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3 years ago

14

M is the midpoint of LN. what is LM?

2 answers:

Serjik [45]3 years ago

7 0

Given,

M is the midpoint of LN.

Thus,

LM = MN

3x = 2x + 2

3x - 2x = 2

x = 2

Hence,

LM = 3x = 3 * 2 = 6

Hence, LM is 6 units.

kherson [118]3 years ago

4 0

Answer: LM = 6 units.

Step-by-step explanation: Given that the point M is the mid-point of the line segment LN shown in the figure.

We are to find the length of LM.

From the figure, we note that

LM = 3x and MN = 2x + 2.

Since M is the mid-point of LN, so it will divide LN in two equal parts.

That is, we must have

$LM=MN\\\\\Rightarrow 3x=2x+2\\\\\Rightarrow 3x-2x=2\\\\\Rightarrow x=2.$

Therefore, we get

$LM=3\times2=6~\textup{units}.$

Thus, LM = 6 units.

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The figure of the rectangle ABCD is attached to the answer.

We are given that Parallelogram ABCD is a rectangle.

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Diagonal BD and AC intersect each other at a point labeled as X.

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Answer:

Part 1) $-17\frac{8}{9}$ -----> $-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}$

Part 2) $-15.11$ ------> $-12.48-(-2.99)-5.62$

Part 3) $-19\frac{8}{9}$ -----> $-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})$

Part 4) $-201.65$ -----> $-353.92-(-283.56)-131.29$

Part 5) $74$ ------> $83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})$

Step-by-step explanation:

Part 1) we have

$-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}$

To calculate the subtraction convert the mixed numbers to an improper fractions

$6\frac{4}{9}=\frac{6*9+4}{9}=\frac{58}{9}$

$3\frac{2}{9}=\frac{3*9+2}{9}=\frac{29}{9}$

$8\frac{2}{9}=\frac{8*9+2}{9}=\frac{74}{9}$

substitute

$-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=-\frac{(58+29+74)}{9}=-\frac{161}{9}$

Convert to mixed number

$-\frac{161}{9}=-(\frac{153}{9}+\frac{8}{9})=-17\frac{8}{9}$

Part 2) we have

$-12.48-(-2.99)-5.62$

To calculate the subtraction eliminate the parenthesis first

$-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11$

Part 3) we have

$-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})$

To calculate the subtraction convert the mixed numbers to an improper fractions

$19\frac{2}{9}=\frac{19*9+2}{9}=\frac{173}{9}$

$4\frac{1}{9}=\frac{4*9+1}{9}=\frac{37}{9}$

$3\frac{4}{9}=\frac{3*9+4}{9}=\frac{31}{9}$

substitute

$-\frac{173}{9}-\frac{37}{9}-(-\frac{31}{9})$

Eliminate the parenthesis

$-\frac{173}{9}-\frac{37}{9}+\frac{31}{9}=\frac{(-173-37+31)}{9}=-\frac{179}{9}$

Convert to mixed number

$-\frac{179}{9}=-(\frac{171}{9}+\frac{8}{9})=-19\frac{8}{9}$

Part 4) we have

$-353.92-(-283.56)-131.29$

To calculate the subtraction eliminate the parenthesis first

$-353.92+283.56-131.29=-201.65$

Part 5) we have

$83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})$

To calculate the subtraction convert the mixed numbers to an improper fractions

$83\frac{1}{5}=\frac{83*5+1}{5}=\frac{416}{5}$

$108\frac{2}{5}=\frac{108*5+2}{5}=\frac{542}{5}$

$99\frac{1}{5}=\frac{99*5+1}{5}=\frac{496}{5}$

substitute

$\frac{416}{5}-\frac{542}{5}-(-\frac{496}{5})$

Eliminate the parenthesis

$\frac{416}{5}-\frac{542}{5}+\frac{496}{5}=\frac{(416-542+496)}{5}=\frac{370}{5}=74$

3 0

3 years ago