9514 1404 393
Answer:
b = 71 m
A = 83°
C = 29°
Step-by-step explanation:
Many calculators can solve triangles. Apps are available for phone and tablet, or on the internet, like the one used here. In general, it takes less time to use one of these than to type your question into Brainly.
Given two sides and the angle between them, the Law of Cosines is the appropriate relation to use for finding the third side.
b = √(a² +c² -2ac·cos(B))
b = √(76² +37² -2·76·37·cos(67.75°)) ≈ √5015.48
b ≈ 70.82005 ≈ 71 . . . meters
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One a side and its opposite angle are known, the remaining angles are found using the Law of Sines.
sin(A)/a = sin(B)/b
A = arcsin(a·sin(B)/b) = arcsin(76·sin(67.75°)/70.82005) ≈ 83.33°
A ≈ 83°
C = arcsin(37·sin(67.75°)/70.82005) ≈ 28.92°
C ≈ 29°
Or, you can find the remaining angle from 180° -68° -83° = 29°.
Answer:
- <em><u>average yearly salary of an individual whose final degree is a masters:</u></em><u> $ 66 thousand</u>
<u></u>
- average yearly salary of an individual whose final degree is a bachelors:<u> $ 56 thousand</u>
Explanation:
You can set a system of equation using the following steps:
1. Name the variables:
- average yearly salary of an individual whose final degree is a masters: x
- average yearly salary of an individual whose final degree is a bachelors: y
2. Set the equations that relate the variables:
- the average yearly salary of an individual whose final degree is a masters is $46 thousand less than twice that of an individual whose final degree is a bachelors:
equation (1): x = 2y - 46
- combined, two people with each of these educational attainments earn $122 thousand:
equation (2): x + y = 122
3. Solve the system:
- x = 2y - 46 . . . equation (1)
- x + y = 122 . . . equation (2)
Substitute equation (1) into equation (2)
Solve for y:
- y = 56 (this means that the average yearly salary with a bachelors degree is $ 56 thousand).
Subsitute the value on y in equation 1, to find the value of x:
- x = 2y - 46 = 2(56) - 46 = 112 - 46 = 66.
Thus, the average yearly salary of a person with a masters degree is $ 66 thousand.
Answer:
The second option
Step-by-step explanation:
The answer is negative (The blue line is below the x axis)
for all x values between -2 and -6 is a true statement
The first option is incorrect because the function is negative between -4 and -2.
The third option is incorrect because the function is negative between -3 and -2.
The forth option is incorrect because the function is positive for x < -6.
Answer:
P=3
Step-by-step explanation:
8p =24
P= 24/8
P= 3
Solve for y...
2xy=1
y=1/(2x)
So this is a function as each x value (with the exception of x=0) produces just one value for y. However, technically there is a vertical asymptote about the vertical line x=0. So there is a discontinuity as x=0.
I say this technically, because most would say that this function is true even with the discontinuity (as they do with say y=tana), but technically the discontinuity makes this not a function because another requirement of a function is for their to be an actual output value for each input value. In this case division by zero when x=0 is undefined and cannot be included as part of a function. So if you are picky about being absolute, 2xy=1 is really two functions. One with a domain of (-oo,0) and another with a domain of (0,+oo).
