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timofeeve [1]
3 years ago
7

WILL GIVE BRAINLIEST 20 POINTS

Mathematics
2 answers:
allochka39001 [22]3 years ago
8 0

Step-by-step explanation:

hope it helps you!!!!!!!!!!!

Gala2k [10]3 years ago
6 0

Answer:

x = - 3

Step-by-step explanation:

Given the 2 equations

y = \frac{1}{3} x + 7 → (1)

y = 3x + 15 → (2)

Since both equations express y in terms of x, equate the right sides

3x + 15 = \frac{1}{3} x + 7

Subtract \frac{1}{3} x from both sides

\frac{8}{3} x + 15 = 7 ( subtract 15 from both sides )

\frac{8}{3} x = - 8 ( multiply both sides by 3 )

8x = - 24 ( divide both sides by 8 )

x = - 3

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1. A sine function has the following key features:
andrew11 [14]
Problem 1

See the attached image (figure 1)

16pi seems like a typo. I'm going to assume that it's a fraction and it is 1/(6pi)
f = 1/(6pi) = frequency
T = 1/f = 1/(1/(6pi)) = 6pi
Amplitude = 2
a = 2
b = 2pi/T = 2pi/(6pi) = 1/3
Midline: y = 3
d = 3

The function is
y = a*sin(bx-c)+d
y = 2*sin(1/3*x-0)+3
y = 2*sin(x/3)+3

===============================================

Problem 2

See the attached image (figure 2) 

T = 12 is the period
a = 4 is the amplitude
b = 2pi/T = 2pi/12 = pi/6
y = 1 is the midline so d = 1
The y intercept is (0,1) which is the midline, which indicates no phase shifts have occurred so c = 0

The function is
y = a*sin(bx-c)+d
y = 4*sin((pi/6)x-0)+1
y = 4*sin((pi/6)x)+1

===============================================

Problem 3

See the attached image (figure 3)

Period = 4pi
T = 4pi
b = 2pi/T = 2pi/(4pi) = 1/2 = 0.5
Amplitude = 2
a = 2
Midline: y = 3
d = 3
y-intercept: (0,3)
The function is a reflection of its parent function over the x-axis, so 'a' is negative meaning a = -2 instead of a = 2

The function is
y = a*sin(bx-c)+d
y = -2*sin(0.5x-0)+3
y = -2*sin(0.5x)+3

===============================================

Problem 4

See the attached image (figure 4)

a = 10 which is half of the distance between the highest and lowest points
T = 8 is the period
b = 2pi/T = 2pi/8 = pi/4
c = -pi/2 is the phase shift since its really a cosine graph
d = 0 is the midline

The function is
y = a*sin(bx-c)+d
y = 10*sin((pi/4)*x+(-pi/2))+0
y = 10*sin((pi/4)*x+pi/2)

===============================================

Problem 5

See the attached image (figure 5)

a = 2 is the amplitude since it bobs up and down this distance from the midline
T = 8 seconds is the period (double that of the time it takes for it to go from the highest to the lowest point)
b = 2pi/T = 2pi/8 = pi/4
c = 0 is the phase shift as the buoy starts at normal depth of 20 meters
d = 20 is the midline

The function is
y = a*sin(bx-c)+d
y = 2*sin((pi/4)x-0)+20
y = 2*sin((pi/4)x)+20

===============================================

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Point Q' is the image of Q(5, -3) after a translation down 2 units and right 4 units. What are the coordinates of Q'?
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Answer:

A. (9,-5)

Step-by-step explanation:

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aev [14]
The is The 103.8 Cause Of the math is correct
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