What is a the equation of the line passing through the point (2,-4) that is parallel to the line y=3x+2

Cot (15 degrees)

STatiana [176]

Answer:

Part I: cot(15 degrees) = cot(45 - 30)

Part II: Evaluation is below

Step-by-step explanation:

Everything is done in degrees

Two angles that differ by 15 degrees that is easy to evaluate is 30 degrees and 45 degrees. The cot(15 degrees) = cot(45 - 30) = 1/tan(45-30) = (1+tan45tan30)/(tan30 - tan45) = (1+ sqrt(3))/(sqrt(3) - 1)

We rationalize this by multiplying 1+ sqrt(3) in the top and bottom, getting:

(4 + 2sqrt(3))/2 = 2 + sqrt(3)

I hope this helps! :)

8 0

3 years ago

Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D'E'F'G'H'I': Hexagon DEFGHI and Hexagon D prime E

MatroZZZ [7]

(x, y)→(x − 8, y − 7) is the correct translation. Take point D for example. The coordinate of D is (2, 5). The coordinate of D' (after translation) is (-6, -2). Since 2-8=-6, 5-7=-2, only the first choice is correct. You can also try other points and see why only this is the right translation.

4 0

3 years ago

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On a coordinate plane, a line goes through (negative 12, negative 2) and (0, negative 4). A point is at (0, 6).

mariarad [96]

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st

Step-by-step explanation:

Parallel lines have:

Same slopes
Different y-intercepts

The formula of the slope of a line which passes through points $(x_{1},y_{1})$ and $(x_{1},y_{1})$ is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ The given line passes through points (-12 , -2) and (0 , -4)

∴ $x_{1}$ = -12 , $x_{2}$ = 0

∴ $y_{1}$ = -2 , $y_{2}$ = -4

- Use the formula of the slope above to find the slope of the given line

∵ $m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}$

∴ The slope of the given line is $\frac{-1}{6}$

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = $\frac{-1}{6}$

∵ The parallel line passes through point (0 , 6)

- The form of the linear equation is y = mx + b, where m is the slope

and b is the y-intercept (y when x = 0)

∵ m = $\frac{-1}{6}$ and b = 6

∴ The equation of the parallel line is y = $\frac{-1}{6}$ x + 6

Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line

Point (-12 , 8)

∵ x = -12 and y = 8

∵ y = $\frac{-1}{6}$ (-12) + 6

∴ y = 2 + 6 = 8

- The value of y is equal the y-coordinate of the point

∴ Point (-12 , 8) is on the line

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/9527422

#LearnwithBrainly

4 0

4 years ago

Read 2 more answers

What is 4/5 divided by 8

gladu [14]

(4/5) / 8....when ur dividing with fractions, flip what u r dividing by, then multiply

4/5 * 1/8 = 4/40 reduces to 1/10 <=

6 0

3 years ago

Need help on number one and three

Naya [18.7K]

An example for #1 would be that: 15 is divisible by 3, but not 9. every third multiple of 3, (9, 18, 27,...) is divisible by 9 because 9 is three times the size of 3.

For part two the first number that I thought of is 23.

4 0

3 years ago