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Varvara68 [4.7K]
2 years ago
6

Which triangle is similar to ΔJKL? ΔJKM, ΔMKL, ΔKML, ΔLJK.

Mathematics
2 answers:
kirill [66]2 years ago
7 0
The answer would be ΔKML because the right angle of ΔKML is in the same place as <span>ΔJKL</span>
nadezda [96]2 years ago
4 0

Answer:

Triangle \triangle KML is similar to the given triangle \triangle JKL.

Step-by-step explanation:

Let us analyze the given options one by one.

\triangle JKM is not similar to the triangle \triangle JKL because it is not written in correct order. The way we write the triangle (order of vertices) is very important. Since angles K of both the triangles are not equal, therefore, order is messed up. If the order had been \triangle JMK then this would have been correct.

\triangle MKL is not similar to triangle \triangle JKL because the corresponding angles are not equal. Again the order it not right. If the order had been \triangle KML, then this option would have been correct.

\triangle KML is similar to the given triangle \triangle JKL because corresponding angles of both the triangles are equal.

\triangle LJK is not similar to the given triangle \triangle JKL because the corresponding angles of the two triangles are not equal.

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Answer: The distance between the girls is 362.8 meters.

Step-by-step explanation:

So we have two triangle rectangles that have a cathetus in common, with a length of 160 meters.

The adjacent angle to this cathetus is 40° for Anna, then the opposite cathetus (the distance between Anna and the tower) can be obtained with the relationship:

Tan(A) = opposite cath/adjacent cath.

Tan(40°) = X/160m

Tan(40°)*160m = 134.3 m

Now, we can do the same thing for Veronica, but in this case the angle adjacent to the tower is 55°

So we have:

Tan(55°) = X/160m

Tan(55°)*160m = X = 228.5 m

And we know that the girls are in opposite sides of the tower, so the distance between the girls is equal to the sum of the distance between each girl and the tower, then the distance between the girls is:

Dist = 228.5m + 134.3m = 362.8m

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Phil has 3 times as many rocks as Peter. Together, they have 48 rocks. How many more rocks does Phil have than Peter?
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Let x = the number of marbles for Phil
Then 3x = the number of marbles for Peter
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Let S(x) denote "x has a good attitude," where the domain is the set of people in the class. Express the negation of the proposi
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Answer:

See below

Step-by-step explanation:

Remember, we have two quantifiers, the existential quantifier ∃, and the universal quantifier ∀. The existential ∃ translates to English as "for some" or "there exists", whereas ∀ means "for all" or "every". We will also use the negation operator ¬.

First, let's write the proposition using quantifiers. "There is someone in this class who does not have a good attitude" translates to "(∃x)(¬S(x))". ∃x means that there exists a person in this class x. ¬S(x) means that x, the person that exists because of the quantifier, does not have a good attitude.

The negation is "¬(∃x)(¬S(x))" or equivalently "(∀x)(S(x))". To negate a proposition using quantifiers, change the quantifier (existential to universal and viceversa) and negate the predicate (in this case we negated ¬S(x)).

In English, "(∀x)(S(x))" means "Every person in this class has a good attitude".

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