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PtichkaEL [24]
3 years ago
8

Suppose you need to minimize the cost of fencing in a rectangular region with a total area of 450 square feet. The material that

will be used for three sides costs $15 per linear foot, and the material that will be used for the fourth side costs $18 per linear foot. Write a function that expresses the cost of fencing the region in terms of the length, x, of the two opposite sides of the region with material costs of $15 per linear foot.
Mathematics
1 answer:
Yuri [45]3 years ago
8 0

Answer:

30*x + 14850/x

Step-by-step explanation:

Let x be the length of the two opposite sides of the region with material costs of $15 per linear foot.

Let y be the length of the other two sides

Now, we have the following equations

Area of the rectangular región = x * y = 450 ft2

Total cost of fencing = 15*x + 15*x + 15 *y + 18*y

Total cost of fencing = 30*x + 33 *y

We now that area is equal to 450 ft2 = x*y

So y = 450/x

Now we can substitute y in equation for Total cost of fencing and obtain a function that expresses the cost of fencing the region in terms of the length, x

Total cost of fencing = 30*x + 33 *(450/x)

Total cost of fencing = 30*x + 14850/x

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Step-by-step explanation:

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2 years ago
Below is the graph of y= x.<br> Translate it to make it the graph of y=<br> x-1 + 4.
Oduvanchick [21]
  • First, to shift the graph of y=x 1 unit to the right, so y=x-1
  • Second, to shift the graph of y=x-1 4 units to the left, so y=x-1+4

<h2>Explanation:</h2>

To translate the graph of a function is part of Rigid Transformations because the basic shape of the graph is unchanged

Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:

\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c

\bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)

In this case, we have the graph of:

y=x

And we need to translate it to make it the graph of:

y=x-1+4

According to our rules we need:

  • First, to shift the graph of y=x 1 unit to the right, so y=x-1
  • Second, to shift the graph of y=x-1 4 units to the left, so y=x-1+4

But y=x-1+4 is the same as y=x+3, so the previous steps can be simplified as:

  • Shifting the graph of y=x 3 unit to the left.

Below are shown those graphs:

  • The blue one is y=x
  • The red one is y=x-1+4

<h2>Learn more:</h2>

Shifting graphs: brainly.com/question/10010217

#LearnWithBrainly

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3 years ago
Examine the system of equations. y = 3 2 x − 6, y = −9 2 x + 21 Use substitution to solve the system of equations. What is the v
nadezda [96]

Answer:

<h2>y = -4/9</h2>

Step-by-step explanation:

Given the system of equations y = 3/2 x − 6, y = −9/2 x + 21, since both expressions are functions of y, we will equate both of them to find the variable x;

3/2 x − 6 = −9/2 x + 21,

Cross multiplying;

3(2x+21) = -9(2x-6)

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collecting the like terms;

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24x = -9

x = -9/24

x = -3/8

To get the value of y, we will substitute x = -3/8 into any of the given equation. Using the first equation;

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y = 3/{2(-3/8)-6}

y = 3/{(-3/4-6)}

y = 3/{(-3-24)/4}

y = 3/(-27/4)

y = 3 * -4/27

y = -4/9

Hence, the value of y is -4/9

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Answer:

14% and 1/7

Step-by-step explanation:

4 0
3 years ago
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