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e-lub [12.9K]
2 years ago
6

Max points easy math problem

Mathematics
2 answers:
11Alexandr11 [23.1K]2 years ago
4 0

Solution:

Given:

  • x = -4
  • y = 4

<u>Substitute the values into the equation:</u>

  • x⁶ - x/4y
  • => [(-4)⁶] - (-4)/4(4)

<u>Simplify the numerator and the denominator:</u>

  • => [(-4) x (-4) x (-4) x (-4) x (-4) x (-4)] + 4/16
  • => [(-64) x (-64)] + 4/16
  • => [4096] + 4/16
  • => 4100/16

<u>Simplify the fraction:</u>

  • => 4100/16
  • => 1025 x 4/4 x 4
  • => 1025/4

Correct option is B.

Nataly [62]2 years ago
4 0

Answer:

[-\frac{1023}{4} ]

Step-by-step explanation:

\frac{x^6-x}{4y}

x = -4

y = 4

Replace all the variables with the corresponding values given:

\frac{-4^6-(-4)}{4(4)}

Now solve,

-4 to the power of 6 is equal to -4096

\frac{-4096-(-4)}{4(4)}

we see that we are subtracting a negative number, meaning that it'll cancel out and turn into an addition sign. Therefore:

-4096 + 4

-4092

\frac{-4092}{4(4)}

4(4) is equal to 16

\frac{-4092}{16}

When divided, you'll get a mixed fraction of -255\frac{3}{4}

To turn into an improper fraction, simply multiply the whole number by the denominator, then add the numerator to the result.

-255 * 4 + 3

[-\frac{1023}{4} ]

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(48^ \frac{1}{2})

This is equivalent to \sqrt{48}, so now, we just simplify:

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Read 2 more answers
1. What are the solutions (coordinate points) to the system of equations?
Leto [7]

Question 1

The given system of equations is:

y =  {x}^{2}  + 5x + 6 \\ y = 3x + 6

Equate the two equations:

{x}^{2}  + 5x + 6 = 3x + 6

Rewrite in standard form:

{x}^{2}  + 5x - 3x + 6 - 6 = 0

{x}^{2}   + 2x = 0

x(x + 2) = 0

x = 0 \: or \: x =  - 2

When we put x=0, in y=3x +6, we get:

y = 3(0) + 6 = 6

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

y = 3( - 2) + 6 = 0

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

f(x) =  {x}^{6}  -  {x}^{4}

Let us put x=-x,

f( - x) =  {( - x)}^{6}  -  {( - x)}^{4}

This gives:

f( - x) =  {x}^{6}  -  {x}^{4}

We can observe that:

f(x) = f( - x)

This is the property of an even function.

Question 3:

The given function is

f(x) =  {x}^{2}  + 3x - 2

The average rate of change of f(x) from x=a to x=b is given as:

\frac{f(b) - f(a)}{b - a}

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

=  \frac{f(6) - f(2)}{6 - 2} \\   =  \frac{ {6}^{2}  + 3 \times 6 -  2 -  {2}^{2}   -  3 \times 2  + 2 }{4} \\   =  \frac{36 + 18 - 4  - 6}{4}  \\  =  \frac{44}{4}   \\ = 11

The average rate of change is 11

3 0
3 years ago
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