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1 year ago

What is the answer of 12x - 6 = 54

Mathematics

2 answers:

Bogdan [553]1 year ago

7 0

Answer:

x = 5

Step-by-step explanation:

12x - 6 + 6 = 54 + 6

12x = 60

12/12 = 60/12

X = 5

Flauer [41]1 year ago

6 0

Answer:

x = 5

Step-by-step explanation:

54 + 6

60/12

= 5

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Loris dog eats 3.82 pounds of food in one week. how much food will the dog eat in 18 weeks?

shtirl [24]

Answer: the dog eats 68.76 lbs of food in 18 weeks

Step-by-step explanation: 3.82x 18=68.76

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2 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:

Part A

Price Function $= 580 - 10x$

The revenue function

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

The marginal revenue function

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

Part B

(Fixed Cost)

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 .

Marginal Cost Function

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

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

Part C

Profit Function

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$

Part D

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$

The number of cakes that maximizes profit is 4.

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2 years ago

The area of a rectangle is 72 cm square. The length of the rectangle is 6 cm longer than the width. What is the width of the rec

miskamm [114]

The correct option will be : B) 6 cm.

Explanation

Suppose, the width of the rectangle is $x$ cm.

As, the length is 6 cm longer than the width, so the length will be: $(x+6) cm.$

Formula for the Area of rectangle is: $(Length)*(Width)$

Given that, the area of a rectangle is 72 cm²

So....

$x(x+6)=72\\ \\ x^2+6x-72=0\\ \\ (x+12)(x-6)=0$

Using zero-product property, we will get...

$x+12=0\\ x= -12$ (Negative value is ignored as width can't be negative)

and

$x-6=0\\ x=6$

So, the width of the rectangle is 6 cm.

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3 years ago

(X+2) (x+8) expand and simplify

Nutka1998 [239]

Answer:

X+2=2x

x+8=8x

(2x).(8x)=16x

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2 years ago

Joseph read 9 books in 15 months. what was his rate of being in books per month?

inna [77]

Answer:

0.6 books

Step-by-step explanation:

Divide 9 by 15 to get 0.6 books a month

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3 years ago