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3 years ago

Three squares are placed next to each other as shown. The vertices A, B, and C are collinear. Find the dimension n. Replace the

lengths 4 and 7 by m and k, respectively. Express k in terms of m and n.

Mathematics

1 answer:

Anna007 [38]3 years ago

5 0

$\frac{k-m}{m} = \frac{n-k}{k} 
\\
\\k^2-mk=mn-mk
\\k^2=mn
\\k= \sqrt{mn} 
\\$

$7^2=4n
\\
\\n= \frac{49}{4}$

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The prime factorization of 336

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2^4 * 3 * 7

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The counters in a bag are red or blue one fifth of the counters are red work out the ratio of red counters to blue counters

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The counters in a bag are red or blue. Assume 5 in total.

Step-by-step explanation:

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The square root of a negative number, such as StartRoot negative 144 EndRoot, is undefined. Explain why the square root of –x, S

monitta

Part A

The reason why the (√(-x)) is not necessarily undefined, is because x is a placeholder, such that x can take on a negative value for which (-x) is a positive number, therefore, √(-x) = √(+ve number) is a defined real number.

Part B

The domain is x ≤ 0

The range is f(x) ≥ 0

<h3>What is Real Number?</h3>

A real number is a value of a continuous quantity that can represent a distance along a line.

Here, The given and required information:

Given that √(-144) = Undefined, why is √(-x) not necessarily undefined

The given function, f(x) = √(-x)

Part A

The square root of a real number with a negative value is an imaginary number

The square root of a real number with a positive value or zero, is a real number

√(144) = ±12

A variable, x, is an input value of a function that is a quantity place holder in the function which is a function argument

The given function is f(x) = √(-x)

Where;

x = An argument of the function

When x ≤ 0, such that x is a negative real number or zero, we have;

x = R⁻ or 0

Therefore;

-x= -R⁻ or 0 = R⁺ or 0

-x = R⁺

From which we get;

f(-x)= √(-x) = √(R⁺) = Defined

f(-x) = √(R⁺) ≥ 0 The range of the function is f(x) ≥ 0

An example, when x = -16, we have;

-x = -(-16) = 16

√(-x) √(16) = 4 (Defined)

Part B;

Thee domain where the function is defined is where x = -R⁻, x ≤ 0

The output of the function f(x) is defined which is the range = f(x) ≥ 0

Thus, the reason why the √(-x) is not necessarily undefined, is because the value of x can represent a negative real number or zero.

Learn more about real numbers here;

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2 years ago

In History, you earned an exam score of X-85 where the exam average was μ-65 with a standard deviation of σ-5. In Biology, you e

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Answer: D. History

Step-by-step explanation:

To answer this question, we need to use the z-score formula written below:

$\frac{x-pop. mean}{stan. devi.}$

Now we'll just plug in the numbers and solve.

History:

$\frac{85-65}{5} = 4$

Biology:

$\frac{90-85}{10} =0.5$

As we can see, history wields a higher z-score than biology, thus leaving us with option D. History

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3 years ago

11. The price of a bottle of water at a store decreases from $1.65 to $1.40. Rounded to the nearest

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Answer:

A. 15.2%

Step-by-step explanation:

Subtract the new price from the old one to find the dollar amount that the water bottle price was reduced.

$1.65-1.40=0.25$

The price was reduced by 25 cents, but we need to find the percentage. To do that, we divide the price reduction by the original price.

$0.25/1.65=0.152$

And then move the decimal place over two spots (multiply by 100)

15.2

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3 years ago