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2 months ago

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Simplify the function f (x) = one-half (27) Superscript StartFraction 2x Over 3 EndFraction. Then determine the key aspects of t

he function.

2 answers:

Inessa [12.5K]2 months ago

6 0

Answer:

(Refer to the explanation)

Step-by-step explanation:

The function is:

$f(x) = \frac{1}{2}\cdot 27 \cdot \frac{2\cdot x}{3}$

Its simplified version is presented as follows:

$f(x) = 9\cdot x$

The resulting expression represents a linear function, classified as a first-order polynomial, and its domain and range encompass all real numbers.

PIT_PIT [12.4K]2 months ago

6 0

Answer: intersecting with its domain is: 1/3, 27, all real numbers, y>0

Step-by-step explanation:

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The annual net income of a company for the period 2007–2011 could be approximated by P(t) = 1.6t2 − 11t + 44 billion dollars (2

babunello [11817]

Answer:

$P'(t) = 3.2 t -11$

To identify the critical point, we set the derivative equal to zero, resulting in:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

Calculating the second derivative yields:

$P''(t) = 3.2 >0$

This indicates that t = 3.4375 marks the minimum value for the function. Substituting this back into the original function gives us:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

Thus, the minimum annual income is found at t = 3.43 (between the years 2008 and 2009), with a value of 25.094

Step-by-step explanation:

In this scenario, we have the function:

$P(t) = 1.6 t^2 -11t +44$

Where P represents the annual net income from 2007-2011, and $2 \leq t \leq 7$

t is the number of years since early 2005

To discover the lowest income, we utilize the derivative given by:

$P'(t) = 3.2 t -11$

Setting this derivative to zero allows us to find the critical point, leading to:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

Calculating the second derivative reveals:

$P''(t) = 3.2 >0$

Therefore, we conclude that t = 3.4375 is the minimum value, substituting into the original function results in:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

Thus, the minimum annual income occurs at t = 3.43 (between 2008 and 2009) with the value being 25.094

5 0

2 months ago

Points A, P, and B are collinear on AB, and PB:AB = 2/7. A is located on the origin (0,0), P is located at (10, -5), and B is lo

tester [12383]

The x-axis is nearer to point B. Since the ratio PB:AB = 2/7 is positive, this indicates internal division of the line. We utilize the coordinate formula for a point dividing a line internally. Thus, x = (mx₂ + nx₁)/(m + n) and y = (my₂ + ny₁)/(m + n), where PB/AB = 2/7 translates to n/m, giving n = 2 and m = 7. With point A at (0,0) and point P at (10, -5), we substitute these coordinates to find x and y. The calculations yield coordinates for B at 7⁷/₉ and -3⁸/₉. Therefore, B is -3⁸/₉ units from the x-axis and 7⁷/₉ from the y-axis, confirming that the x-axis is closer to B.

4 0

1 month ago

Which table contains only corresponding x-values and y-values where the value of y is one more than the product of x and 2?

zzz [12365]

Answer:

Option (C)

Step-by-step explanation:

The value of y exceeds the multiplication of x by 2.

The equation that describes this condition is:

y = 2x + 1

Thus, by inserting x values into this equation, we can produce a table reflecting the corresponding input and output values:

x 0 1 2 3 4

y 1 3 5 7 9

Consequently, the table provided in Option (C) is indeed the correct choice.

4 0

2 months ago

Andros has an oil fired heating system. In a 30-day period he used a full tank of oil at a constant rate per day. At a different

Leona [12618]

To resolve this, we multiply the 30-day timeframe by 7, resulting in a total of 210 days.

3 0

1 month ago

Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three number

tester [12383]

Answer:Part a) $2,50,18$

Part b) When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , the result is an integer.

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For $x=2$

$\sqrt{2}*\sqrt{2}=\sqrt{4}=2$ -----> the product results in an integer

thus

The number $x=2$ could potentially be Jenny's favorite positive integer

2) For $x=50$

$\sqrt{50}*\sqrt{2}=\sqrt{100}=10$ -----> the product results in an integer

thus

The number $x=50$ could potentially be Jenny's favorite positive integer

3) For $x=18$

$\sqrt{18}*\sqrt{2}=\sqrt{36}=6$ -----> the product results in an integer

thus

The number $x=18$ could potentially be Jenny's favorite positive integer

Part B)

1) For $x=2$

$\sqrt{2}/\sqrt{2}=\sqrt{1}=1$ -----> the outcome is an integer

2) For $x=50$

$\sqrt{50}/\sqrt{2}=\sqrt{25}=5$ -----> the outcome is an integer

3) For $x=18$

$\sqrt{18}/\sqrt{2}=\sqrt{9}=3$ -----> the outcome is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she obtains an integer as a result.

4 0

1 month ago