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2 years ago

Select the correct answer. What is the domain of the function f(x) = 2x + 5?

1 answer:

4 0

The domain of the function is the complete set of possible values of the independent variable. (−∞,∞),{x|x ∈ R}

<h3>What is the domain function?</h3>

The domain is the set of values for which the given function is defined.

The given function;

f(x) = 2x + 5

The domain of the given function is all real numbers except where the function is undefined.

In this case, there is no real number that makes the function undefined.

The domain of the function is the complete set of possible values of the independent variable.

(−∞,∞),{x|x ∈ R}

The range is the set of all valid y values.

Learn more about appropriate domain here:

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Y = (x) = (1/9)^x<br> Find f(x) when x = (1/2)<br> Round your answer to the nearest thousandth.

irina [24]

Answer:

0.333

Step-by-step explanation:

6 0

3 years ago

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

A speed of 220 feet per minute is equal to how many miles per hour

garik1379 [7]

Answer: 2.5 miles per hour

Step-by-step explanation:

this problem is all about conversions

220 ft per minute

first get it to hours, since there is 60 minute in an hour multiply by a factor of 60

220 ft per minute becomes 13200 ft per hour

then you need to covert from ft to mi, there are 5280 ft in 1 mi so divide by 5280

13200 ft per hour becomes 2.5 miles per hour

3 0

3 years ago

After a 2 1/2 hour rainstorm, there are 5 inches of water in a bucket outside. What is the rate per inch?

xeze [42]

Answer:

2 inches per hour

Step-by-step explanation:

2 1/2 hours is equivalent to 150 minutes.

Set up a proportion; let x equal inches of rain

$\frac{5}{150}$ = $\frac{x}{60}$

Cross multiply -> 150x=300

Divide both sides by 150 to get -> x=2

5 0

3 years ago

Im having a hard time on this question and I hope you can help.

Masja [62]

The answer would be x ≠ 0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

First start with the left side, doing distributive property

So... -2(x) = -2x and -2(5) = -10 Therefore on the left side you now have -2x -10

Next do the same on the right side

-2(x) = - 2x and -2(-2) = 4 so you have -2x + 4 + 5 and you add 4 and 5, leaving you with -2x + 9

Now that you have simplified both sides the problem now looks like this:

-2x - 10 = -2x + 9

Because you have equal terms on both sides (-2) those cancel out so you have -10 = 9

Just from looking at this we know that the statement is false because -1o does not equal 9

*The symbol, "≠" means not equal to"

3 0

3 years ago

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