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olga nikolaevna [1]
3 years ago
8

Factor 18v⁹+33v⁸+14v⁷ completely ​

Mathematics
1 answer:
marin [14]3 years ago
8 0

Answer:

v^{7} x (6v+7) x (3v+2)

Step-by-step explanation:

18v^9 + 33v^8 +14v^7

Factor out v^7 from the expression

v^7 x (18v^2+33v+14)

write 33v as a sum

v^7 x (18v^2+21v+12v+14)                  *like this 21v+12v

Factor out 3v from the expression

v^7 x (3v x (6v+7)+12v+14)

Factor out 2 from the expression

c^7 x (3v x (6v+7)+2(6v+7)

Factor out 6v+7 from the expression

v^7 x (6v+7) x (3v+2)

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4. To determine if a triangle is a right triangle, given that you know the length of its sides, you have to check if its lengths follow the Pythagorean theorem.

This theorem states that the square of the hypothenuse (c) is equal to the sum of the squares of the legs of the triangle (a and b), following the expression:

a^2+b^2=c^2

The triangle is:

We have to check that a²+ b² is equal to c².

The square of the hypothenuse is:

\begin{gathered} c^2=10^2 \\ c^2=100 \end{gathered}

The sum of the squares of the legs of the triangle is:

\begin{gathered} a^2+b^2=8^2+6^2 \\ a^2+b^2=64+36 \\ a^2+b^2=100 \end{gathered}

As you can see, the sum of the squares of the legs of the triangle is 100, which is the same as the square of the hypothenuse. The triangle follows the Pythagorean theorem and can be considered a right triangle.

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1 year ago
What is the opposite of 12.75 on a number line
RoseWind [281]
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8 0
3 years ago
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Craig bought a 3 foot long baguette and then made 4 equally sized sandwiches with it
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Answer:12

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3 years ago
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In a certain computer, the probability of a memory failure is 0.01, while the probability of a hard disk failure is 0.02. If the
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Answer:

We need to remember that we have independent events when a given event is not affected by previous events, and we can verify if two events are independnet with the following equation:

P(A \cap B) = P(A) *P(B)

For this case we have that:

P(A) *P(B) = 0.01*0.02= 0.0002

And we see that 0.0002 \neq P(A \cap B)

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Step-by-step explanation:

For this case we can define the following events:

A= In a certain computer a memory failure

B= In a certain computer a hard disk failure

We have the probability for the two events given on this case:

P(A) = 0.01 , P(B) = 0.02

We also know the probability that the memory and the hard drive fail simultaneously given by:

P(A \cap B) = 0.0014

And we want to check if the two events are independent.

We need to remember that we have independent events when a given event is not affected by previous events, and we can verify if two events are independnet with the following equation:

P(A \cap B) = P(A) *P(B)

For this case we have that:

P(A) *P(B) = 0.01*0.02= 0.0002

And we see that 0.0002 \neq P(A \cap B)

So then we can conclude that the two events given are not independent and have a relationship or dependence.

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2 years ago
In which direction must the graph of f(x) = |x| be shifted to produce the graph of g(x) = |x + 4|?
Tamiku [17]

Answer:

Left on the x-axis

Step-by-step explanation:

The opposite of the coefficient's amount of units is how much the graph will be moved.

Table comparisons

g(x)=|x+4|

x  1   -2   <u>-4</u>

y  5   2    <u>0</u>

Underlined is the x-int of the equation.

f(x)=|x|

x  1  <u>0</u>  -1  3

y  1  <u>0</u>   1  3

5 0
3 years ago
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