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3 years ago

Find the value of x in the diagram given that triangle LMN is congruent to the triangle RST.

Mathematics

1 answer:

Rzqust [24]3 years ago

7 0

Answer:

x=8 y=19

Step-by-step explanation:

A triangle's angles should up to 180 degrees. With that being said, you can add up the two known angles, 93+63 = 156, so we only need 24 degrees to reach a true triangle. Considering that the unknown angle "3x" is the only angle left, then the equation would be 3x=24, so this means x=8. Then you plug in 8 inside 3x+y and we get 24+y. Since the triangle is congruent, then we must equal this phrase to the side's corresponding side on the other triangle. So it should look like 24+y=43, and after simplifying, you will get y=11

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A family has two children. M represents male, and F represents female.

astraxan [27]

Answer:

Option c) Sample space $=\{\bf FM, FF, MM, MF\}$

Step-by-step explanation:

Given that a family has two children.

Let M represents male, and F represents female.

In probability theory, the sample space (also called sample description space or possibility space) of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set. It is common to refer to a sample space by the labels S, $\Omega$ , or $\cup$ (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols. They can also be finite, countably infinite, or uncountably infinite.

Let S be the sample space of the given data.

Here the sample space is typically the set {male, female}, commonly written $\{M, F\}$

ie, S is the set $\{male, female\}$ or $S=\{M, F\}$

For the gender of the children, corresponding sample space would be $\{(male,male), (male,female), (female,male), (female,female)\}$ , commonly written as

$\{MM,MF,FM,FF\}$

S is the set $\{(male,male), (male,female), (female,male), (female,female)\}$ or $S=\{MM,MF,FM,FF\}$

6 0

3 years ago

Un cuerpo es dejado caer desde una altura de 3000 centímetros

Mashcka [7]

Answer:

what is your question

Step-by-step explanation: am not trying to steal ur points

6 0

3 years ago

The drop down options are explicit and recursive.

Oksanka [162]

Answer:

Recursive

Explicit

Step-by-step explanation:

An arithmetic sequence an be represented by a recursive rule which gives the first term and defines the nth term by relating it to the previous term, or by an explicit rule which defines the nth term as a function of n.

The recursive rule is that we have the initial term. To find the subsequent term, we will take that <em>previous term</em> and add it to our common difference.

Hence, we are <em>relating the previous terms</em> to define the nth term.

For the explicit rule, we simply have a function of n. To find the nth term, we can substitute our desired term n for n and evaluate.

5 0

3 years ago

Marty ate 4/6 of his pizza and Luis ate 5/6. Marty ate more how is this possible

emmainna [20.7K]

Because Marty's pizza is bigger than Luis'.

4 0

3 years ago

A father and his son walked 240 meters. During this trip, the father made 100 fewer steps than did his son. Find the distance ea

Alexxandr [17]

<h2>Hello!</h2>

The answer is:

The father's step is 80 cm

The son's step is 60 cm.

To solve the problem, we need to write equations in order to create a relation between the father's and son's steps, and the distance covered by them.

We know thay they covered 240 meters, and the father's step is 20 cm (0.2m)greater than his son's step, so, we can write the following relation:

$NumberOfSteps_{Son}=\frac{240m}{x}$

and,

$NumberOfSteps_{Father}=\frac{240m}{x+0.2m}$

Now, if the know that the father made 100 fewer steps than his son, we have:

$NumberOfSteps_{Son}-100=\frac{240m}{x+0.2m}$

Then, substituting the first equation into the second equation, we have:

$\frac{240m}{x}-\frac{240m}{x+0.2m}=100\\\\\frac{240m(x+0.2m)-240mx}{x(x+0.2m)}=100\\\\240mx+0.2m*240m-240mx=(x)(x+0.2m)*100\\\\48m^{2}=100*(x^{2}+0.2mx)=100x^{2} +20mx\\\\48m^{2}=100x^{2}+20mx\\\\100x^{2}+20mx-48m^{2}$

We have a quadratic equation:

$100x^{2}+20mx-48m^{2}=0$

Where,

$a=100\\b=20\\c=-48$

So, solving it applying the quadratic formula, we have:

$\frac{-b+-\sqrt{b^{2} -4ac} }{2a}$

$\frac{-20+-\sqrt{20^{2} -4*100*-48} }{2*100}=\frac{-20+-\sqrt{400+19200} }{200}\\\\\frac{-20+-\sqrt{400+19200} }{200}=\frac{-20+-\sqrt{19600} }{200}\\\\\frac{-20+-\sqrt{19600} }{200}=\frac{-20+-(140)}{200}\\\\x_{1}=\frac{-20+140}{200}=0.6\\\\x_{2}=\frac{-20-140}{200}=-0.8$

Then, since distance cannot be negative, we need to take the positive value, so, the son's step is 0.6m or 60 cm.

Now, calculating the father's step, we have:

$FatherStep=SonStep+20cm\\\\FatherStep=60cm+20cm=80cm$

Hence, we have that the father's step is 80 cm.

Have a nice day!

6 0

4 years ago