What is the equation of the line in slope-intercept form?

Suppose you have 40 meters of fencing what is the greatest rectangular area that you can enclose

Gelneren [198K]

It'd help if you could sketch this situation. Note that the area of a rectangle is equal to the product of its width and length: A = L W.

Consider the perimeter of this rectangular area. It's P = 2 L + 2 W. Note that P = 40 meters in this problem.

Thus, if we choose to use W as our independent variable, then P = 40 meters = 2 L + 2 W. Let's express L in terms of W. Divide both sides of the following equation by 2: 40 = 2 L + 2 W. We get 20 = L + W. Thus, L = 20 - w.

Then the area of the rectangle is A = ( 20 - W)*W.

Multiply this out. Your result will be a quadratic equation. Graph this quadratic equation (in other words, graph the function that represents the area of the rectangle). For which W value is the area at its maximum?

Alternatively, find the vertex of this graph: remember that the x- (or W-) coordinate of the vertex is given by

W = -b/(2a), where a is the coefficient of W^2 an b is the coefficient of W in your quadratic equation.

Finally, substitute this value of W into your quadratic equation, to calculate the maximum area.

8 0

4 years ago

Here is a table of values for y = f(x).

Firlakuza [10]

The true statements are:

B. f(-1) = 6

D. The domain for f(x) is the set {-2 , -1 , 0 , 1 , 2 , 3 , 4 , 5 , 6}

Step-by-step explanation:

The table:

→ x : -2 : -1 : 0 : 1 : 2 : 3 : 4 : 5 : 6
→ y : 5 : 6 : 7 : 8 : 9 : 10 : 11 : 12 : 13

∵ y = f(x)

∴ x is the domain of the function

∴ y is the range of the function

Use the table to find them

∵ The values of x are -2 , -1 , 0 , 1 , 2 , 3 , 4 , 5 , 6

∴ The domain of f(x) is the set {-2 , -1 , 0 , 1 , 2 , 3 , 4 , 5 , 6}

∵ The values of y are 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13

∴ The range of f(x) is the set {5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13}

∵ f(5) means the value of y at x = 5

∵ The value of y at x = 5 is 12

∴ f(5) = 12

∵ f(-1) means the value of y at x = -1

∵ The value of y at x = -1 is 6

∴ f(-1) = 6

The true statements are:

B. f(-1) = 6

D. The domain for f(x) is the set {-2 , -1 , 0 , 1 , 2 , 3 , 4 , 5 , 6}

Learn more:

You can learn more about the function in brainly.com/question/7128279

#LearnwithBrainly

5 0

3 years ago

Is the line through points P(0, –9) and Q(2, –8) perpendicular to the line through points R(1, 4) and S(3, 3)? Explain

Serjik [45]

The quickest way to tell if a line is perpendicular is to find the slope, so you'll need to get the slope for both lines

PQ = ((-8) - (-9))/(2 - 0) = 1/2

and, for reference, a perpendicular slope is the negative reciprocal of the original (so we're looking for -2)

RS = (3 - 4)/(3 - 1) = -1/2

so, no, these two lines aren't perpendicular because the slope of RS is only the negative of PQ, not the negative <em>reciprocal</em>.

3 0

3 years ago

Read 2 more answers

I need help please!!!! Thank you :)

Likurg_2 [28]

Answer:

The correct options are: Option A, C and D

Step-by-step explanation:

We need to choose correct options by solving the given system of equations.

$3x+4y=18\\2x-2y=2$

Let:

$3x+4y=18--eq(1)\\2x-2y=2--eq(2)$

First Multiply equation 2 by 2 and add both equations.

$3x+4y=18\\4x-4y=4\\------\\7x=22\\x=\frac{22}{7}\\x=3.14$

Now, we will put value of x in equation 2 to find value of y

$2x-2y=2\\2(3.14)-2y=2\\6.28-2y=2\\-2y=2-6.28\\-2y=-4.28\\y=\frac{-4.28}{-2}\\y=2.14$

So, we get x = 3.14 and y = 2.14

Solution set is (3.14,2.14)

The given solution set (2,3) is not the solution of system of equations.

If we put x=2 and y =3 in the first equation:

$3x+4y=18\\3(2)+4(3)=18\\6+12=18\\18=18$

(2,3) when substituted in the First equation the equation is True.

If we put x=2 and y =3 in the second equation:

$2x-2y=2\\2(2)-2(3)=2\\4-6=2\\-2\neq 2$

So, (2,3) when substituted in the second equation the equation is false.

The correct options are: Option A, C and D

6 0

3 years ago

Determine whether or not it is a function

Brrunno [24]

This is indeed a function because every domain is only used once, a domain can indeed share a range but can’t be the same for which it’s a function due to the fact that no domain is repeated with a different outcome

4 0

3 years ago