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BartSMP [9]
3 years ago
13

Factor x^4+xy^3+x^3+y^3 out completely. Hint: first factor out a monomial.

Mathematics
1 answer:
adelina 88 [10]3 years ago
3 0

Answer:

(x + y)(x² - xy + y²)(x + 1)

Step-by-step explanation:

Given

x^{4} + xy³ + x³ + y³ ( factor out x from the first 2 terms )

= x(x³ + y³) + 1(x³ + y³) ← factor out (x³ + y³) from each term

= (x³ + y³)(x + 1)

x³ + y³ is a sum of cubes and factors as (x + y)(x² - xy + y²)

Thus

x^{4} + xy³ + x³ + y³ = (x + y)(x² - xy + y²)(x + 1)

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Find the 14th term of the geometric sequence 5,-10,20
tamaranim1 [39]

In this specific case, the <em>initial term</em> (a) is 5 and the <em>common ratio</em> (r) is -2

Henceforth, after determining what a and r are, we use the formula for the <em>nth term</em>. Which is:

a_n = a \times r^{n-1}

Therefore, the 14th term is :

\implies 5 \times  { (- 2)}^{14 - 1}  \\\implies 5 \times  {( - 2)}^{13}  \\ =\boxed { -40,960}

Hope it helps!

7 0
2 years ago
Find the distance between each set of points. Round to the nearest tenth, when necessary. (-3, 2) and (1, -6)
vovangra [49]

Answer:

<h2>The answer is 8.9 units</h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  } \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3, 2) and (1, -6)

The distance between them is

d =   \sqrt{ ({ - 3 - 1})^{2}  +  ({2 + 6})^{2} }   \\  =  \sqrt{ ({ - 4})^{2} +  {8}^{2}  }  \\  =  \sqrt{16 + 64}  \\  =  \sqrt{80}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 4 \sqrt{5}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 8.9442719...

We have the final answer as

8.9 units to the nearest tenth

Hope this helps you

6 0
3 years ago
What is times positive 9 times negative 5
Ber [7]
Negative 45 or -45 because different signs with multiplication are always negative
5 0
3 years ago
In a certain manufacturing plant, the first operation can be done on any one of five machines, the second operation on only one
Ymorist [56]
Let's see all the steps: 
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2) only one option: we ignore it
3) the third operation: 6 options
4): 2 options.


So we have 5 options, 6 options and 2 options: and they are independent of each other. This means that we multiply the numbers, and 5*6*2=60 So the answer is 60!
5 0
3 years ago
Read 2 more answers
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Monica [59]
66 more min. he used which could be 1 hour and 6 min.
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