Find Arc Measures of two diameters
1 answer:
Answer:
m arc ACD =310
m arc AC = 130
Step-by-step explanation:
drawing the figure helps
if you do, should get something like the figure below
filling in arc ad as 50 degrees tells you that the angle describing it is also 50 degrees; it's a central angle.
and we know that 1/2 of a circle is 180 degrees. so if you subtract 50 from 180 you'll get 130 which will be your measurement for arc AC (because it is a central angle and AC
+AD completes the 180 half.).
as well as that to get ACD, well 1st we know that arc AC is within arc ACD. that would mean that ACD has to be more than 130.
what you can do is subtract 50 from 360. the entire circle is 360, but seeing as the arc is ACD (The rest of the circle excluding arc AD since we aren't looking for that measurement) we can just subtract.
subtracting 50 from 360 will give you 310
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Answer:
Step-by-step explanation:
Answer:
y = 3x +2
Step-by-step explanation:
It is helpful to be acquainted with the parts of at least a couple of different forms of the equation for a line.
You are given the equation of a line in "slope-intercept" form. It looks like ...
... y = mx + b . . . . . . . where m=-1/3 and b=-1
The coefficient of x, which is m, is the slope of the line. That is -1/3 for the given line.
The relationship between the slopes of perpendicular lines is that they multiply to give -1. We say each is the opposite reciprocal of the other. If we let "m" stand for the slope of the perpendicular line, it satisfies the equation ...
...(m)(-1/3) = -1
... m = -1/(-1/3) = 3 . . . . . the slope of the perpendicular line is 3.
____
Here's where another form of the equation for a line is useful. We can write the "point-slope" form* as ...
... y = m(x -h) +k . . . . . . for a line of slope m through point (h, k)
We want our line of slope = 3 to go through the point (1, 5), so its equation can be ...
... y = 3(x -1) +5 . . . . . . . variation of "point-slope" form
The given equation is in slope-intercept form, and the question asks for "the" equation of the line, so we probably should write our answer in the same form as the given equation. We can do this by eliminating the parentheses and simplifying the equation we have.
... y = 3x -3 +5 . . . . eliminate parentheses using the distributive property
... y = 3x +2 . . . . . . collect terms
The graph shows our result is at least plausible: it looks like it is perpendicular, and it goes through the given point.
___
<em>*Comment on point-slope form</em>
Usually, you will see "point-slope" form written as ...
... y -k = m(x -h) . . . . . . . . standard version of "point-slope" form
When our intent is to use this form to get to slope-intercept form, it is more convenient to add k to this equation to get ...
... y = m(x -h) +k . . . . . . . occasionally useful version
