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Natali [406]
3 years ago
5

Prove algebraically that (m + 2)2 – m 2 – 12 is always a multiple of 4

Mathematics
1 answer:
Julli [10]3 years ago
3 0

Answer:

(m + 2)^{2} - m^{2}  - 12 = 4(m - 2)

Step-by-step explanation:

Step 1:

Write the expression

(m+2)^{2} - m^{2}  - 12

Step 2: Expand (m + 2)^{2}

(m+2)^{2} - m^{2} - 12\\(m+2)(m+2) - m^{2}  - 12\\m^{2} + 2m + 2m + 4 - m^{2}  - 12

Step 3: Collect similar terms

m^{2}  - m^{2}  + 4m + 4 - 12\\4m - 8

Step 4: Factor 4 out of the expression to prove that the expression is a multiple of 4.

Therefore\\4m - 8 = 4(m - 2)\\Hence,\\(m+2)^{2}  - m^{2} -  12 is a multiply of 4 because the expression is equal to 4(m-2)

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Please answer this correctly without making mistakes
serious [3.7K]

Answer:

554/5,948

Step-by-step explanation:

burgers with pickles: 554

burgers without pickles: 5,394

total burgers = 554 + 5,394 = 5,948

ratio of numbers of burgers with pickles to total burgers: 554/5,948

6 0
3 years ago
Please help me find x
Ghella [55]

Answer:

x = 53

Step-by-step explanation:

Remember that the sum of all 3 interior angles in a triangle is 180∘ so

74 + x + x = 180

74 + 2x = 180

2x = 180 - 74

2x = 106

x = 106/2

x = 53

3 0
3 years ago
Read 2 more answers
A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in t
Zinaida [17]

Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

c) Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

Step-by-step explanation:

Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.

To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.

             b) Find the profit function P(x).

             c) Find the price of per room per day the motel should charge in order to maximize its profit.

Proof -

a)

Let

(x, y) be the point

where x represents number of rooms occupied

and y represents price of room per day.

Now,

Given that,

a room is priced at $60 per day, all 80 rooms of the motel are occupied.

So, point becomes (80, 60)

And  given that For every $3 rise in the charge per room per day, one more room is vacant.

So, point becomes (79, 63)

Now, we have two points (80, 60), (79, 63)

Let us assume that,

p(x) be the price charged for each room per day

Now,

By using point - slope formula , we get

p -60 = \frac{(63 - 60}{(79 - 80)} (x - 80)

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

b)

Given that,

Each occupied room costs an additional $15 per day to maintain.

Let C(x) be the cost function,

Then C(x) =15 x

now,

Revenue function,

R(x) =x*p

      = x*(300 -3 x )

      = 300 x - 3 x²

⇒R(x) = 300 x - 3 x²

Now,

We know

Profit function = Revenue function - Cost function

⇒P(x) = R(x)-C(x)

⇒P(x) = (300 x -3 x²) -15 x

⇒P(x) = -3 x² + 285 x

c)

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = \frac{285}{6}

⇒x= 47.5

∴ we get

Maximize profit is when price, p = 300 - 3x

                                                      = 300 -3(47.5)

                                                      = $157.5

⇒Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

5 0
2 years ago
A customer went to a garden shop and bought some potting soil for $17.50 and 4 shrubs. The total bill was $53.50. Choose the equ
olga2289 [7]
4x + 17.50 = 53.50

the prices of each shrub would be 9 dollars each
6 0
3 years ago
5) Your stock investments went from $450 in 2013 to $350 ir
Hatshy [7]

The most appropriate choice for percentage will be given by Percentage decrease in the investment is 22.22%

<h3>What Does Percent Mean?</h3>

Using a percentage of 100, we may express a ratio as a %.

Stock investments in this case decreased from $450 in 2013 to $350 in 2014.

Decrease in stock equals $100 ($450 - $355)

Decrease in percentage: 100/450 100 = 22.22%

<h3>What format does a percentage use?</h3>

The definition of percentage is "out of 100." In mathematics, percentages are used to represent parts of a whole, much as fractions and decimals. A total is considered to be made up of 100 equal parts when expressed as a percentage. The symbol % or, less commonly, the abbreviation 'pct' can be used to represent a percentage.

To learn more about percentage, refer to the link : brainly.com/question/24304697

#SPJ9

3 0
1 year ago
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