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2 years ago

3. The area of a rectangular deck, in square meters, is given by the polynomial 40p2 + 24p.

Mathematics

1 answer:

lorasvet [3.4K]2 years ago

4 0

Answer:

Length = 5p + 3

Perimeter = 26p + 6

Step-by-step explanation:

Given

Area = 40p² + 24p

Width = 8p

Solving for the length of deck

Given that the deck is rectangular in shape.

The area will be calculated as thus;

Area = Length * Width

Substitute 40p² + 24p and 8p for Area and Width respectively

The formula becomes

40p² + 24p = Length * 8p

Factorize both sides

p(40p + 24) = Length * 8 * p

Divide both sides by P

40p + 24 = Length * 8

Factorize both sides, again

8(5p + 3) = Length * 8

Multiply both sides by ⅛

⅛ * 8(5p + 3) = Length * 8 * ⅛

5p + 3 = Length

Length = 5p + 3

Solving for the perimeter of the deck

The perimeter of the deck is calculated as thus

Perimeter = 2(Length + Width)

Substitute 5p + 3 and 8p for Length and Width, respectively.

Perimeter = 2(5p + 3 + 8p)

Perimeter = 2(5p + 8p + 3)

Perimeter = 2(13p + 3)

Open bracket

Perimeter = 2 * 13p + 2 * 3

Perimeter = 26p + 6

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2 years ago

Adam sells medical magazine and books. the table shows price for both Magazine £8

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Adam earned a total of £265.10 last week.

Step-by-step explanation:

Step 1; Adam earns a basic pay of £200 each week. He earns 10% of the magazine price for each sold and 15% of the book price for each sold. Each magazine costs £8 and each book costs £15. He sells 42 magazines and 14 books.

Money earned for selling a magazine = 10% × £8 = 0.10 × £8 = £0.80,

Money earned for selling a book = 15% × £15 = 0.15 × £15 = £2.25,

Money earned for selling 42 magazines = 42 × £0.80 = £33.60,

Money earned for selling 14 books = 14 × £2.25 = £31.50,

Money earned for selling 42 magazines and 14 books = £33.60 + £31.50 = £65.10.

Step 2; Now we have to calculate his last week's salary which is his weekly pay and his earnings from selling magazines and books. We found that he earned £31.50 from selling books and magazines. His weekly salary is £200.

Last week's salary = £200 + £65.10 = £265.10.

5 0

1 year ago

Read 2 more answers

Ramina found the length of two pieces of ribbon to be 47.6 inches and 39.75 inches. Which is an effective estimation strategy fo

lukranit [14]

Answer:

<h3>Add 47.6 and 39.75, then round the answer</h3>

Step-by-step explanation:

If Ramina found the length of two pieces of ribbon to be 47.6 inches and 39.75 inches, the effective strategy of finding the sum of the two lengths is to:

1) First is to add the two values together

47.6 + 39.75

= (47+0.6)+(39+0.75)

= (47+39)+(0.6+0.75)

= 86 + 1.35

= 87.35

2) Round up the answer to nearest whole number.

87.35 ≈ 87 (note that we couldn't round up to 88 because the values after the decimal point wasn't up to 5)

Option C is correct

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1 year ago

Read 3 more answers

Determine if each of the following sets is a subspace of ℙn, for an appropriate value of n. Type "yes" or "no" for each answer.

xxMikexx [17]

Answer:

1. Yes.

2. No.

3. Yes.

Step-by-step explanation:

Consider the following subsets of Pn given by

1.Let W1 be the set of all polynomials of the form $p(t)=at^2$ , where a is in ℝ.

2.Let W2 be the set of all polynomials of the form $p(t)=t^2+a$ , where a is in ℝ.

3. Let W3 be the set of all polynomials of the form $p(t)=at^2+at$ , where a is in ℝ.

Recall that given a vector space V, a subset W of V is a subspace if the following criteria hold:

- The 0 vector of V is in W.

- Given v,w in W then v+w is in W.

- Given v in W and a a real number, then av is in W.

So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.

- First property:

Note that for W2, for any value of a, the polynomial we get is not the zero polynomial. Hence the first criteria is not met. Then, W2 is not a subspace of Pn.

For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.

- Second property:

W1. Consider two elements in W1, say, consider a,b different non-zero real numbers and consider the polynomials

$p_1 (t) = at^2, p_2(t)=bt^2$ .