Answer:
20 feet
Step-by-step explanation:
1st piece = x
2nd piece = 2x
3rd piece = 6x
x+2x+6x=180
9x=180
x=20
so the first piece is 20 feet, the second is 40, and the third is 120.
Answer:
$2 for 1 rose bush and $2 for one shrub
Step-by-step explanation:
32=2x+14y
26=11x+2y
32=2(2)+14(2)
32=4+28
32=32
26=11(2)+2(2)
26=22+4
26=26
Since both equations come out correct the cost of 1 rose bush is 2 dollars and the cost of one shrub is 2 dollars. kinda cool
Answer:
1 and - 1
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope ( gradient ) )
y = x ← is in this form
with gradient m = 1
Parallel lines have equal gradients
Then the gradients of lines parallel to the given line is 1
Given a line with gradient m then the gradient of a line perpendicular to it is
= - 
= - 
= - 1
Then the gradients of lines perpendicular to this line is - 1
Answer:
The building is 36 feet tall.
Step-by-step explanation:
Divide 6 by 4 then multiply by 24.
<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)
===========================================
<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
=====================================================
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>
