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3 years ago

What polynomial equation of the least degree has -2,-2,3, and 3 as four of its roots?

Mathematics

1 answer:

Grace [21]3 years ago

5 0

Answer:

f(x) = $x^{4}$ - 2x³ - 11x² + 12x + 36

Step-by-step explanation:

given that x = a and x = b are the roots of a polynomial then

(x - a) and (x - b) are it's factors and the polynomial is the product of the factors

here x = -2 ( repeated ) and x = 3 (repeated), hence the factors are

(x + 2)² and (x - 3)² → the square denotes a repeated root

f(x) = (x + 2)²(x - 3)² ← expand factors and simplify

= (x² + 4x + 4)(x² - 6x +9)

= $x^{4}$ - 2x³ - 11x² + 12x + 36 ← is a possible equation

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A credit card company charges 18.6% percent per year interest. Compute the effective annual rate if they compound, (a) annualy,

Darina [25.2K]

Answer:

a) Effective annual rate: 18.6%

b) Effective annual rate: 20.27%

c) Effective annual rate: 20.43%

d) Effective annual rate: 20.44%

Step-by-step explanation:

The effective annual interest rate, if it is not compounded continuously, is given by the formula

$I=C(1+\frac{r}{n})^{nt}-C$

where

<em>C = Amount of the credit granted </em>

<em>r = nominal interest per year </em>

<em>n = compounding frequency </em>

<em>t = the length of time the interest is applied. In this case, 1 year. </em>

In the special case the interest rate is compounded continuously, the interest is given by

$I=Ce^{rt}-C$

(a) Annually

$I=C(1+\frac{0.186}{1})-C=C(1.186)-C=C(1.186-1)=C(0.186)$

The effective annual rate is 18.6%

(b) Monthly

<em>There are 12 months in a year </em>

$I=C(1+\frac{0.186}{12})^{12}-C=C(1.2027)-C=C(0.2027)$

The effective annual rate is 20.27%

(c) Daily

<em>There are 365 days in a year </em>

$I=C(1+\frac{0.186}{365})^{365}-C=C(1.2043)-C=C(0.2043)$

The effective annual rate is 20.43%

(d) Continuously

$I=Ce^{0.186}-C=C(1.2044)-C=C(0.2044)$

The effective annual rate is 20.44%

3 0

3 years ago

The figures are similar. Find the missing length.

saw5 [17]

Step-by-step explanation:

<h2>Answer:-</h2><h3>Given ,</h3>

The figure is Similar.

Observation:-

Similar figures have similar sides. If we see carefully in smaller triangle, 3 has been added to each side and they are similar. We need to find y.

We have :-

5+3=8 as similar sides.

So, applying same algorithm,

$y + 3 = 5$

$y = 5 - 3$

$\boxed{ \tt{y = 2 \ cm}}$

is the answer.

Hope it helps :)

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3 years ago

Shawna won 40 super bouncy balls playing

patriot [66]

Answer:

13 not including Shawna

Step-by-step explanation:

First, you have to take into account that the remainder is 1, so you must subtract 1 from 40, giving you 39. 39/3 is 13, so 13 is your final answer.

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2 years ago

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Help pls! will give brainliest!<br> what is a 11 percent markup of $18

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Answer:

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Step-by-step explanation:

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3 years ago

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A sports survey taken at THS shows that 48% of the respondents liked soccer, 66% liked basketball and 38% liked hockey. Also,30%

In-s [12.5K]

Answer:

a) The Venn diagram is presented in the attached image to this answer.

b) 0.82

c) 0.16

Step-by-step explanation:

a) The Venn diagram is presented in the attached image to this answer.

n(U) = 100%

n(S) = 48%

n(B) = 66%

n(H) = 38%

n(S n B) = 30%

n(B n H) = 22%

n(S n H) = 28%

n(S n B n H) = 12%

The specific breakdowns for each subgroup is calculated on the Venn diagram attached.

b) The probability that a randomly selected student likes basketball or hockey.

P(B U H)

From the Venn diagram,

n(B U H) = n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) = 26 + 10 + 18 + 12 + 16 + 0 = 82%

P(B U H) = 82/100 = 0.82

c) The probability that a randomly selected student does not like any of these sports.

P(S' n B' n H')

n(S' n B' n H') = n(U) - [n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) + n(S n B' n H')]

n(S' n B' n H') = 100 - (26 + 10 + 18 + 12 + 16 + 0 + 2) = 100 - 84 = 16%

P(S' n B' n H') = 16/100 = 0.16

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3 years ago