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myrzilka [38]
3 years ago
9

TIMED PLEASE HURRY HELP WITH 2 EASY QUESTIONS

Mathematics
1 answer:
Alex_Xolod [135]3 years ago
8 0
<h2>                         Question # 1</h2><h2>Which statements are true?</h2><h2 /><h3><u>Analyzing and solving the first statement:</u></h3>
  • 4g^2-g=g^2\left(4-g\right)

Solving the expression

4g^2-g

\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c

g^2=gg

So,

4gg-g

\mathrm{Factor\:out\:common\:term\:}g

g\left(4g-1\right)

So,

4g^2-g:\quad g\left(4g-1\right)

Therefore, the statement 4g^2-g=g^2\left(4-g\right) is NOT CORRECT.

<h3><u>Analyzing and solving the second statement:</u></h3>
  • 35g^5-25g^2=\:5g^2\left(7g^3-5\right)

Solving the expression

35g^5-25g^2

\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c

g^5=g^3g^2

So,

35g^3g^2-25g^2

\mathrm{Rewrite\:}25\mathrm{\:as\:}5\cdot \:5

\mathrm{Rewrite\:}35\mathrm{\:as\:}5\cdot \:7

5\cdot \:7g^3g^2-5\cdot \:5g^2

\mathrm{Factor\:out\:common\:term\:}5g^2

5g^2\left(7g^3-5\right)

So,

35g^5-25g^2=\:5g^2\left(7g^3-5\right)

Therefore, the statement 35g^5-25g^2=\:5g^2\left(7g^3-5\right) is CORRECT.

<h3><u>Analyzing and solving the third statement:</u></h3>
  • 24g^4+18g^2=\:6g^2\left(4g^2+3g\right)
<h3 />

Solving the expression

<h3>24g^4+18g^2</h3><h3>24g^2g^2+18g^2</h3><h3>\mathrm{Rewrite\:}18\mathrm{\:as\:}6\cdot \:3</h3><h3>\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4</h3><h3>6\cdot \:4g^2g^2+6\cdot \:3g^2</h3><h3>\mathrm{Factor\:out\:common\:term\:}6g^2</h3><h3>6g^2\left(4g^2+3\right)</h3>

So,

<h3>24g^4+18g^2=6g^2\left(4g^2+3\right)</h3>

Therefore, the statement 24g^4+18g^2=\:6g^2\left(4g^2+3g\right)  is CORRECT.

<h3><u>Analyzing and solving the fourth statement:</u></h3>
  • 9g^3+12=\:3\left(3g^3+4\right)

Solving the expression

9g^3+12

\mathrm{Rewrite\:}12\mathrm{\:as\:}3\cdot \:4

\mathrm{Rewrite\:}9\mathrm{\:as\:}3\cdot \:3

3\cdot \:3g^3+3\cdot \:4

\mathrm{Factor\:out\:common\:term\:}3

3\left(3g^3+4\right)

So,

9g^3+12=\:3\left(3g^3+4\right)

Therefore, the statement 9g^3+12=\:3\left(3g^3+4\right) is CORRECT.

<h2>                         Question # 2</h2><h2>Which expressions are completely factored?</h2>

<u>Solving first expression</u>

Considering the expression

  • 30a^6-24a^2

30a^6-24a^2

30a^4a^2-24a^2

\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4

\mathrm{Rewrite\:}30\mathrm{\:as\:}6\cdot \:5

6\cdot \:5a^4a^2-6\cdot \:4a^2

\mathrm{Factor\:out\:common\:term\:}3a^2

3a^2\left(10a^4-8\right)

Thus, the expression 30a^6-24a^2=3a^2\left(10a^4-8\right)\: is completely factored.

<u>Solving second expression</u>

Considering the expression

  • 12a^3-8a

12a^3-8a

\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c

a^3=a^2a

So,

12a^2a-8a

\mathrm{Rewrite\:}8\mathrm{\:as\:}4\cdot \:2

\mathrm{Rewrite\:}12\mathrm{\:as\:}4\cdot \:3

4\cdot \:3a^2a-4\cdot \:2a

\mathrm{Factor\:out\:common\:term\:}4

4\left(3a^3-2a\right)

Thus, the expression 12a^3-8a=\:4\left(3a^3-2a\right) is completely factored.

<u>Solving third expression</u>

  • 16a^5-20a^3\:\:\:\:\:\:\:\:\:\:\:\:

16a^5-20a^3

\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c

a^5=a^2a^3

So,

16a^2a^3-20a^3

\mathrm{Rewrite\:}20\mathrm{\:as\:}4\cdot \:5

\mathrm{Rewrite\:}16\mathrm{\:as\:}4\cdot \:4

4\cdot \:4a^2a^3-4\cdot \:5a^3

\mathrm{Factor\:out\:common\:term\:}4a^3

4a^3\left(4a^2-5\right)

Thus, the expression 16a^5-20a^3\:=4a^3\left(4a^2-5\right) is completely factored.

<u>Solving fourth expression</u>

  • 24a^4+18

24a^4+18

\mathrm{Rewrite\:}18\mathrm{\:as\:}6\cdot \:3

\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4

6\cdot \:4a^4+6\cdot \:3

\mathrm{Factor\:out\:common\:term\:}6

6\left(4a^4+3\right)

Thus, the expression 24a^4+18=6\left(4a^4+3\right) is completely factored.

Keywords: expression, factoring

Learn more about expression factoring from brainly.com/question/14051207

#learnwithBrainly

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I select two cards from a standard deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black
lilavasa [31]

Answer:

B) S= {(red, red), (red, black), (black, red), (black, black)}

See explanation below.

Step-by-step explanation:

Previous concepts

The sample space of an experiment by definition "is the set of all possible outcomes or results of that experiment".

Solution to the problem

We know that we have 52 cards. 26 of them red and the other 26 black. And we are going to select two cards at random. We are interested on the correct sampling space. We analyze one by one the options given.

A) S= {red, black}

False. We can obtain two red cards for example or two black cards and these pairs are not included in the sample space provided.

B) S= {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red."

True. The cardinality for the sample space is 2^2 = 4 possible outcomes. And as we can see here we have all the possible options included (red, red), (red, black), (black, red), (black, black). So then that's the correct option for the sampling space.

C) S= {(red, red), (red, black), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red."

False, the cardinality of the sample space is 2^2 = 4 and on this case the sample space provided have just 3 elements or possible outcomes. We don't have include the possibl option (black, red).

D) S= {0, 1, 2}.

False the sample space are related to red and black cards and we can't have numbers as the possible outcomes for the experiment.

E) All of the above.

False, option B is correct.  

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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$0.24     1.2 oz

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