The answer is 6.1 = 6 1/10
Answer:
2x + 20 = 3x-10
2x -3x = -20-10
-x = -30
x= 30
Checking part:
2x+20 = 2(30) +20 = 60+20 = 80
3x-10 = 3(30) - 10 = 90-10 = 80
Hence, the final answer is x = 30.
Step-by-step explanation:
<span>1. a sine curve with amplitude 2, and period 4pi radians
</span>
the general equation of the sine curve ⇒⇒ y = a sin (nθ)
where: a is the amplitude and n = 2π/perid
∵ <span>amplitude 2, and period 4pi radians
</span>
∴ y = 2 sin (θ/2)
The correct answer is option D. y = 2 sin (θ/2)
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<span>2.The period and amplitude of the function ⇒⇒ y = 5 cos 2θ
</span>
<span>comparing with y = a cos nθ
</span>
where : a is the amplitude and n = 2π/period
<span>amplitude = 5 , period = 2π/n = 2π/2 = π
</span>
The correct answer is option B. Period: pi radians: Amplitude:5
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3. tan (2π/3) = tan 120° = -√3
120° lie in the second quadrant and its reference angle = 180° - 120° = 60°
tan function in the second quadrant is negative
∴ tan 120° = - tan 60 = -√3
The correct answer is C. -sqrt3
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4. <span>Tan 5π/6 = tan 150° = -(√3)/3
</span>
150° lies in the second quadrant and its reference angle = 180° - 150° = 30°
tan function in the second quadrant is negative
∴ tan 150° = - tan 30 = -(√3)/3
The correct answer is <span>B.-sqrt3/3</span>
Answer:
30t - 4
Step-by-step explanation:
Remember to follow PEMDAS. First, distribute -6 to all terms within the parenthesis:
2 -6(-5t + 1) = 2 + (-6 * -5t) + (-6 * 1)
2 + (30t) + (-6) = 2 + 30t - 6
Simplify. Combine like terms:
2 + 30t - 6 = 30t + (-6 + 2) = 30t - 4
30t - 4 is your answer.
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Answer:
b = 7√3
Step-by-step explanation:
This 30°- 60°- 90° triangle has the proportions:
side opposite of the 30° angle = x
side opposite of the 60° angle = x√3
side opposite of the 90° angle = 2x
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Given the side opposite of the 30° angle which is 7 units long, this can be thought of as x. Knowing the proportions of the other sides, we can find b knowing that this is the side opposite of the 60° angle which is x√3.
Since x = 7, x√3 = 7√3, and therefore
b = 7√3.
