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Mathematics

1 answer:

Iteru [2.4K]3 years ago

4 0

Answer:

Step-by-step explanation:

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Work out the area of the rectangle give your answer as a mixed number

AlladinOne [14]

We'll first convert the mixed fractions to "improper" and then get their product, since the area of a rectangle is the product of its length and width.

$\bf \stackrel{mixed}{5\frac{1}{6}}\implies \cfrac{5\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{31}{6}}
\\\\\\
\stackrel{mixed}{2\frac{2}{7}}\implies \cfrac{2\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{16}{7}}
\\\\\\
\cfrac{31}{6}\cdot \cfrac{16}{7}\implies \cfrac{496}{42}\implies \stackrel{simplified}{\cfrac{248}{21}}\implies 11\frac{17}{21}$

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3 years ago

Write a polynomial with rational coefficients having roots 3,3+i and 3-i

Elena L [17]

Part 1: If the roots of a polynomial are a, b, and c, then the factors can be written in the form (x - a), (x - b), and (x - c). In this case, we have (x - 3), (x - [3 + i]), and (x - [3 - i]). The three factors are (x - 3)(x - 3 - i)(x - 3 + i).

Part 2: The two factors with complex terms are (x - 3 - i)(x - 3 + i), and multiplying these terms as a difference of two squares can give:
(x - 3)^2 - i^2 = x^2 - 6x + 9 - (-1) = x^2 - 6x + 10

Part 3: We now multiply (x^2 - 6x + 10) by the remaining factor of (x - 3). This results in the cubic expression:
(x^2 - 6x + 10)(x - 3)
= x^3 - 3x^2 - 6x^2 + 18x + 10x - 30
= x^3 - 9x^2 + 28x - 30

3 0

3 years ago

Sean has 5.50 in dimes and quarters. he has 8 more quarters than dimes. how many quarters does he have

MA_775_DIABLO [31]

18 quarters 10 dimes

6 0

3 years ago

If an hourglass takes an average of 1 hour to empty a full cycle, what probability of time does it take longer than 72 minutes i

Arturiano [62]

Answer:

0.82%

Step-by-step explanation: