Answer:
Step-by-step explanation:
4x > -16 reduces to x > -4: All numbers greater than x = -4 (shaded area to the right of -4).
6x < -48 reduces to x < -8: All numbers to the left of -8 (shaded area to the left of -8).
Solution: (-infinity, -4) ∪ (-8, infinity)
The number line between -8 and -4 is not part of the solution set (is not shaded or darkened)
Draw an open circle at -8 and extend an arrow to the left of this circle. Then draw an open circle at -4 and extend an arrow to the right of this circle.
5p squared - 2p - 8 - 8 over p+3
Answer:75 mph
Step-by-step explanation:
<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)
