HELP ME PLEASE!! TOPIC: GEOMETRY
if QE = 2m + 3 and EI = m + 10 then find m and QI
if TU = 34 and EU = 4 n + 1 , then find N. click the picture:>
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HELP ME PLEASE!! TOPIC: GEOMETRY
if QE = 2m + 3 and EI = m + 10 then find m and QI
if TU = 34 and EU = 4 n + 1 , then find N. click the picture:>
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Answer:
n = 3/10, or N = 0.3
Step-by-step explanation:
For the first problem:
Since QE = QI + EI, we can substitute the given values to get:
2m + 3 = QI + (m + 10)
Simplifying this equation gives:
QI = m - 7
To find m, we can substitute QI back into the original equation and solve for m:
QE = 2m + 3 = QI + EI = (m - 7) + (m + 10) = 2m + 3
Simplifying this equation gives:
2m + 3 = 2m + 3
This means that the equation is true for any value of m, so m can be any real number.
Therefore, m is undefined, and QI = m - 7 is also undefined.
For the second problem:
We are given that TU = 34 and EU = 4n + 1. We can use this information to find N by solving for n:
TU = TE + EU
TE = TU - EU = 34 - (4n + 1) = 33 - 4n
We know that TE = TN + NE, so we can substitute the given values to get:
TN + NE = 33 - 4n
Since NE = EU = 4n + 1, we can substitute this into the equation to get:
TN + 4n + 1 = 33 - 4n
Simplifying this equation gives:
TN = 32 - 8n
We also know that TN = TM + MN, so we can substitute the given value of TU to get:
TU = TM + TN + NE
Substituting the values we've found for TN and NE gives:
34 = TM + (32 - 8n) + (4n + 1)
Simplifying this equation gives:
TM = -5n + 1
We know that TM = TN + NM, so we can substitute the given value of TE to get:
TE = TN + NM
Substituting the values we've found for TM and TN gives:
33 - (4n + 1) = (32 - 8n) + NM
Simplifying this equation gives:
NM = 5n - 2
Therefore, we have found that TM = -5n + 1 and NM = 5n - 2. To find N, we can set these equations equal to each other:
-5n + 1 = 5n - 2
Simplifying this equation gives:
10n = 3
Therefore, n = 3/10, or N = 0.3.