Parabola is (6, 3). What is the vertex of the function defined as g(x) = f(x) + 3?

Mathematics

1 answer:

MrRissso [65]1 year ago

3 0

Answer:

Step-by-step explanation:

f(x) is a parabola with vertex (6,3). f(x) means the function is reflected about the y axis. That means the vertex will become (-6, 3) (the x-value gets multiplied by -1). Then adding 3 will move the vertex in the y-direction by +3 (add 3 to the y-value).

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In some country the budget for defense exceeded the budget for education by $660.4 billion. If x represents the budget for edu

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Answer:

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Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Budget for education is $ 660.4 billion less than budget for defense in some country

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2. How can the budget for defense be represented?

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Misha Larkins [42]

Answer:

a) The slope of the function is 3.

c) The equation is represented by $n(t) = 3\cdot t + 35$ .

d) The y-intercept of the function is 35.

Step-by-step explanation:

a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:

$n(t) = m\cdot t + n_{o}$ (1)

Where:

$m$ - Slope, measured in number of pieces per minute.

$t$ - Time, measured in minutes.

$n_{o}$ - Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.

$n$ - Current number of pieces of mail that must be hand-sorted, measured in pieces.

From Geometry, we know that a line can be formed by know two distinct points. If we know that $n(15\,min) = 80\,p$ and $n(45\,min) = 170\,p$ , then the following system of linear equations is formed: