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photoshop1234 [79]
2 years ago
9

How can the associative, commutative, and additive inverse properties be useful when adding and subtracting rational numbers?

Mathematics
1 answer:
ludmilkaskok [199]2 years ago
7 0
Associative and commutative can move terms that are easy to combine and then add them. The additive inverse property helps you combine terms that are opposite to get 0
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Please help me with my homework<br><br> <img src="https://tex.z-dn.net/?f=%5Cbf%7B%28x%2B9%29%5E5%7D" id="TexFormula1" title="\b
Brut [27]

Answer:

x⁵+ 45x⁴+ 810x³+ 7290x²+ 32805x +59049

Step-by-step explanation:

Greetings !

Given expression

(x + 9) {}^{5}

write 5 as a sum

(x + 9) {}^{3 + 2}

use \: a {}^{m + n}  = a {}^{m}  \times a {}^{n} to \: expand \: the \: expression.

(x + 9) {}^{3}  \times (x + 9) {}^{2}

Use (a+b)³=a³+3a²b+b³ to expand the expression

(x {}^{3}  + 27x {}^{2}  + 243x + 729) \times (x + 9) {}^{2}

Use (a+b)²=a²+2ab+b² to the second expression to expand it

(x {}^{3}  + 27x {}^{2}  + 243x + 729) \times(x {}^{2}  + 18x + 81)

Finally, simplify the expression gives

x {}^{5}  + 45x {}^{4}  + 810x {}^{3}  + 7290x {}^{2}  + 32805x + 59049

Hope it helps!

3 0
2 years ago
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7x+5/9 ​(Simplify your answer. Use integers or fractions for any numbers in the​ expression.)
Black_prince [1.1K]

nothing can be further simplify in this problem

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2 years ago
An electric motor pumps water into a pool at a rate of 500 liters per hour. After a tune up, its rate increases by x liters per
Alex73 [517]

Answer: 3(500+x)=1800

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3 years ago
A box contains 3 green marbles, 5 blue marbles, and 7 red marbles. Three marbles are selected at random from the box, one at a t
USPshnik [31]

Answer:

The probability is  P(K)  =   \frac{ 28 }{195}

Step-by-step explanation:

From the question we are told that

   The number of green marbles is  n_g  =  3

    The number of red marbles is  n_b  =  5

     The number of red marbles is  n_r  =  7

Generally the total number of marbles is mathematically represented as

       n_t  =  n_r  +  n_g + n_ b

        n_t  =  7 +  3 + 5

         n_t  = 5

Generally total number of marbles that are not red is  

     n_k  =  n_g +  n_ b

=>  n_k  =   3 +   5

=>  n_k  =  8

The probability of the first ball not being red is mathematically represented as  

      P(r') =  \frac{n_k}{n_t}

=>  P(r') =  \frac{ 8}{15}

The probability of the second ball not being red is mathematically represented as

      P(r'') =  \frac{n_k - 1}{n_t -1}

=>  P(r'') =  \frac{ 8 -1 }{15-1} (the subtraction is because the marbles where selected without replacement  )

=>  P(r'') =  \frac{ 7 }{14}

The probability that the first two balls  is  not red is mathematically represented as

    P(R) =  P(r') *  P(r'')

=>  P(R) =  \frac{ 8}{15} *   \frac{ 7 }{14}

=>  P(R) =  \frac{ 8 }{30}

The probability of the third ball being red is mathematically represented as

   P(r) =  \frac{n_r}{ n_t -2} (the subtraction is because the marbles where selected without replacement  )

     P(r) =  \frac{7}{ 15 -2}

=>    P(r) =  \frac{7}{ 13}

Generally the probability of the first two marble not being red and the third marble being red is mathematically represented as

        P(K)  =  P(R) * P(r)

         P(K)  =   \frac{ 8 }{30} * \frac{7}{ 13}

=>      P(K)  =   \frac{ 28 }{195}

6 0
3 years ago
What is the volume of this square pyramid? Enter your answer in the box.
musickatia [10]
Answer:400. 10^2 x 12/3 = 400.
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