For this case what you should do is use the following trigonometric relationship:
sin (x) = C.O / h
Where
x: angle
C.O: opposite leg
h: hypotenuse
Substituting the values we have:
sen (60) = long / h
sen (60) = 3 / h
h = 3 / sin (60)
h = 3.46
Answer:
h = 3.46
X = -3
Pull out the like terms: -7x - 21 = -7 × ( x + 3)
Solve: -7 = 0
Solve: x + 3 = 0
Subtract 3 from both sides of the equation
So, x = -3
Answer:
28
Step-by-step explanation:
The binomial coefficient is calculated as:
It means that there are nCx ways to select x elements from a group of n elements.
So, If the researcher wants to determine the probability that 6 out of the next 8 individuals in his community are in favor of the president, we can replace n by 8 and x by 6 and calculated the binomial coefficient as:
<h3>
Answer: Choice D) 31.2 miles</h3>
This value is approximate.
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Explanation:
Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.
Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.
Based on those two interior angles, angle C must be...
A+B+C = 180
107+42+C = 180
149+C = 180
C = 180-149
C = 31
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To sum things up so far, we have these known properties of triangle ABC
- angle A = 107 degrees
- side c = side AB = 24 miles
- angle B = 42 degrees
- angle C = 31 degrees
Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).
b/sin(B) = c/sin(C)
b/sin(42) = 24/sin(31)
b = sin(42)*24/sin(31)
b = 31.1804803080182 which is approximate
b = 31.2 miles is the distance from the storm to station A
Make sure your calculator is in degree mode.
The solution to the composite function f(g(x)) is 9x² - 78x + 165.
<h3>
What is composite function?</h3>
A composite function is generally a function that is written inside another function.
Function composition is an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g.
From the given composite function, the solution is determined as follows;
to solve for f(g(x)), we use the following methods.
f(x) = x² + 2x - 3, g(x) = 3x - 14
f(g(x)) = (3x - 14)² + 2(3x - 14) - 3
= 9x² - 84x + 196 + 6x - 28 - 3
= 9x² - 78x + 165
Thus, the solution to the composite function f(g(x)) is 9x² - 78x + 165.
Learn more about composite function here: brainly.com/question/10687170
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The complete question is below:
F(x) =x2+2x-3 g(x)=3x-14, find f(g(x))
