The problem statement tells you ∠MLK is 61°, so ∠LMK = 180° -68° -61° = 51°. Since a tangent is always perpendicular to a radius, triangles LJM and LJK are right triangles.
Trigonometry tells you ...
tangent = opposite / adjacent
so you can write two relations involving LJ.
tan(51°) = LJ/JM
tan(68°) = LJ/JK
The second equation can be used to write an expression for LJ that can be substituted into the first equation.
LJ = JK*tan(68°) = 3*tan(68°)
Substituting, we have
tan(51°) = 3*tan(68°)/JM
Multiplying by JM/tan(51°), we get
JM = 3*tan(68°)/tan(51°)
JM ≈ 6.01
The radius of circle M is about 6.01.
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HMO, confirmed.
<h3>
Answer: Exponential growth. The growth rate is 6%</h3>
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Explanation:
The general form of an exponential function is
y = a*b^x
where 'a' is the initial starting amount and b helps determine if we have exponential decay or exponential growth, and how much of it.
We have a = 330 as the initial amount. Since b = 1.06 is larger than 1, this means we have exponential growth. If 0 < b < 1, then we would have exponential decay.
Solving 1+r = 1.06 leads to r = 0.06 = 6%, showing we have a growth rate of 6%
This means that if we started with say 100 people, and the population grew by 6%, then at the end of the time unit (say 1 year), then we'd have 106 people.
Angle BCA
Step-by-step explanation:
You can see this due to the angle having the name amount of congruent angle marks.
Answer:
D, (4,-4) satisfies both equations.
Step-by-step explanation:
The answer to a system of equations is where the lines intersect, and these lines intersect at (4,-4)