Answer:
Step-by-step explanation:
- <u>CD is angle bisector of angle ACB:</u>
- ∠BCD = ∠ACD = 90°/2 = 45°
- ∠CBD = 45° as ∠CDB = 90°
- CD = BD as triangle CDB is isosceles right triangle
- BC = CD√2 as per property of 45° right triangle
- CD = BC/√2 = 3/√2 = 3√2/2 = 2.12 in
Among the students who did not make the honor roll. Then the relative frequency of having no curfew will be 7.
<h3>How to find the relative frequency?</h3>
Relative frequency is the ratio of the considered sub-group count to the total count. (so its frequency of the considered sub-group relative to the total frequency).
Curfew No Curfew No
Honor Roll: 18 10
No Honor Roll: 2 7
Among the students who did not make the honor roll.
Then the relative frequency of having no curfew will be 7.
Learn more about relative frequency here:
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First of all, lets say a is the shortest side, b the second and c the longest.
We can therefore write the following equations:
a=(1/2)b=(1/3)c
-> b=2a and c=3a (in order to have the three of them with the same variable)
Perimeter = a + b + c
P= a + 2a + 3a
P=6a
Now if we compare c to the perimeter (using ratio) we get:
c/6a = 3a/6a = 1/2
Therefore, the longest side is equal to half the perimeter
The square root of 13^2 - 6^2
The answer is approximately 11.5 cm option B
<h3>2
Answers: Choice C and choice D</h3>
y = csc(x) and y = sec(x)
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Explanation:
The term "zeroes" in this case is the same as "roots" and "x intercepts". Any root is of the form (k, 0), where k is some real number. A root always occurs when y = 0.
Use GeoGebra, Desmos, or any graphing tool you prefer. If you graphed y = cos(x), you'll see that the curve crosses the x axis infinitely many times. Therefore, it has infinitely many roots. We can cross choice A off the list.
The same applies to...
- y = cot(x)
- y = sin(x)
- y = tan(x)
So we can rule out choices B, E and F.
Only choice C and D have graphs that do not have any x intercepts at all.
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If you're curious why csc doesn't have any roots, consider the fact that
csc(x) = 1/sin(x)
and ask yourself "when is that fraction equal to zero?". The answer is "never" because the numerator is always 1, and the denominator cannot be zero. If the denominator were zero, then we'd have a division by zero error. So that's why csc(x) can't ever be zero. The same applies to sec(x) as well.
sec(x) = 1/cos(x)