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dezoksy [38]
3 years ago
5

What is the end behavior of the graph of f(x) = x5 – 8x4 + 16x3?

Mathematics
2 answers:
ryzh [129]3 years ago
7 0

Answer:

Step-by-step explanation:

f(x) = x⁵ – 8x⁴ + 16x³

As x approaches +∞, the highest term, x⁵, approaches +∞.

As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).

Now let's factor:

f(x) = x³ (x² – 8x + 16)

f(x) = x³ (x – 4)²

f(x) has roots at x=0 and x=4.  x=4 is a repeated root (because it's squared), so the graph touches the x-axis but does not cross at x=4.

The graph crosses the x-axis at x=0.

jeyben [28]3 years ago
7 0

Answer:

The graph touches, but does not cross, the x–axis at x = .4

The graph of the function crosses the x–axis at x = .0

Step-by-step explanation:

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The legs of an isosceles right triangle are 5 inches long. What is the length of the hypotenuse of the triangle to the nearest i
In-s [12.5K]
The legs are 5 inches long.

Use the Pythagorean theorem:
5^2+5^2=c^2 \\
25+25=c^2 \\
50=c^2 \\
c=\sqrt{50} \\
c=\sqrt{25 \times 2} \\
c=5 \sqrt{2} \\
c \approx 7

The length of the hypotenuse of the triangle is approximately 7 inches long.
6 0
4 years ago
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Is it true that George Washington LOVED political parties?
Alik [6]

Answer:

No, It's false.

Step-by-step explanation:

In the long history of the United States, only one president, George Washington, did not represent a political party.

4 0
2 years ago
A bag contains blue marbles and red marbles, 56 in total. The number of blue marbles is 8 more than 2 times the number of red ma
Nikolay [14]

24 Blue marbles.

Explanation:

56 - 8 = 48

48 / 2 = 24

so if there are 24 blue marbles, 24 x 2 = 48, and then 8 more is 56.

8 0
3 years ago
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If ∠BAC ≅ ∠DCA, is ABE ≅ CDE? Explain.
Tanzania [10]

Answer:

The answer is A.

Step-by-step explanation:

It is A because both sides match up except for the last pair, where they are the same. Hope this helped!

7 0
3 years ago
Find the slope of the line that goes through the given points.<br> (0,8) and (- 4,0)
Ronch [10]

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 8) and (x₂, y₂ ) = (- 4, 0)

m = \frac{0-8}{-4-0} = \frac{-8}{-4} = 2

6 0
3 years ago
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