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3 years ago

What is the simplified form of the following expression? 7(^3 square root 2x) - 3 (^3 square root 16x) -3 (^3 square root 8x)

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

5 0

Answer:

The third option listed: $\sqrt[3]{2x} -6\sqrt[3]{x}\\$

Step-by-step explanation:

We start by writing all the numerical factors inside the qubic roots in factor form (and if possible with exponent 3 so as to easily identify what can be extracted from the root):

$7\sqrt[3]{2x} -3\sqrt[3]{16x} -3\sqrt[3]{8x} =\\=7\sqrt[3]{2x} -3\sqrt[3]{2^32x} -3\sqrt[3]{2^3x} =\\=7\sqrt[3]{2x} -3*2\sqrt[3]{2x} -3*2\sqrt[3]{x}=\\=7\sqrt[3]{2x} -6\sqrt[3]{2x} -6\sqrt[3]{x}$

And now we combine all like terms (notice that the only two terms we can combine are the first two, which contain the exact same radical form:

$7\sqrt[3]{2x} -6\sqrt[3]{2x} -6\sqrt[3]{x}=\\=\sqrt[3]{2x} -6\sqrt[3]{x}$

Therefore this is the simplified radical expression: $\sqrt[3]{2x} -6\sqrt[3]{x}\\$

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The total distance jim traveled on his bicycle during a 5 hour period is shown in the graph below.

spayn [35]

Answer:

100 miles

follow the line up from 5

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2 years ago

Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and on

Nookie1986 [14]

Answer:

The probability that he ends up with a full house is 0.0083.

Step-by-step explanation:

We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.

We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).

We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);

If he is given with two kings.
If he is given one king and one ace.

Only in these two situations, he will end up with a full house.

Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.

So, the ways in which we can draw two kings from available three kings is given by = $\frac{^{3}C_2 }{^{47}C_2}$ {∵ one king is already there}

= $\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}$ {∵ $^{n}C_r = \frac{n!}{r! \times (n-r)!}$ }

= $\frac{3}{1081}$ = 0.0028

Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by = $\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}$

= $\frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}$

= $\frac{6}{1081}$ = 0.0055

Now, probability that he ends up with a full house = $\frac{3}{1081} + \frac{6}{1081}$

= $\frac{9}{1081}$ = <u>0.0083</u>.

3 0

3 years ago

Read 2 more answers

WILL GIVE BRAINLIEST AND 100 PNTS!! Which of the tables represents a function? Table A Input Output 5 3 5 2 4 1 Table B Input Ou

expeople1 [14]

Answer:

Table B

Step-by-step explanation:

Table A Input Output

5 3

5 2

4 1

Has an input that goes to 2 different outputs, not a function

Table B Input Output

1 2

3 2

5 3

one to one relation which is a function

Table C Input Output

0 0

1 2

1 3

Has an input that goes to 2 different outputs, not a function

Table D Input Output

4 2

4 3

4 4

Has an input that goes to 2 different outputs, not a function

4 0

3 years ago

How to order -14.4, -14, -14 1/5 from least to greatest

ElenaW [278]

Think of thermometer the negative degrees are the coldest so are the lowest on the vertical column

first convert -14 1/5 to decimals = -14.2

so the order is

-14.4 , -14 1/5 , -14.

8 0

3 years ago

Cos (a + 60 ) + Cos (a-60)

Nadusha1986 [10]

Answer:

the answer is 0.9988747935

hope that works!!

8 0

2 years ago