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
Answer: m=
1
3
√2 or m=
−1
3
√2
Step-by-step explanation:
Answer:
40%
Step-by-step explanation:
6/15=favorable amount/total amount
6/15=2/5
2/5*20
Answer:
x ≤ - 2
Step-by-step explanation:
Given the inequality :
3x+5≤−1
Subtract 5 from both sides
3x + 5 - 5 ≤ - 1 - 5
3x ≤ - 6
Divide both sides by 3
3x/3 ≤ - 6/3
x ≤ - 2
Mr.Choe's error was that he changed the inequality sign. The inequality sign in this case does not need to be changed.
The sum of the interior angles of all triangles is 180 degrees. This is a right triangle, thus we know two interior angle values (90 degrees and 29 degrees). To find the third, set the sum of all interior angle values equal to 180 and solve for g.
180 = 90 + 29 + g
Collect like terms.
180 = 119 + g
Subtract 119 from both sides.
61 = g
Find the sum using 61 for g to check work.
180 = 90 + 29 + g
180 = 90 + 29 + 61
180 = 180
Answer:
m∠g = 61°
