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2 years ago

Find the measure of angle k

Mathematics

2 answers:

tatiyna2 years ago

8 0

Answer:

Step-by-step explanation:

artcher [175]2 years ago

6 0

Answer: 30 Degrees

Step-by-Step Explanation:

As we know, a line is 180 degrees.

Hence, 65 + 85 + k = 180
= 65 + k = 180 - 85 = 95
=> k = 95 - 65 = 30

Therefore, k = 30

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3 years ago

Classify each of the power functions based on their end behavior (increasing or decreasing) as x = ∞

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Answer: right side behavior:

f(x) is Decreasing

g(x) is Increasing

h(x) is Increasing

j(x) is Decreasing

Step-by-step explanation:

The rules for end behavior are based on 2 criteria: Sign of leading coefficient and Degree of polynomial

Sign of leading coefficient (term with greatest exponent):

If sign is positive, then right side is increasing
If sign is negative, then right side is decreasing

Degree of polynomial (greatest exponent of polynomial:

If even, then end behavior is the same from the left and right
If odd, then end behavior is opposite from the left and right

f(x) = -2x²

Sign is negative so right side is decreasing
Degree is even so left side is the same as the right side (decreasing)

as x → +∞, f(x) → +∞ Decreasing

as x → -∞, f(x) → -∞ Decreasing

g(x) = (x + 2)³

Sign is positive so right side is increasing
Degree is odd so left side is opposite of the right side (decreasing)

as x → +∞, f(x) → +∞ Increasing

as x → -∞, f(x) → -∞ Decreasing

$h(x)=-1+x^{\frac{1}{2}}\implies h(x)=x^{\frac{1}{2}}-1$

Sign is positive so right side is increasing
Degree is an even fraction so left side is opposite of the right side as it approaches the y-intercept (-1)

as x → +∞, f(x) → +∞ Increasing

as x → -∞, f(x) → -1 Decreasing to -1

$j(x)=\dfrac{1}{2}(-x)^5\implies j(x)=\dfrac{1}{2}(-1)^5(x)^5\implies j(x)=-\dfrac{1}{2}x^5$

Sign is negative so right side is decreasing
Degree is odd so left side is opposite of the right side (increasing)

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as x → -∞, f(x) → -∞ Increasing

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4 years ago