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olga2289 [7]
2 years ago
6

Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Mathematics
1 answer:
luda_lava [24]2 years ago
4 0

Both triangles are congruent by either ASA or AAS Congruence Theorem. hence, the right answer is A: Yes, they are congruent by either ASA or AAS.

<h3>What is ASA Congruence Theorem?</h3>

The ASA Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent included sides.

The AAS Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent non-included sides.

Triangle LMQ is shown in the figure attached below.

Thus, Proving

Triangle MNL ≅ triangle QNL (ASA)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <MLN and <QLN

Also, they have a common side: side LN (included side).

Therefore, Triangle MNL and triangle QNL are congruent by ASA.

Triangle MNL ≅ triangle QNL ( by AAS)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <NML and <NQL

Also, they have a common side: side LN (non-included side).

Thus, Triangle MNL and triangle QNL are congruent by ASA.

Hence, the right answer is: A: Yes, they are congruent by either ASA or AAS.

Learn more about the ASA and AAS Congruence Theorem on:

brainly.com/question/2102943

#SPJ1

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Allan plays a video game in which he starts with 0 points. In round 1, he loses 3 1/2 points, in rounds 2, he wins 28 1/2 points
weqwewe [10]

Answer:

Step-by-step explanation:

start with 0

round 1 : lose 3 1/2

round 2: wins 28 1/2

round 3 : lose 3 1/2

0 - 3 1/2 + 28 1/2 - 3 1/2 =

28 1/2 - 7 =

21 1/2 <==== thats 21 and 1/2 points

5 0
3 years ago
The fish population in a local stream is decreasing at a rate of 3% per year. The original population was 48,000. Write an expon
ElenaW [278]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Decrease rate (d)= 7%

Number of periods (n)= 7 years

Current population (PV)= 48,000

<u>First, to calculate the future value, we need to use the following decrease exponential formula:</u>

<u />

FV= PV*[(1+d)^-n]

<u>After 7 years:</u>

FV= 48,000*(1.07^-7)

FV= 29,892

8 0
3 years ago
Is 4x + the square root of y = 12 a linear function
ivolga24 [154]
I wouldn't say so, as if you rearrange that equation you get sqr root y = 12 - 4x. Then you square everything to get the value of y so you would end up with 144 - 16x^2.
Therefore, the x value has a power, so it would be a curved line
3 0
3 years ago
Need help sovling this for class
Reil [10]

By the knowledge and application of <em>algebraic</em> definitions and theorems, we find that the expression - 10 · x + 1 + 7 · x = 37 has a solution of x = 12. (Correct choice: C)

<h3>How to solve an algebraic equation</h3>

In this question we have an equation that can be solved by <em>algebraic</em> definitions and theorems, whose objective consists in clearing the variable x. Now we proceed to solve the equation for x:

  1. - 10 · x + 1 + 7 · x = 37     Given
  2. (- 10 · x + 7 · x) + 1 = 37   Associative property
  3. -3 · x + 1 = 37     Distributive property/Definition of subtraction
  4. - 3 · x = 36     Compatibility with addition/Definition of subtraction
  5. x = 12     Compatibility with multiplication/a/(-b) = -a/b/Definition of division/Result

By the knowledge and application of <em>algebraic</em> definitions and theorems, we find that the expression - 10 · x + 1 + 7 · x = 37 has a solution of x = 12. (Correct choice: C)

To learn more on linear equations: brainly.com/question/2263981

#SPJ1

4 0
2 years ago
Solve the formula for the specified variable. A=6P+4Prt for t
KatRina [158]
Your answer will be t = -3P/2Pr + A/4Pr. :)
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