what is the same expression as 3x+1 when x equals 4

Final answer:

A negative y-intercept in a real-world context indicates that the system or condition being measured starts below the baseline or has a deficit to begin with. It can represent an initial loss in economics, such as starting with debt or needing initial investment. The slope of the line is critical to understanding how changes in one variable affect another.

Explanation:

A negative y-intercept in a real-world application can have various implications depending on the context. In many scientific experiments, the y-intercept represents the baseline level of the system without any experimental conditions applied. If the y-intercept is negative, this might indicate that in the absence of a certain factor (represented by the x-variable), the system has a deficit or a reduction in the measured quantity. For instance, if we are plotting a graph of growth over time, a negative y-intercept could imply that there was an initial debt or loss before measurements began.

When it comes to economics and data models, a negative y-intercept on a graph could represent a starting deficit. For example, a company might have initial losses (negative y-intercept) that it seeks to overcome as production (x-variable) increases. Supply and demand models, cost projections, and similar economic graphs can also have negative y-intercepts indicating starting positions below zero on the graph—such as starting with a debt or having to invest before seeing any return.

The y-intercept and the slope (m-term) together specify a particular line on a graph that can offer a reasonable approximation of real-world data. Economists find the slope particularly useful as it shows the relationship between two variables, like how a change in price affects the quantity supplied.

[tex]\dfrac{x}{3} > -1\ \ \ \ |\cdot3\\\\x > -3\to x\in(-3;\ \infty)[/tex]

Step-by-step explanation: Given radical expression 4√12 + √75.

Let us simplify each of the radical separately first.

√12 = √(2×2×3) = 2√3

Therefore, 4√12 = 4 × 2√3 = 8√3.

√75 = √(3×5×5) = 5√3

Therefore 4√12 + √75  => 8√3 + 5√3.

Adding like radicals, we get

8√3 + 5√3 = 13√3.

The correct option is "option A" , i.e., √3 .

In the question some options are given which consists of some numbers.

We have to find out which number is not a rational number.

What is the difference between rational and irrational numbers ?

Irrational numbers can not be represented in the form of rational numbers or in other words the irrational number cannot be expressed in the p/q form.

As per the definition , Let's check which one is not rational.

A) √3

    = 1.723

This can't be represented in p/q form . So , this is not rational number.

By checking all other options we get to know that these all are rational numbers as we can express them in p/q form.

Thus , the correct option is "option A" , i.e., √3 .

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Danielle's estimate of earning about $20,000 per year is accurate, as the calculation based on her hourly wage and weekly hours worked gives an actual annual income of $20,020.

Danielle's estimate of earning about $20,000 per year is accurate based on her hourly wage and weekly hours worked. To assess the accuracy of her estimate, we need to calculate her actual annual income.

Danielle earns $11 per hour and works 35 hours a week. Therefore, her weekly earnings are:

35 hours/week × $11/hour = $385/week.

As there are typically 52 weeks in a year, her estimated annual income would be:

52 weeks/year × $385/week = $20,020/year.

This calculation shows that Danielle's estimate of making about $20,000 per year is indeed accurate.

A quadrilateral cannot have 4 obtuse angles

From the question, we have the following parameters that can be used in our computation:

A quadrilateral

By definition, the sum of angles in a quadrilateral is 360

And an obtuse angle is greater than 90

So, we have

Sum = 4 * greater than 90

Evaluate

Sum = greater than 360

This means that a quadrilateral cannot have 4 obtuse angles

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The equation that models the balance b after m months is b = 1800 - 150m

Initial cost = 1800

Difference in balance = 1350 - 1050 = 300

Number of months used = 5 months - 3 months = 2 months

Therefore, the equation that models the balance b after m months will be:

b = 1800 - (300/2)m

b = 1800 - 150m

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To solve the equation ab + 3c = 2x for b, subtract 3c from both sides and divide by a.

To solve the equation ab + 3c = 2x for b, we need to isolate b on one side of the equation. First, subtract 3c from both sides to get ab = 2x - 3c. Then, divide both sides by a to get the final solution: b = (2x - 3c) / a.

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