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3 years ago

How do I solve this problem?

Mathematics

1 answer:

lesya [120]3 years ago

4 0

Answer:

4x⁻¹

Step-by-step explanation:

4x + 20 25 - x²

_______ ÷ _______ ↷

x² - 5x [x - 5]²

4[x + 5] [-5 + x][5 + x]

_______ ÷ _______

x[x - 5] [x - 5][x - 5]

So what we did here was factor out ALL the Greatest Common Factors [GCFs] in each denominator and numerator, and since we are dividing vertically AND horizontally, according to this, ALL [x - 5] and [x + 5] cancel each other out and all you are left with is this:

4x⁻¹

$\frac{4}{x}$

This, according to the Negative Exponential Rule [Reverse], is how you rewrite it as a fraction. You bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM POSITIVE TO NEGATIVE:

b⁻ⁿ = 1\bⁿ

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

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The area of an equilateral triangle is LaTeX: 108\sqrt[]{3}\:ft^2 108 3 f t 2 . What is the length of one side of the triangle?

Temka [501]

The length of one side is 12√3.

We know that the area of a triangle is given by the formula:

A=1/2(b)(h)

We can substitute the area in:
108√3 = 1/2(b)(h)

Let b be the side of the equilateral triangle. To find the height, we will use the Pythagorean theorem. We know that the height bisects the base, so we will call that leg of the right triangle formed (1/2b). Since the triangle is equilateral, we will call the hypotenuse b as well. We now have:

$(\frac{1}{2}b)^2+h^2=b^2
\\
\\\frac{1}{4}b^2+h^2=b^2
\\
\\\frac{1}{4}b^2+h^2-\frac{1}{4}b^2=b^2-\frac{1}{4}b^2
\\
\\h^2=\frac{3}{4}b^2
\\
\\\sqrt{h^2}=\sqrt{\frac{3}{4}b^2}
\\
\\h=\frac{\sqrt{3}}{2}b$

We will now substitute this in the formula for area we had above:
108√3=(1/2)(b)(√3/2b)
108√3=√3/4b²

Multiply both sides by 4:
(108√3)×4=(√3/4b²)×4
432√3=√3b²

Divide both sides by √3:
432√3/√3 = √3b²/√3
432=b²

Take the square root of both sides:
√432=√b²

Simplifying the radical, we have 12√3.

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4 years ago

Find the area of the figure.

elena-s [515]

Answer:

Step-by-step explanation:

because 6+2+2+2+3+3+3+1=24

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3 years ago

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Which relationship is likely ONLY a correlation and NOT one of causation? A) As the temperature increases, the number of air con

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Answer: The answer is (C) As the number of visitors to a park increases, the number of flowers in bloom at the park increases.

Step-by-step explanation: We are given four options out of which we are to select which relationship is likely ONLY a correlation and NOT one of causation.

Causation is defined as the determination of the cause or reason for some sort of phenomenon while a correlation is simply a recognised relationship between two things or events, but it does not imply causation.In cases of correlation, one thing or event predicts another.

So, in the options (A), (B) and (D), we can see both correlation and causation simultaneously, but in option (C), we can only see correlation, NOT causation.

Thus, the correct option is (C).

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3 years ago

A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries wil

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Answer:

The probability that you test exactly 4 batteries is 0.0243.

Step-by-step explanation:

We are given that a new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found.

Suppose that 90% of all batteries have acceptable voltages.

Let the probability that batteries have acceptable voltages = P(A) = 0.90

So, the probability that batteries have unacceptable voltages = P(U) = 1 - P(A) = 1 - 0.90 = 0.10

Now, the probability that you test exactly 4 batteries is given by the three cases. Firstly, note that batteries will be tested until two acceptable ones have been found.

So, the cases are = P(AUUA) + P(UAUA) + P(UUAA)

This means that we have tested 4 batteries until we get two acceptable batteries.

So, required probability = (0.90 $\times$ 0.10 $\times$ 0.10 $\times$ 0.90) + (0.10 $\times$ 0.90 $\times$ 0.10 $\times$ 0.90) + (0.10 $\times$ 0.10 $\times$ 0.90 $\times$ 0.90)

= 0.0081 + 0.0081 + 0.0081 = <u>0.0243</u>

<u></u>

Hence, the probability that you test exactly 4 batteries is 0.0243.

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3 years ago

Explain the benefits of data analysis in weather systems.

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Answer:

The weather data collected every day can have a range of new benefits if it is made open and interpreted in the right way.

Step-by-step explanation:

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