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2 years ago

What is the simplified form of the rational expression below 5x2-5/3x2+3x

Mathematics

2 answers:

Bingel [31]2 years ago

6 0

Answer:

(5(x-1))/3x

Step-by-step explanation:

FrozenT [24]2 years ago

5 0

Answer:

$\frac{5(x-1)}{3x}$

Step-by-step explanation:

The given expression is

$\frac{5x^{2} -5}{3x^{2}+3x}$

To simplify this rational expression, we need to extract the greatest common factor of each part,

$\frac{5x^{2} -5}{3x^{2}+3x}=\frac{5(x^{2}-1) }{3x(x+1)}$

Then, we observe that the numerator has a difference of two perfect squares, which can be factored as

$a^{2} -b^{2} =(a-b)(a+b)$

Where, $a=x$ and $b=1$

$x^{2} -1=(x-1)(x+1)$

Now, we applied this to the rational expression

$\frac{5x^{2} -5}{3x^{2}+3x}=\frac{5(x^{2}-1) }{3x(x+1)}=\frac{5(x-1)(x+1)}{3x(x+1)}=\frac{5(x-1)}{3x}$

Therefore the simplified form of the given expression is

$\frac{5(x-1)}{3x}$

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Let

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Please help solve this, I’ve tried my best. My answers are a height of 6.7 using 30-60-90 as a last resort, and the glass volume

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Answer:

A) To ensure the correct and exact straight height

B) 15 inches

C) 24.87 in $^{3}$

Step-by-step explanation:

Hello! Lets start!

First, it asks us to explain why the two bases must be parallel. In order to measure the correct and exact height, we must be sure that the bases are parallel, or else there would be a range of heights; in order to ensure that you are measuring a straight distance, they must be parallel!

Second, it asks us to identify the height of cone. To do this, we must make a slope! We can see that, for every time we go down 5 inches, we lose 1 inch of our base! Our slope in this situation would be -5. So, lets continue to see how long before the cone reaches its tip, in which the base would be equal to 0. At 5 inches, our base is 2 inches. At 10 inches, our base is 1 inch. At 15 inches, we do not have a base, as it equals 0! So therefore, our cone height is 15 inches.

Third, it asks us to identify the volume of the cup, which is also called a <em>circular truncated cone. </em>To do so, we can use the formula:

₁ $V = \frac{1}{3} \pi (r_{1}^2 + r_{1}r_{2} + r_2^2)h$

Lets plug in our information!

$V = \frac{1}{3} \pi (1.5^{2} + (1.5)(1) + 1^{2}) (5)\\V = 24.87$

Hope this helps! Remember, math is fun!

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2 years ago