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2 years ago

12. Suppose n is an integer. Select all statements below that are true:

Mathematics

1 answer:

Novay_Z [31]2 years ago

6 0

Answer:

<u>True statements</u>

n is always an even integer when n is even
n is never an even integer when n is odd
n is sometimes an even integer

Step-by-step explanation:

Integer: a whole number that can be positive, negative, or zero
e.g. ...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...

<u>True statements</u>

n is always an even integer when n is even
n is never an even integer when n is odd
n is sometimes an even integer

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Answer:

x = -2

Step-by-step explanation:

We are given the logarithmic base 2 equation of:

$\displaystyle{\log_2 (4x) + \log_2 (x+1) = 3}$

Apply logarithm property of addition where:

$\displaystyle{\log_a M + \log_a N = \log_a MN}$

Therefore, we will write new equation as:

$\displaystyle{\log_2 [4x(x+1)] = 3}$

Apply logarithm to exponential form using:

$\displaystyle{\log_a M = N \to a^N = M}$

Thus, another new rewritten equation is:

$\displaystyle{2^3 = 4x(x+1)}\\\\\displaystyle{8 = 4x(x+1)}\\\\\displaystyle{2=x(x+1)}$

Expand the expression in and arrange the terms in quadratic expression:

$\displaystyle{2=x^2+x}\\\\\displaystyle{0=x^2+x-2}\\\\\displaystyle{x^2+x-2=0}$

Solve for x:

$\displaystyle{(x+2)(x-1)=0}\\\\\displaystyle{x=-2,1}$

These are potential solutions to the equation. To find extraneous solution, you’ll have to know the domain of logarithm function. We know that logarithm’s domain is defined to be greater than 0. Henceforth, anti-logarithm must be greater than 0.

( 1 ) 4x > 0, x > 0

( 2 ) x + 1 > 0, x > -1

Therefore, our anti-log must be greater than 0, so any solutions that are equal or less than 0 will be considered as extraneous solution.

Hence, x = -2 is the extraneous solution.

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2 years ago

The swimming pool is open when the high temperature is higher than 20^\circ\text{C}20∘C20, degrees, start text, C, end text. Lai

Delvig [45]

Answer:

Inequality: 30 - 3d ≤ 20

Rate of decrease from Monday to Thursday: greater than or equal to 10/3 degrees Celsius per day

Step-by-step explanation:

Translate theconditions into mathematical terms:

HIgh temperature on Monday = T₀ = 30°C.

The temperature decrease at a constant rate in the next 3 days. Call d such rate, so T₃ = T₀ - 3d = 30 - 3d

That the pool is open when the high temperature is higher than 20°C means that, if the pool is closed, then the temperature is less than or equal to (≤) 20°C:

30 - 3d ≤ 20

And that is the requested inequality.

From that, you can solve for the rate of temperature decrease, d:

Add 3d to both sides: 30 ≤ 20 + 3d

Subtract 20 from both sides: 10 ≤ 3d

Divide both sides by 3: 10/3 ≤ d

Apply symmetry property: d ≥ 10/3

Hence, the rate of temperature decrease is greater than or equal to 10/3 degrees Celsius per day, from Monday to Thursday.

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