {2} (x-x_ {0})

We have the point through which the line passes:

(x_ {0}, y_ {0}) :( 2, -3)

Thus, the equation is:

y - (- 3) = \frac {3} {2} (x-2)\\y + 3 = \frac {3} {2} (x-2)

We manipulate algebraically:

y + 3 = \frac{3} {2} x- \frac {3} {2} (2)\\y + 3 = \frac{3} {2} x-3

We add 3 to both sides of the equation:

y + 3 + 3 = \frac {3} {2} x\\y + 6 = \frac {3} {2} x

We multiply by 2 on both sides of the equation:

2(y + 6) = 3x\\2y + 12 = 3x

We subtract 3x on both sides:

2y-3x + 12 = 0

We subtract 12 from both sides:

2y-3x = -12

ANswer:

-3x + 2y = -12

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liq [111]

Answer:

0.1425 = 14.25% probability that the individual's pressure will be between 119.4 and 121.4mmHg.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 120, \sigma = 5.6

Find the probability that the individual's pressure will be between 119.4 and 121.4mmHg

This is the pvalue of Z when X = 121.4 subtracted by the pvalue of Z when X = 119.4. So

X = 121.4

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

Z = \frac{121.4 - 120}{5.6}

Z = 0.25

Z = 0.25 has a pvalue of 0.5987

X = 119.4

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

Z = \frac{119.4 - 120}{5.6}

Z = -0.11

Z = -0.11 has a pvalue of 0.4562

0.5987 - 0.4562 = 0.1425

0.1425 = 14.25% probability that the individual's pressure will be between 119.4 and 121.4mmHg.

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Can someone help me please, I will give brainliest as soon as my app allows!!
Delicious77 [7]

Answer:

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Step-by-step explanation:

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I hope this helps you



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