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3 years ago

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The quotient of a number and 5, less 10, is 3

1 answer:

sergejj [24]3 years ago

4 0

Quotient is the result of division. Assign a variable to the unknown number. Let's make it x. Write the statement as an equation.
x/5 - 10 = 3

solve for x

x/5 - 10 = 3
x/5 = 3 + 10
x/5 = 13
x = 5 × 13
x = 65

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(a) Rearrange the equation<br> x<br> + 2y = 6 to make y the subject.

satela [25.4K]

To make y the subject, we must move everything to one side and y on the other.

$x + 2y = 6\\2y = 6 -x\\2y = -x + 6\\y =-\frac{1}{2} x + 3$

Good day and I hoped that helped!

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3 years ago

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The area of the base of a cylinder is 36 square inches and its height is 10 inches. A cone has the same area

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Reason
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2 years ago

6/15 divided by 1/7

mylen [45]

Question-
6/15 divided by 1/7

Answer-
Find the reciprocal of the divisor
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3 years ago

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QUESTION 3 [10 MARKS] A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the nu

Harman [31]

Answer:

(a)Revenue function, $R(x)=580x-x^2$

Marginal Revenue function, R'(x)=580-2x

(b)Fixed cost =900 .

Marginal Cost Function=300+50x

(c)Profit, $P(x)=-35x^2+280x-900$

(d)x=4

Step-by-step explanation:

<u>Part A </u>

Price Function $= 580 - 10x$

The revenue function

$R(x)=x\cdot (580-10x)\\R(x)=580x-x^2$

The marginal revenue function

$\dfrac{dR}{dx}= \dfrac{d}{dx}(R(x))=\dfrac{d}{dx}(580x-x^2)=580-2x\\R'(x)=580-2x$

<u>Part B </u>

<u>(Fixed Cost)</u>

The total cost function of the company is given by $c=(30+5x)^2$

We expand the expression

$(30+5x)^2=(30+5x)(30+5x)=900+300x+25x^2$

Therefore, the fixed cost is 900 .

<u> Marginal Cost Function</u>

If $c=900+300x+25x^2$

Marginal Cost Function, $\frac{dc}{dx}= (900+300x+25x^2)'=300+50x$

<u>Part C </u>

<u>Profit Function </u>

Profit=Revenue -Total cost

$580x-10x^2-(900+300x+25x^2)\\580x-10x^2-900-300x-25x^2\\$Profit,P(x)=-35x^2+280x-900$

<u> Part D </u>

To maximize profit, we find the derivative of the profit function, equate it to zero and solve for x.

$P(x)=-35x^2+280x-900\\P'(x)=-70x+280\\-70x+280=0\\-70x=-280\\$Divide both sides by -70\\x=4$

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3 years ago

Express in the form n:1 give n as a decimal 21:12

Makovka662 [10]

$1.75:1$ which is similar to n:1 where $n=1.75$

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

Here we have to Express in the form n:1 give n as a decimal 21:12 . Let's find out:

Given ratio as 21:12 . Let's convert it into n:1 , where n is decimal

⇒ $21:12$

⇒ $\frac{21}{12}$

⇒ $\frac{3(7)}{3(4)}$

⇒ $\frac{7}{4}$

⇒ $\frac{\frac{7}{4}}{\frac{4}{4}}$ { dividing denominator & numerator by 4 }

⇒ $\frac{\frac{7}{4}}{1}$

⇒ $\frac{1.75}{1}$

⇒ $1.75:1$ which is similar to n:1 where $n=1.75$

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3 years ago