All categories

2 years ago

Simplify -5(3m2 + 7n2) + 8n2

Mathematics

2 answers:

Blababa [14]2 years ago

6 0

Answer:

$\boxed{\red{= - 3(5 {m}^{2} + 9 {n}^{2} )}}$

Step-by-step explanation:

$- 5(3 {m}^{2} + 7 {n}^{2} ) + 8 {n}^{2} \\ - 15 {m}^{2} - 35 {n}^{2} + 8 {n}^{2} \\ = - 15 {m}^{2} - 27 {n}^{2} \\ = - 3(5 {m}^{2} + 9 {n}^{2} )$

son4ous [18]2 years ago

5 0

Answer:

Step-by-step explanation:

-5(3m² + 7n²) + 8n²

Expand brackets.

-15m² + -35n² + 8n²

Combine like terms.

-15m² + -27n²

You might be interested in

Smith High School offers a baseball camp that is $75 for 4 days of camp and a basketball camp that is $100 for 5 days of camp. W

laiz [17]

75 100
4 * 5
300 500 it would be baseball camp. exactly

6 0

3 years ago

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.

6 0

2 years ago

Write the expression a2b3c2d in expanded form.

Zanzabum

Answer:

a*2+b*2+c*2+d

Step-by-step explanation:

If i's meant to be Pythagorean theorem, a*a+b*b=c*c

8 0

2 years ago

A migrating bird flies 390 miles in 15 hours. How many miles does it fly in 4 hours?

viva [34]

Answer:

104

Step-by-step explanation:

390/15=26

26 times 4 is 104

6 0

2 years ago

Wendy is comparing two checking account. one has a monthly fee of $9 and a per-check fee of $0.50, and the other has a monthly f

Ilya [14]

I need this answer too

7 0

3 years ago

Read 2 more answers