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3 years ago

Unit 3: Parallel and Perpendicular Lines Homework 5: Slopes of Lines

Mathematics

1 answer:

NISA [10]3 years ago

5 0

Use the option number 5 and draw a parallel and perpendicular line across to make the slope of the lines collapse

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A Boston subway train traveling at constant speed traveled 10.1 miles in half an hour. What was the speed of the subway train? m

viva [34]

Answer: 20.2 mph

Step-by-step explanation:

Given

Train travels 10.1 miles in half an hour i.e.

Distance $d=10.1\ \text{miles}$

time $t=0.5\ hr$

we know, $\text{distance=speed}\times\text{time}$

Insert the values

$\Rightarrow 10.1=v\times 0.5\\\Rightarrow v=20.2\ mph$

6 0

3 years ago

1. A line segment has endpoints of Y(2,-3) and Z(-6,-1).

Orlov [11]

The answers will be :

a. The length of the line segment will be equal to 8.24 units.

b. The midpoint of the line segment will be ( -2 , -2 ).

c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0

What is slope of a line segment ?

The ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.

It is given that a line segment has endpoints of Y(2,-3) and Z(-6,-1).

Let's solve the given parts based on the above data.

The length of the line segment will be given by :

YZ = $\sqrt({x_{2} - x_{1})^2 + (y_{2}- y_{1})^2}$

YZ = √ [( -6 -(2)]^2 + [ -1 - (-3)]^2}

YZ = √ (-8)² + 2²)

YZ = √68

YZ = 8.24 units

The midpoint (say M) of the line segment will be given by :

M = ( $\frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2}$ )

M = [(2-6)/2 , (-3-1)/2]

M = ( -2 , -2 )

And the equation of line passing through points Y and Z will be :

$y_{2} - y_{1}$ = m ( $x_{2} - x_{1}$ )

Let's calculate value of slope (m) firstly which will be :

m =( $y_{2} - y_{1}$ ) / ( $x_{2} - x_{1}$ )

m = ( -1 + 3 ) / (-6 - 2)

m = 2 / -8

m = -1 / 4

m = -0.25

Using the value of slope (m) : we get the equation of line as :

$y - y_{1}$ = - 0.25 ( $x - x_{1}$ )

(y + 3) = - 0.25 ( x - 2)

y + 3 = -0.25 x + 0.50

y + 0.25 x - 2.5 = 0

If we multiply by 4 throughout the equation ; then the equation of line can also be written as :

4y + x - 10 = 0

Therefore the answers will be :

a. The length of the line segment will be equal to 8.24 units.

b. The midpoint of the line segment will be ( -2 , -2 ).

c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0

Learn more about line segment here ;

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5 0

1 year ago

May someone help, please ? Thank you ♥️

xeze [42]

The answer is c. A right triangle is one where a^2 + b^2 = c^2, where c is the longest side.

4 0

3 years ago

Read 2 more answers

If y varies inversely with x and y = 8...<br><br> the question is in the picture

pshichka [43]

Answer:

I believe the answer is 4.

Step-by-step explanation:

Since y = 8 when x = 4, y is double or 2 times x. So, when x = 2, y is 2 x 2, or 4.

8 0

3 years ago

I need help! (HAPPY MLK DAY!!!)

olga2289 [7]

The slope and length of the given sides of the quadrilateral can be

found by using the coordinates of the vertices.

Correct responses:

$Slope \ of \ \overline{IJ} = \underline{-\dfrac{7}{6} }$ , Length of $\overline{IJ}$ = $\underline{\sqrt{85} }$

$Slope \ of \ \overline{JK} = \underline {-\dfrac{2}{9}}$ , Length of $\overline{JK}$ = $\underline{\sqrt{85} }$

$Slope \ of \ \overline{KL} = \underline{-\dfrac{7}{6} }$ , Length of $\overline{KL}$ = $\underline{\sqrt{85}}$

$Slope \ of \ \overline{LI} = \underline{ -\dfrac{2}{9} }$ , Length of $\overline{LI}$ = $\underline{\sqrt{85} }$

<h3>Methods used to find the slope and length of a line</h3>

The given coordinates of the vertices are;

K(-7, 0), J(2, -2), I(8, -9), L(-1, -7)

$Slope = \mathbf{\dfrac{y_2 - y_1}{x_2 - x_1}}$

$Length \ of \ line = \mathbf{ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

Therefore;

$Slope \ of \ \mathbf{\overline{IJ}} = \dfrac{-2 - (-9)}{2 - 8} = \dfrac{7}{-6} = \underline{ -\dfrac{7}{6}}$

$Length \ of \ \mathbf{\overline{IJ}} = \sqrt{(2 - 8)^2 + (-2 - (-9))^2} = \underline{\sqrt{85}}$

$Slope \ of \ \mathbf{\overline{JK}} = \dfrac{0 - (-2)}{-7 - 2} = \dfrac{2}{-9} = \underline{-\dfrac{2}{9}}$

$Length \ of \ \mathbf{\overline{JK}} = \sqrt{(-7 - 2)^2 + (0 - (-2))^2} = \underline{ \sqrt{85}}$

$Slope \ of \ \mathbf{\overline{KL}} = \dfrac{0 - (-7)}{-7 - (-1)} = \dfrac{7}{-6} = \underline{ -\dfrac{7}{6}}$

$Length \ of \ \mathbf{\overline{KL} }= \sqrt{(-7 - (-1))^2 + (0 - (-7))^2} =\underline{ \sqrt{85}}$

$Slope \ of \ \mathbf{\overline{LI}} = \dfrac{(-9 - (-7))}{(8 - (-1))} = \dfrac{-2}{9} = \underline{-\dfrac{2}{9}}$

$Length \ of \ \mathbf{\overline{LI}} = \sqrt{(8 - (-1))^2 + (-9 - (-7))^2} = \underline{\sqrt{85}}$

Learn more about finding the slope and length of a line here:

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5 0

3 years ago