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
Evgen [1.6K]
3 years ago
13

S KM ∥ JN? Why or why not?

Mathematics
2 answers:
atroni [7]3 years ago
7 0
This is the concept of linear proportionality, triangle JLN and triangle KLM are similar, this implies that:
KL/KJ=ML/MN
which implies that:
16/10=24/15
therefore we conclude that the answer is :
Yes, because 16/10=24/15
bixtya [17]3 years ago
4 0

Given: We have the given figure through which we can see

LK=16,

KJ=10,

LM=24,

MN=15

To Find: Whether KM || JN and the reasoning behind it.

Solution: Yes, KM || JN because \frac{16}{10}= \frac{24}{15}

Explanation:

For this solution, we use the concept of Similar Triangles.

Now, KM || JN if ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Now, ∠MLK=∠NLJ

To prove similarity of the two triangles, we have to show that the sides are proportional. In other words, LK:KJ = LM:LN

LK:KJ=LM:LN\\\\ \frac{LK}{KJ} =\frac{LM}{LN}\\\\\frac{16}{26}= \frac{24}{39}\\\\

which is true as both sides simplify to \frac{8}{13}

Thus, we see that ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Therefore, KM || JN.

To come to the reasoning, notice that

\frac{LK}{LJ} =\frac{LM}{LN}\\\\\frac{LK}{LK+KJ} =\frac{LM}{LM+MN}\\\\\frac{LK+KJ}{LK} =\frac{LM+MN}{LM}\\\\1+\frac{KJ}{LK}=1+ \frac{MN}{LM}\\\\\frac{LK}{KJ} =\frac{LM}{MN}

In other words, \frac{16}{10}= \frac{24}{15}


You might be interested in
How many triangles can be constructed with angles measuring 60 degrees 60 degrees and 40 degrees
erma4kov [3.2K]
None, a triangle need to have angles measuring 180 degrees , its only possible if the triangle has three angles equaling 60
8 0
3 years ago
Read 2 more answers
Can someone help me with this question????PLEASE
kiruha [24]
Divide the number of quarts of beef soup by the number of cups of vegetables.
1000 / 510

you should get 1.96
If your teacher wants you to round up you should try 2.
3 0
3 years ago
Read 2 more answers
Can you please explain this?​
Leni [432]

Answer:

The question is giving you pairs of points in space which can be used to define lines. It is then asking you to determine if the lines defined by those points are parallel, perpendicular, or neither.

Step-by-step explanation:

Two key things you need to know to solve this is that the lines will be parallel if their slopes are the same, and perpendicular if one slope is the negative reciprocal of the other (i.e. s_{1} = -s_{2}^{-1})

Let's start with question 11. You are given two pairs of points, each of which describes a distinct line:

(3,5)-(1,1) and (0, 2)-(5, 12)

To find the slope of each pair, take the vertex with the lesser x co-ordinate, and subtract it from the vertex with the greater x co-ordinate.  That will give us a valid Δx and Δy to get the slope.

In the first pair, 3 > 1, so we'll subtract the second point from the first:

s = \Delta y / \Delta x\\s = \frac{5 - 1}{3 - 1}\\s = 4/2\\s = 2

So the first pair of vectors describe a line with a slope of 2.  Let's look at the other pair:

s = \Delta y / \Delta x\\s = (12 - 2) / (5 - 0)\\s = 10 / 5\\s = 2

That also gives us a slope of 2, meaning that the two lines are parallel.

This same process will need to be done for the other three questions.  We can't answer questions 12 or 14 here, as the last point is cut off on the edge of the image.  For question 3 though, one line has a slope of 7/3, and the other 3/7. That puts them in the "neither" category, as one is not the negative reciprocal of the other, but instead the positive reciprocal.

6 0
3 years ago
In a fruit cocktail, for every 72 ml of orange juice you need 56 ml of apple juice and 120 ml of coconut milk. What is the ratio
olasank [31]

Answer:

7 : 15 : 9

Step-by-step explanation:

The GCF is 8:

56/8 = 7

120/8 = 15

72/8 = 9

6 0
3 years ago
Read 2 more answers
Should i put a comma after
suter [353]
The answer is before
6 0
3 years ago
Other questions:
  • Find the exact value of tan ^-1 (-root of 3)<br> Write your answer in radians in terms of n.
    8·1 answer
  • Write a sequence of transformations that maps quadrilateral abcd onto quadrilateral a b c d
    11·1 answer
  • Y varies directly as the square of x. If y is 25 when x is 3, find y when x is 2
    5·1 answer
  • HELLO THERE. PLS HELP ME WITH GEOMETRY
    11·1 answer
  • a consumer wants to purchase 1.5 l of antibacterial liquid hand soap. The bottles on the store shelf hold 16oz, 32oz, 48 oz, and
    7·1 answer
  • Lupe has 500 Mexican pesos. If 1 U.S. dollar equals 12.87333 pesos, about how many dollars can Lupe buy for her pesos?
    9·1 answer
  • HELP ME PLZZZZ ASAP!!!
    11·1 answer
  • A box contains 100 colored chips; some are pink and some are blue. Milton chooses a chip at random, records the color, and place
    12·2 answers
  • A ramp must be in the form of a right triangle where every vertical length(leg) of 1 ft has a horizontal length(leg) of 12 ft. W
    14·1 answer
  • Which equation has infinitely many solutions?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!