Answer:
x ≥ 4
Step-by-step explanation:
–4(8 – 3x) ≥ 6x – 8
Distribute
-32 +12x ≥ 6x – 8
Subtract 6x from each side
-32 +12x-6x ≥ 6x-6x – 8
-32 +6x ≥ – 8
Add 32 to each side
-32 +32 +6x≥ 32– 8
6x ≥ 24
Divide by 6
6x/6 ≥ 24/6
x ≥ 4
Answer:
Step-by-step explanation:
In a geometric sequence, the next term is a constant times the previous term. This constant is determined by dividing the second term by the first, here giving 5. The remaining terms are checked to see that each is 5 times the previous. 75 is 15×5, 375 is 75×5.
Alternately, the nth term is first term times k^(n-1).
Here, that's 3×5^(10-1), 3×5^9=5859375
Answer: f(120°) = (√3) + 1/2
Step-by-step explanation:
i will solve it with notable relations, because using a calculator is cutting steps.
f(120°) = 2*sin(120°) + cos(120°)
=2*sin(90° + 30°) + cos(90° + 30°)
here we can use the relations
cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)
sin(a + b) = cos(a)*sin(b) + cos(b)*sin(a)
then we have
f(120°) = 2*( cos(90°)*sin(30°) + cos(30°)*sin(90°)) + cos(90°)*cos(30°) - sin(90°)*sin(30°)
and
cos(90°) = 0
sin(90°) = 1
cos(30°) = (√3)/2
sin(30°) = 1/2
We replace those values in the equation and get:
f(120°) = 2*( 0 + (√3)/2) + 0 + 1/2 = (√3) + 1/2
The answer is true. A conditional probability is a measure
of the probability of an event given that (by assumption, presumption,
assertion or evidence) another event has occurred. If the event of interest is
A and the event B is known or assumed to have occurred, "the conditional
probability of A given B", or "the probability of A in the condition
B", is usually written as P (A|B). The conditional probability of A given
B is well-defined as the quotient of the probability of the joint of events A
and B, and the probability of B.
Answer:
feet
Step-by-step explanation:
In a 30-60-90 triangle, the ratios of the side lengths of the triangle is 
Where 1 is the shortest leg, root(3) is the longer leg, and 2 is the hypotenuse.
First we can set x equals to the length of the original pole, and so the shorter leg has a length of x/3 and using the ratio of side lengths, we can find that:

Solving for x, we find that

So the length of the original pole would be
feet
If you found this answer helpful, please consider marking it as brainliest, or give it a thanks and a 5 star review. Thanks!