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2 years ago

11. What is the domain of the function? Please show how you solved it and explain.

Mathematics

1 answer:

joja [24]2 years ago

8 0

Answer:

domain: $x\leq -7, x\geq 3$

Step-by-step explanation:

$f(x)=\sqrt{x^2+4x-21}$

Factor $x^2+4x-21$ :

$x^2+4x-21=(x-3)(x+7)$

Therefore,

$f(x)=\sqrt{(x-3)(x+7)}$

$\implies f(x)=\sqrt{(x-3)}\sqrt{(x+7)}$

Find non-negative values for radicals:

$\sqrt{(x-3)} \implies x\geq 3$

$\sqrt{(x+7)} \implies x\leq -7$

Therefore, domain: $x\leq -7, x\geq 3$

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Answer:

The correct option is option (c).

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Step-by-step explanation:

Right angled triangle:

One angle must be 90° and other two angles are acute angle.
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It follows the Pythagorean Theorem.

Given that,

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we know that,

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3 years ago

The property tax on a house with an assessed value of $624,000 is $7280. Determine the property tax on a house with an assessed

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Using proportions, the property tax on a house with an assessed value of $762,000 is of $8,890.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax rate, as a proportion, is:

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More can be learned about proportions at brainly.com/question/24372153

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1 year ago

Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the pro

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Answer:

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Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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This means that $\mu = 0, \sigma = 1$