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2 months ago

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Segment JK has a length of 4.5 units. If segment LM has end points of L (3,1) and M (-1,4), how much longer than segment JK is s

egment LM?

2 answers:

lawyer [12.5K]2 months ago

6 0

Answer:

Segment LM measures 0.5 units longer than segment JK.

Step-by-step explanation:

It is known that segment JK has a length of 4.5 units, while segment LM has end points L (3,1) and M (-1,4).

To determine the length of segment LM, we will apply the distance formula.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plugging in the known values:

$D=\sqrt{(3-(-1))^2+(1-4)^2}$

$D=\sqrt{(3+1)^2+(-3)^2}$

$D=\sqrt{(4)^2+(-3)^2}$

$D=\sqrt{16+9}$

$D=\sqrt{25}$

$D=5$

Thus, the length of segment LM is 5 units.

Next, we will calculate the difference in length between segment LM and JK as follows:

$\text{Difference between LM and JK}=5-4.5$

$\text{Difference between LM and JK}=0.5$

Consequently, segment LM is 0.5 units longer than segment JK.

Leona [12.6K]2 months ago

4 0

Distance formula:
$d= \sqrt{ (x_{2}-x_{1}) ^{2}+( y_{2} - y_{1} )^{2}}\\ d= \sqrt{ (3-(-1)) ^{2}+(1 - 4 )^{2}}\\ d= \sqrt{ (4) ^{2}+(-3)^{2}}\\ d=\sqrt{16+9}\\ d=\sqrt{25}\\ d=5$

5 units-4.5 units=0.5 units

Segment LM exceeds segment JK by 0.5 units.

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Maia had 2064 more beads than Jenny. After Maia used 144 beads to make a necklace, she had 5 times as many beads as Jenny. A) ho

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B) Maia had 2544 beads at first.

Step-by-step analysis:

Let x denote the beads with Jenny and y for Maia.

The information provided states that Maia possesses 2064 beads more than Jenny, which can be represented mathematically as:

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Additionally, after Maia made a necklace with 144 beads, she had five times more beads than Jenny.

This can also be formulated as an equation:

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$\text{Number of beads Maia had more than Jenny in the end}=1920$

Thus, Maia is left with 1920 beads more than Jenny.

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By inserting equation (1) into equation (2), we arrive at:

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