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Iteru [2.4K]
3 years ago
9

Which of the following is the graph of y = 0.5 sec (X +pi/3 ) -2

Mathematics
1 answer:
prisoha [69]3 years ago
6 0

Answer:

See answers and explanations below (along with a graph)

Step-by-step explanation:

<u>For a secant function y = a * sec(bx + c) + d:</u>

Period: 2π/|b|

Phase shift: -c/b

Midline: d

Amplitude: |a|

<u>For the given function y = 0.5sec(x + π/3) - 2: </u>

Period: 2π (cycle repeats every 2π units)

Phase shift: -π/3 (π/3 units to the left of the parent function)

Midline: d = -2

Amplitude: a = 0.5

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1.) -2(6 - 2x) = 4(-3 + x)<br> 2.) 5 - 1(2x + 3) = -2(4 + x)
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Let's solve your equation step-by-step.

Question 1:   −2(6−2x) =4(−3+x)

 

Step 1: Simplify both sides of the equation.

−2(6−2x) =4(−3+x)

(−2) (6) +(−2) (−2x) =(4)(−3)+(4)(x)(Distribute)

−12+4x=−12+4x

4x−12=4x−12

 

Step 2: Subtract 4x from both sides.

4x−12−4x=4x−12−4x

−12=−12

 

Step 3: Add 12 to both sides.

−12+12=−12+12

0=0

Answer: All real numbers are solutions.

Question 2:  

Let's solve your equation step-by-step.

5−1(2x+3) =−2(4+x)

 

Step 1: Simplify both sides of the equation.

5−1(2x+3) =−2(4+x)

5+(−1) (2x) +(−1) (3) =(−2) (4)+(−2)(x)(Distribute)

5+−2x+−3=−8+−2x

(−2x) +(5+−3) =−2x−8(Combine Like Terms)

−2x+2=−2x−8

−2x+2=−2x−8

 

Step 2: Add 2x to both sides.

−2x+2+2x=−2x−8+2x

2=−8

 

Step 3: Subtract 2 from both sides.

2−2=−8−2

0=−10

 

Answer: There are no solutions.

 

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