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2 years ago

Solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.

Mathematics

1 answer:

Illusion [34]2 years ago

4 0

Answer: $x\in (0,1)\cup (4,\infty)$

Step-by-step explanation:

Given

In equality is $x^3+4x>5x^2$

Taking terms one side

$\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0$

Using wavy curve method

$x\in (0,1)\cup (4,\infty)$

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3 years ago

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A pack of cards is numbered 1 to 24. A card is chosen at random. Find the probability that the number on the card is divisible b

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Step-by-step explanation:

It's simple. So the only cards which are divisible by 2 or 3 are: 2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24. The formula of probability is P= m/n. Where m-Number of ways it can happen and n- Total number of outcomes.

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3 years ago

How many cubes with side lengths of 1/2 cm does it take to fill up the prism

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24 cubes can filled up the prism

Solution:

The image of the question is attached below.

Given data:

Length of the prism = 2 cm

Breadth of the prism = 1 cm

Height of the prism = $$\frac{3}{2}$ cm

Volume of the prism = length × breadth × height

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Volume of the prism = 3 cubic cm

Side length of the cube = $$\frac{1}{2}$ cm

Volume of the cube = side × side × side

$$=\left(\frac{1}{2}\right)^{3}$

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Volume of the cube = $\frac{1}{8}$ cm

$$\text{Number of cubes} =\frac{\text{Volume of the prism}}{\text{Volume of the cube}}$

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2 years ago

A biker cycles 9 miles in 2 3 of an hour.

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Answer:

2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles

Step-by-step explanation:

1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)

2.) 2 hours: 13.5 * 2 = 27 miles

3.) 3 hours: 13.5 * 3 = 40.5 miles

4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles

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3 years ago

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3 years ago

Solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.​

Solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.