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makkiz [27]
3 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]3 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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The correlation coefficient is -0.87; strong correlation

<h3>How to determine the correlation coefficient?</h3>

The given parameters are:

x = Time spent working out

y = lbs Overweight

Next, we enter the table of values in a graphing tool.

From the graphing tool, we have the following summary:

<u>X Values</u>

  • ∑ = 27.1
  • Mean = 2.71
  • ∑(X - Mx)2 = SSx = 22.569

<u>Y Values</u>

  • ∑ = 89
  • Mean = 8.9
  • ∑(Y - My)2 = SSy = 778.9

<u>X and Y Combined</u>

  • N = 10
  • ∑(X - Mx)(Y - My) = -114.19

<u>R Calculation</u>

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -114.19 / √((22.569)(778.9))

r = -0.8613

Approximate

r = -0.87

This means that the correlation coefficient is -0.87

Also, the correlation coefficient is a strong correlation, because it is closer to -1 than it is to 0

Read more about correlation coefficient at:

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6 0
2 years ago
A line is parallel to y = 3x + 8 and
Ad libitum [116K]

Answer:

y= 3x+16

Step-by-step explanation:

y = 3x + 8 ║ y= mx +b

Since lines are parallel, m=3

y= 3x+b

(-3, 7) intersect

  • 7= 3*(-3) + b
  • b= 7+9
  • b= 16

y= 3x+16

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Step-by-step explanation:

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(8a^3÷27x^-3)1÷3 simplify<br>​
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Read 2 more answers
The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2 respectively. Let A de
antoniya [11.8K]

Answer:

a) P(A) =P(a)+P(b) +P(c)= 0.1+0.1+0.2 = 0.4

b) P(B) =P(c) +P(d)+P(e)=0.2+0.4+0.2=0.8

c) P(A') = 1-P(A) =1-0.4=0.6

d) P(A \cup B) =0.4 +0.8-0.2 =1.0

e)  The intersection between the set A and B is the element c so then we have this:

P(A \cap B) = P(c) =0.2

Step-by-step explanation:

We have the following space provided:

S= [a,b,c,d,e]

With the following probabilities:

P(a) =0.1, P(b)=0.1, P(c) =0.2, P(d)=0.4, P(e)=0.2

And we define the following events:

A= [a,b,c], B=[c,d,e]

For this case we can find the individual probabilities for A and B like this:

P(A) = 0.1+0.1+0.2 = 0.4

P(B) =0.2+0.4+0.2=0.8

Determine:

a. P(A)

P(A) =P(a)+P(b) +P(c)= 0.1+0.1+0.2 = 0.4

b. P(B)

P(B) =P(c) +P(d)+P(e)=0.2+0.4+0.2=0.8

c. P(A’)

From definition of complement we have this:

P(A') = 1-P(A) =1-0.4=0.6

d. P(AUB)

Using the total law of probability we got:

P(A \cup B) =P(A) +P(B)-P(A \cap B)

For this case P(A \cap B) = P(c) =0.2, so if we replace we got:

P(A \cup B) =0.4 +0.8-0.2 =1.0

e. P(AnB)

The intersection between the set A and B is the element c so then we have this:

P(A \cap B) = P(c) =0.2

8 0
3 years ago
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