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3 years ago

if a 35 year old women has averaged 8 hours of sleep each 24 hours how many days of her life has she spent

Mathematics

2 answers:

ikadub [295]3 years ago

5 0

1/3 of her life or....35/3?

Masteriza [31]3 years ago

4 0

(8•365)•35 is the correct answer because 8 hrs of sleep each day times 365 days in a year = 2920 hrs slept in one year. Now you must take 2920 and multiply it by the 35 years she has been alive to get 102,200 hrs of sleep.

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Triangle ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the s

Allisa [31]

For line B to AC: y - 6 = (1/3)(x - 4); y - 6 = (x/3) - (4/3); 3y - 18 = x - 4, so 3y - x = 14

For line A to BC: y - 6 = (-1)(x - 0); y - 6 = -x, so y + x = 6

Since these lines intersect at one point (the orthocenter), we can use simultaneous equations to solve for x and/or y:

(3y - x = 14) + (y + x = 6) => 4y = 20, y = +5; Substitute this into y + x = 6: 5 + x = 6, x = +1

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3 years ago

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Nimfa-mama [501]

First of all, we can observe that

$x^2-6x+9 = (x-3)^2$

So the expression becomes

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Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask

$x^2-4 \geq 0 \iff x\leq -2 \lor x\geq 2$

Since we can't accept 3 as an answer, the actual solution set is

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2 years ago

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3 years ago

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julsineya [31]

I hope this helps you

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2 years ago

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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1 year ago