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Brilliant_brown [7]
3 years ago
6

What is the slope of the line that passes through the given points (3 2) and (5 12)

Mathematics
1 answer:
Anika [276]3 years ago
5 0
Find slope by finding the change in y over the change in x, or rise over run.

12-2/5-3
10/2
5

Final answer: A
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Write an equation of the line passing through point p that is parallel to the given line.
Thepotemich [5.8K]

Answer:

Step-by-step explanation:

y=-3x+13

y = mx + b, where m is the slope and b is the y-intercept.

A line parallel to this line will have the same slope, -3.  We can start by writing:

y = -3x + b

No matter what is chosen for the value of b, this line will be parallel.  We do want the line to go through point (6,10), however.  The way that can be done is to find a value of b that would shift the line to go through (6,10).

Find b by entering the point (6,10) into the equation, and then solve for b:

y = -3x + b

10 = -3(6) + b

10 = -18 + b

b = 28

The line becomes y = 3x + 28

See the attachment.

8 0
3 years ago
What is the solution to the following system
Archy [21]

C is the answer.............

3 0
3 years ago
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Difference between x+5 and 2x+3
solniwko [45]
-x+8
I wrote out the problem above to my best knowledge

7 0
3 years ago
1. Derive the half-angle formulas from the double
lilavasa [31]

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

<h3>How to apply trigonometry on deriving formulas and transforming points</h3>

1) The following <em>trigonometric</em> formulae are used to derive the <em>half-angle</em> formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a <em>half</em> angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a <em>half</em> angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a <em>half</em> angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in <em>rectangular</em> form to <em>polar</em> form are obtained by <em>trigonometric</em> functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in <em>polar</em> form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in <em>rectangular</em> form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the <em>linear</em> function y = 5 · x - 8, we proceed to use the following <em>substitution</em> formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

To learn more on trigonometric expressions: brainly.com/question/14746686

#SPJ1

4 0
2 years ago
Complete the remainder of the
allsm [11]

The corresponding values needed will be -23, -8, 7 and 22

<h3>Functions and Tables</h3>

Given the function y = 5x - 8

<h3>Get the domains and range</h3>

We are to get the range of the function for the given domains

If the value of x is -3

y = 5(-3) - 8

y = -15 - 8

y = -23

If the value of x is 0

y = 5(0) - 8

y = 0 - 8

y = -8

If the value of x is 3

y = 5(3) - 8

y = 15 - 8

y = 7

If the value of x is 6

y = 5(6) - 8

y = 30 - 8

y = 22

Hence the corresponding values needed will be -23, -8, 7 and 22

Learn more on tables of function here: brainly.com/question/3632175

4 0
2 years ago
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