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max2010maxim [7]

3 years ago

13

2. Solve the quadratic by taking square roots. Write your answer with no spaces as x=a,-a where a and -a are the values you foun

d when solving. Round to the nearest tenth. 2x secondpower - 9 = 121

1 answer:

natulia [17]3 years ago

6 0

Answer:

x=√65 and x=-√65

Step-by-step explanation:

Givn the expression 2x^2 - 9 = 121

Add 9 to both sides

2x^2 - 9 + 9 = 121 + 9

2x^2 = 130

Divide both sides b 2

2x^2/2 = 130/2

x^2 = 65

x = ±√65

x=√65 and x=-√65

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According to Internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while

KonstantinChe [14]

Answer:

0.0656

Step-by-step explanation:

For each message, we have these following probabilities:

90% probability it is spam.

10% probability it is legitimate.

Compute the probability that the first legitimate e-mail she finds is the fifth message she checks:

The first four all spam, each with a 90% probability.

The fifth legitimate, with a 10% probability.

$P = (0.9)^{4} \times 0.1 = 0.0656$

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3 years ago

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

3 years ago

A backpack normally costs $25 but it is on scale for $16.25. What percentage is on discount? Please help, I have a test rn:((

joja [24]

Answer: 16%

Step-by-step explanation:

$25 - $21 = $4

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2 years ago

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Dafna1 [17]

Answer:

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Step-by-step explanation:

bodmas

yeah

ahaha

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3 years ago

How do I solve ?? It’s cylinders

UkoKoshka [18]

V= 3.14r^2h
10/2= r
5^2= 25
(3.14)(25)(6)
V=471

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3 years ago