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agasfer [191]
2 years ago
7

A) Write an equation in terms of x that represents the problem. (b) Solve the problem.

Mathematics
1 answer:
Andreas93 [3]2 years ago
4 0

Answer:

Part 1: (n÷2)-7 = -12

Part 2: n = -10

Step-by-step explanation:

Part 1:

Let's first write "the quotient of a number and 2" using numbers and variables. Let "n" represent "a number". The key word that we see here is quotient, meaning we have to divide something by something else. "The quotient of a number and 2 means that "a number" is the dividend (number that is divided) and "2" is the divisor (number that divides the dividend). Therefore we obtain:

n÷2

The first part says "seven less than the quotient of a number and 2". The keyword here is less, meaning we have to use subtraction. Therefore:

(n÷2)-7

The last part says "is equal to -12". Therefore the whole expression we just wrote is equivalent to -12:

(n÷2)-7 = -12

Part 2

Remember the Order of Operations:

Parentheses

Exponents

M/D: Multiplication/Division (whichever comes first in the equation)

A/S: Addition/Subtraction (whichever comes first in the equation)

Start by adding 7 to both sides

(n÷2) = -5

Then, multiply both sides by 2

\frac{n}{2}=-5\\n=-10

Note: I used a fraction to display the division because it is easier to see why we have to multiply both sides by 2; to cancel out the denominator.

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A manufacturer finds that the revenue generated by selling of cortan commodity is given by function R(x)=80x-0.2x^ 2 , where he
Nina [5.8K]

The maximum units is 200 and , Total revenue is $8,000

<u>Step-by-step explanation:</u>

Here we have , A manufacturer finds that the revenue generated by selling of cortan commodity is given by function R(x)=80x-0.2x^ 2 , where he maximum reveremany should be manufactured to obtain this maximum units .Let's find out:

We have following function as R(x)=80x-0.2x^ 2 . Let's differentiate this and equate it to zero to find value of x for which the function is maximum!

⇒ R(x)=80x-0.2x^ 2

⇒ \frac{d(R(x))}{dx}=\frac{d(80x-0.2x^ 2)}{dx}

⇒ \frac{d(R(x))}{dx}=\frac{d(80x)}{dx}-\frac{d(0.2x^ 2)}{dx}}

⇒ 0=80-2x(0.2)

⇒ \frac{80}{0.4}=x

⇒ x=200

Now , Value of function at x=200 is :

⇒ R(200)=80(200)-0.2(200)^ 2

⇒ R(200)=16000-8000

⇒ R(200)=8000

Therefore , The maximum units is 200 and , Total revenue is $8,000

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3 years ago
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Read 2 more answers
Factor out the greatest common factor <br>-5x^2 - 5x^3 - 15x^4
vaieri [72.5K]
Our answer is -5x^{2} (3x^{2} +x+1)

Our greatest common factor, or GCF, is -5x^{2}, so when we factor is out, our divide each term by -5x^{2}, we get our answer. To check this, we can multiply the -5x^{2} back across the parenthesis and see if we get the same result as our initial question.

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