Since J is the midpoint of HK, that means HK is split into two sections HJ and JK that are the same length.
1) You are told that the m<span>easure of segment HJ = 9x-2 and that of segment JK = 4x+13. Since you also know they are equal lengths, you can set these equations equal to each other to find the value of x!
HJ = JK
</span>9x-2 = 4x+13
5x = 15
x = 3
2) Now you know x = 3. Plug that into your given equations for HJ and JK to find the length of each segment (or a shortcut would be to find one of them, and then you also know the other is the same length. I'm doing both, just to make sure I don't make a silly mistake!):
HJ = <span>9x-2
</span>HJ = 9(3) - 2
HJ = 27 - 2
HJ = 25
JK = 4x + 13
JK = 4(3) + 13
JK = 12 + 13
JK = 25
3) Finally, the length of HK is just the length of HJ + JK, or HK = 25 + 25 = 50.
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Answer: HJ = 25, JK = 25, HK = 50
She spent 5.4 on tip so her overall total is $41.40
Y=mx+b b is the y intercept which is 4
m is the slope which is rise over run which is -4/2 which is -2
Linear y=-2x+4
Considering the period of the cosine function, it is found that it takes 40 seconds for the wheel to complete one turn.
<h3>What is the period of the cosine function?</h3>
The cosine function is defined by:
f(x) = acos(bx + c) + d.
For the period, we have to look at coefficient b, and the period is:
P = 2π/|B|
For this problem, the function is given by:
h(x) = 15 cos(π/20)
Hence B = π/20, and the period is:
P = 2π/|B| = 2π/(π/20) = 2 x 20 = 40 seconds.
Hence it takes 40 seconds for the wheel to complete one turn.
More can be learned about the period of trigonometric functions at brainly.com/question/12502943
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