Ask question

Ask question

All categories

3 years ago

10

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:

Vera_Pavlovna [14]3 years ago

6 0

Answer:

Segment LM is 0.5 units longer than segment JK.

Step-by-step explanation:

We have been given that segment JK has a length of 4.5 units. If segment LM has end points of L (3,1) and M (-1,4).

We will find length of segment LM using distance formula.

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

Substitute given values:

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

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

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

$D=\sqrt{16+9}$

$D=\sqrt{25}$

$D=5$

Therefore, the distance of segment LM is 5 units.

Now, we will find the difference between segment LM and JK as:

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

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

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

stepan [7]3 years 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

LM is 0.5 units longer than LM.

You might be interested in

PLEASE HELP 50 points

hoa [83]

Answer:

r > 7 (C)

Step-by-step explanation:

3r−7>14

Step 1: Add 7 to both sides.

3r−7+7>14+7

3r>21

Step 2: Divide both sides by 3.

3r

3

>

21

3

r>7

Hope this helps and makes sense!! Good luck and have a wonderful day! <33

Imagine this < as a alligater and itś eating the greater number!!

8 0

3 years ago

Read 2 more answers

If 5 + 20 times 2^2 minus 3x = 10 times 2^- 2x + 5, what is the value of x?

LUCKY_DIMON [66]

The answer to the problem is going to be 3

4 0

3 years ago

XYZ has coordinates X(2, 3), Y(1,4), and Z(8,9). A translation maps X to X'(4,7). What are the coordinates for Y' and Z' for thi

Rashid [163]

Answer:

The coordinates are $Y'(x,y) = (3, 8)$ and $Z'(x,y) = (10, 13)$ .

Step-by-step explanation:

First, we have to derive an expression for translation under the assumption that each point of XYZ experiments the same translation. Vectorially speaking, translation from X to X' is defined by:

$X'(x,y) = X(x,y) + T(x,y)$ (1)

Where $T(x,y)$ is the vector translation.

If we know that $X(x,y) = (2,3)$ and $X'(x,y) = (4,7)$ , then the vector translation is:

$T(x,y) = X'(x,y)-X(x,y)$

$T(x,y) = (4,7) - (2,3)$

$T(x,y) = (2, 4)$

Then, we determine the coordinates for Y' and Z':

$Y'(x,y) = Y(x,y) + T(x,y)$

$Y'(x,y) = (1,4) + (2,4)$

$Y'(x,y) = (3, 8)$

$Z'(x,y) = Z(x,y) + T(x,y)$

$Z'(x,y) =(8,9) + (2,4)$

$Z'(x,y) = (10, 13)$

The coordinates are $Y'(x,y) = (3, 8)$ and $Z'(x,y) = (10, 13)$ .

7 0

3 years ago

Slav-nsk [51]

<span>x^2 + 15x + 56.25 = 105.25

"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.

Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?" Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25

Now take the square root of each side
(x+7.5) = sqrt(105.25)

And let's use both the positive and negative square roots.
So x+7.5 = 10.25914226
and
x+7.5 = -10.25914226

And let's find X.
x+7.5 = 10.25914226
x = 2.759142264

x+7.5 = -10.25914226
x = -17.75914226

So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>

3 0

3 years ago

Read 2 more answers

PLEASE HELP ME ASAP, WORK DUE IN AN HOUR!!!!!!! WILLING TO GIVE ANYTHING

Tju [1.3M]

38 boxes on the top shelf

6 0

3 years ago

Read 2 more answers