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kap26 [50]
3 years ago
10

(x²-y²)³+(y²-z²)³+(z²-x²)³/(x-y)³+(y-z)³+(z-x)³ evaluate

Mathematics
1 answer:
svlad2 [7]3 years ago
6 0
We use the fact that if x+y+z = 0, then x³+y³+ z³ = 3 x y z.<span>

(x</span>²-y²) + (y²-z²) + (z²-x²)  = 0<span>
also: (x-y) + (y-z)+ (z-x) = 0
we assume that:  x </span>≠y ≠ z.
<span>

hence,

(x²-y²)³ + (y²-z²)³ + (z²-x²)³  ÷  (x-y)³ + (y-z)³ + (z-x)³
=  3 (x</span>²-y²) (y²-z²) (z²-x²) ÷ [3 (x-y) (y-z) (z-x)]
<span>=  (x+y) (y+z) (z+x)
</span>
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In a class of c children there are 16 boys what fraction of the class are boys​
lakkis [162]

Answer:

c/16

Step-by-step explanation:

7 0
3 years ago
9. Determine if x + 1 is a factor of x ^ 4 - 4x ^ 2 - 4x - 1 Justify your answer.
Elden [556K]

Answer:

No

Step-by-step explanation:

x + 1 is not a factor of the polynomial because the remainder is 2 and not 0

5 0
2 years ago
What is the slope of this line?
nataly862011 [7]

Answer: -\frac{8}{5}

Remember: RISE/RUN (y/x). Lines that are increasing have a positive slope, and lines that are decreasing have a negative slope.

You can find the slope in two ways:

1. Useful if the line is graphed: count the units between 2 points on the line.

  • Let's use the points (-1, 4) and (4, -4).
  • (-1, 4) is 8 units higher than (4, -4) and 5 units to the left of (4, -4).
  • Because the line is decreasing, the slope is negative.
  • Therefore, the slope is -\frac{8}{5}.

2. Useful if the line is not graphed: find the difference between the y-coordinate values divided by the difference of the x-coordinate values.

  • Let's use the points (-1, 4) and (4, -4).
  • \frac{-4 - 4}{4 - (-1)} = \frac{-8}{5}
  • Therefore, the slope is -\frac{8}{5}.
4 0
3 years ago
Read 2 more answers
Evaluate the expression 4+−4√2+−1√ and write the result in the form a+bi.
castortr0y [4]

In the expression, the real number a equals 12 and the real number b equals -16.

<h3>How to explain the information?</h3>

It should be noted that the expression given is:

= (4 - 2i)²

Therefore, we need to expand the expression. This will be:

= (4 - 2i)(4 - 2i)

= 16 -8i -8i + 4i²

= 16 -16i +4i²

Substitute -1 for i²

= 16 - 16i + 4(-1)

= 16 - 16i - 4

= 12 - 16i

Therefore, the value of the expression is 12 - 16i.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

Evaluate the expression ( 4 − 2 i )² and write the result in the form a + b i.

8 0
2 years ago
A cash register contains $10 bills and $20 bills with a total value of $520. If there are 32 bills total, then how many of each
ohaa [14]

12 is the number of $10 bills

20 is the number of $20 bills

<u><em>Step-by-step explanation:</em></u>

<u><em /></u>

Hello,

<u>Let's note</u>

a    the number of $10 bills

b    the number of $20 bills

The total value is $520 so we can write the first equation (1)

    \boxed{\sf 10a \ + \ 20b \ = \ 520 }

We know that there are 32 bills in total so we can write the second equation (2)

    \boxed{\sf a \ + \ b \ = \ 32 }

(1) - 10*(2) gives

10a + 20b - 10(a+b) = 520 - 320 = 200

10a + 20b - 10a - 10b = 10b = 200

So b = 200/10=20

and then from (2) a = 32 - 20 = 12

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0
3 years ago
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