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3 years ago

Is —2x+3y=12 parallel, perpendicular, or neither

Mathematics

2 answers:

bixtya [17]3 years ago

7 0

Answer:neither

Step-by-step explanation:

AfilCa [17]3 years ago

6 0

$\text{Solve the equation:}\\\\-2x+3y=12\\\\3y=2x+12\\\\y=\frac{2}{3}x+4\\\\\text{In order for the line to be parellel, or perpendicular, we need to know}\\\text{what the other equation is}\\\\\text{In this case, we can't tell what the other equation is, but we know that}\\\text{this is a parallel line}$

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the school newspaper has a circulation of 500 and sells for $.035 a copy. the students decide to raise the price to increase the

Alik [6]

Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

$.35+.05x$

Let y be the newspaper they sell, then the income will be

$y(.35+.05x)$

Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be

$y=500-20x$

Plugging the value of y in the first expression we have that the income will be

$\begin{gathered} f(x)=(500-20x)(.35+\text{0}.5x)=175+25x-7x-x^2 \\ =-x^2+18x+175 \end{gathered}$

Then the income is given by the function

$f(x)=-x^2+18x+175$

To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,

$\begin{gathered} \frac{df}{dx}=\frac{d}{dx}(-x^2+18x+175) \\ =-2x+18 \end{gathered}$

no we equate the derivative to zero and solve for x.

$\begin{gathered} \frac{df}{dx}=0 \\ -2x+18=0 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}$

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

$\begin{gathered} \frac{d^2f}{dx^2}=\frac{d}{dx}(\frac{df}{dx}) \\ =\frac{d}{dx}(-2x+18) \\ =-2 \end{gathered}$

Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.

With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.

Therefore the price to maximize the income is $0.35+$0.45=$0.80.

4 0

1 year ago

Given that f(x) = 4x√3x + 3 and g(x) = 2√x+1, find (f/g)(x)

Tresset [83]

Answer:

$2x\sqrt{3}.$

Step-by-step explanation:

$\frac{f}{g}(x)=\frac{4x\sqrt{3x+3}}{2\sqrt{x+1}}=\frac{2*2*x*\sqrt{3}*\sqrt{x+1}}{2*\sqrt{x+1}}=2x\sqrt{3}.$

8 0

2 years ago

Sara found that the older person is, fewer cartoons that person watches.

Misha Larkins [42]

Answer:

Step-by-step explanation:

The scatter graph shows a decreasing correlation.

Its not A because it's a increasing correlation

its not C because it's neutral

its not D because it's a no correlation graph

4 0

2 years ago

A bookstore had 45 copies of a magazine. Yesterday, it sold 13 of them. Today, it sold 23 of what remained. How many copies does

Elan Coil [88]

Answer:

Step-by-step explanation:

Total initially in bookstore = 45

Sold 13copies, remaining copies = 45-13= 32

Sold 23 copies again, remaining copies = 32-23 = 9

Copies left = 9

6 0

2 years ago

Help: I am a number between 60 and 100. My ones digit is six less than my tens digit. I am a prime number.

Reptile [31]

Answer:

Let's name the digit:

x- ones digit

y - tens digit

we know that x=y-2.

Now, y can be 6,7,8,9 (the number is between 60 and 100 (so depending on your understanding of "between", 0 is also possible. but then the number would have to have -2 as its ones digit, so in any case, it's not possible).

So the possibilities with x=y-2:

Out of those 64 and 86 are even, so they can't be prime.

75 has 5 in its ones number: it's divisible by 5.

so the correct answer is 97.

Step-by-step explanation:

Hope this helps!

5 0

3 years ago

Read 2 more answers