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5 days ago

Keshawn is asked to compare and contrast the domain and range for the two functions.

2 answers:

6 0

He could include two points:
- The domain for both functions consists of all real numbers.
- The range for g(x) is y > 0.

Zina [11.9K]5 days ago

3 0

The response is:

Therefore, option 1 is correct.

Hence, the final option is accurate.

Step-by-step breakdown:

Two functions are presented

. The domain represents the x values possible

. The range represents the y values achievable

. Thus, x can take any real number in functions f(x) and g(x)

. So, option 1 is correct.

For the range aspect

$f(x)=5x$ , f(x) can encompass any real number $g(x)=5^x$

. However, for g(x), the range can only include positive numbers

. Consequently, the last option is accurate, while all other options are incorrect.

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There is an integer n such that 2n2 − 5n + 2 is prime. To prove the statement it suffices to find a value of n such that (n, 2n2

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Response:

n = 0 or 3

Detailed explanation:

2n² - 5n + 2

2n² - 4n - n + 2

2n(n - 2) -1(n - 2)

(n - 2)(2n - 1)

A prime number is defined as one that can only be divided by itself and 1

Setting n-2 = 1 gives n = 3

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The market price of a house is directly proportional to the total area of the house in square feet. If the price of a 1,500 squa

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Answer:

The cost for a 2,000 square foot house is $\$400,000$

Detailed explanation:

Recall that if two variables x and y vary directly, the relationship can be written as $y/x=k$ or $y=kx$ .

Define:

x as the house area in square feet

y as the price of the house

Given point (1500, 300000)

Calculate proportionality constant k:

$k=y/x$

Insert values:

$k=300,000/1,500=200$

The direct variation equation is:

$y=200x$

For x = 2000:

Calculate y:

Replace x in equation:

$y=200(2,000)$

$y=\$400,000$

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1 month ago

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26 days ago

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An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount o

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During an archaeological excavation, an ancient campfire is uncovered. The charcoal is determined to have significantly less than 1/1000 of the standard amount of $^{14}\text{C}$ . Calculate the minimal age of the charcoal, taking into account that $2^{10} = 1024$

Response:

57300 years

Step-by-step breakdown:

Using the relationship of half-life time against fraction, which can be expressed as:

$\dfrac{N}{N_o} = (\dfrac{1}{2})^{\frac{t}{t_{1/2}}$

In this context,

N indicates the current atom

represents the initial atom $N_o$

t signifies the time

denotes the half-life $t_{1/2}$

Since the charcoal was found to contain less than 1/1000 of the typical amount of $^{14}\text{C}$ .

Thus;

$\dfrac{N}{N_o} = \dfrac{1}{1000}$

However; the objective is to estimate the minimum age of the charcoal while noting $2^{10} = 1024$

this means $2^{10} = 1024$ , then:

$\dfrac{1}{1000}> \dfrac{1}{1024}$

$\dfrac{1}{1000}> \dfrac{1}{2^{10}}$

$\dfrac{1}{1000}> (\dfrac{1}{2})^{10}$

$\dfrac{N}{N_o} = \dfrac{1}{1000}$

Then

$\dfrac{N}{N_o} > (\dfrac{1}{2})^{10}$

Consequently, it can be estimated that the minimum time elapsed is 10 half-lives.

For $^{14}\text{C}$ , the standard half-life time is 5730 years

Thus, the estimation of the minimum age of the charcoal is 5730 years × 10

= 57300 years

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