1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Monica [59]
1 year ago
14

I have completed the first three parts of this question, but now need help to finish...I need to calculate the ratios of the 4 l

ine segments LK, LM, ON, and OP. Based on the ratios, what can you conclude about three or more parallel lines that intersect two transversals?

Mathematics
1 answer:
galben [10]1 year ago
7 0

At first, we will find the lengths of LK, Lm, ON, OP, then use them to find the ratios between them

The rule of the distance is

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

For LK

Since L = (3, 6), K = (1,5.33), then

\begin{gathered} LK=\sqrt{(3-1)^2+(6-5.33)^2} \\ LK=\sqrt{4+0.4489} \\ LK=\sqrt{4.4489} \end{gathered}

For LM

Since L = (3, 6), M = (5, 6.67), then

\begin{gathered} LM=\sqrt{(3-5)^2+(6-6.67)^2} \\ LM=\sqrt{4+0.4489} \\ LM=\sqrt{4.4489} \end{gathered}

For ON

Since O = (3, 2.59) and N = (5, 4.2), then

\begin{gathered} ON=\sqrt{(3-5)^2+(2.59-4.2)} \\ ON=\sqrt{4+2.5921} \\ ON=\sqrt{6.5921} \end{gathered}

For OP

Since O = (3, 2.59), P = (1, 0.99), then

\begin{gathered} OP=\sqrt{(3-1)^2+(2.59-0.99)^2} \\ OP=\sqrt{4+2.56} \\ OP=\sqrt{6.56} \end{gathered}

Now let us find the ratios between them

\begin{gathered} \frac{KL}{LM}=\frac{\sqrt{4.4489}}{\sqrt{4.4489}}=1 \\ \frac{PO}{ON}=\frac{\sqrt{6.56}}{\sqrt{6.5921}}=0.9975\approx1 \\ \frac{KL}{LM}=\frac{PO}{ON}=1 \end{gathered}

That means, Parallel lines intercept equal parts

By joining MP

We will have Triangle KPM

Since KL = LM ------- Proved using the distance formula

Since LQ // KP ------ Given

Then MQ = QP ------- Using the theorem down

The theorem

If a line is drawn from a midpoint of one side of a triangle parallel to the opposite side, then it will intersect the 3rd side in its midpoint (Q is the midpoint of MP)

Parallel lines intercept equal parts

You might be interested in
Keeping the properties of exponents in mind, to what power must you raise the expression 7 1/2 to get 7 as a result
zhenek [66]
For this case we have the following expression:
 7 ^ {(1/2)}

 Rewriting the expression we have:
 (7 ^ {(1/2)}) ^ x

 Where,
 x: exponent to which we must raise the expression to obtain 7 as a result.
 We have then:
 7 ^ {((1/2) x)}

 The exponent must be equal to 1:
 (1/2) x = 1

 Clearing x we have: 
 x = 2

 Substituting valres:
 7 ^ {((1/2) 2)}

7 ^ 1

7
 Answer:
 
you must raise the expression to 2
7 0
3 years ago
The average score of all golfers for a particular course has a mean of 61 and a standard deviation of 3.5 . Suppose 49 golfers p
Nadya [2.5K]

Answer:

The probability that the average score of the 49 golfers exceeded 62 is 0.3897

Step-by-step explanation:

The average score of all golfers for a particular course has a mean of 61 and a standard deviation of 3.5

\mu = 61

\sigma = 3.5

We are supposed to find he probability that the average score of the 49 golfers exceeded 62.

Formula : Z=\frac{x-\mu}{\sigma}

Z=\frac{62-61}{3.5}

Z=0.285

Refer the z table for p value

p value = 0.6103

P(x>62)=1-P(x<62)=1-0.6103=0.3897

Hence the probability that the average score of the 49 golfers exceeded 62 is 0.3897

7 0
3 years ago
Can someone help me with this with step by step explanation plssss
liberstina [14]

Answer:

m = - 16/10

= - 1.6

Step-by-step explanation:

m2 + 8m

(the - 16 here is divided into 10 m's as you can see in m2 and 8m)

So, in order to find out what 1m is, you have to <em>divide</em> - 16 by 10, which gives you - 1.6

Good luck!

5 0
3 years ago
Fei Yens dog eats 8 ounces of dog food each day. Fei Yen bought a 28 pound bag of dog food. how many 8 ounce servings are in a 2
steposvetlana [31]
One pound is 16 ounces so 28 pounds is 28x16 which is 448. 448 divided by 8 ounces per serving is 56 ounces per bag
4 0
2 years ago
​ △BCD ​ is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.
zheka24 [161]
<span>here we can use Pythogoras' theorem.
in right angled triangles the square of the hypotenuse is equal to the sum of the squares of the other 2 sides.
hypotenuse is 19 cm. One side is 13 cm and we need to find the length of the third side.
                                                                         
19</span>²<span> = 13</span>²<span> + X</span>²<span> 
X - length of the third side
                                                           
361 = 169 + X</span>²<span> 
X</span>²<span> = 361 - 169
                                                                     
X</span>²<span> = 192
                                                                             
X = 13.85 the length of third side rounded off to the nearest tenth is 13.9 cm</span>
3 0
3 years ago
Other questions:
  • Parallelogram ABCD is reflected over the y-axis, followed by a reflection over the x-axis, and then rotated 180 degrees about th
    10·1 answer
  • What is true of the data in the Dot Plot check on that apply number of televisions per household?​
    14·1 answer
  • A block of sugar maple wood has a mass of 82.8 g and density of 0.69 ​ g/cm3 ​. The block is a rectangular prism with a length o
    6·1 answer
  • Harold’s car has a fuel efficiency of 25 miles/gallon. Harry’s car has a fuel efficiency of 12 km/liter. What is the fuel effici
    13·1 answer
  • The commutative property of multiplication states that the order in which two numbers are multiplied does not change the product
    9·1 answer
  • Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify t
    9·1 answer
  • The first step to use to solve for the missing side?
    8·1 answer
  • What is the COMMON RATIO of the geometric sequence: 3024, 504, 84,<br> 14, ...*<br> 2
    10·1 answer
  • Maura drew a scale drawing of an apartment. She used the scale 1 centimeter : 2 meters. In the drawing, the living room is 3 cen
    12·2 answers
  • Help me to convert the following to redian (1) 300° (2)18° (3) 105°​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!