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3 years ago

Which of the following is a solution of x2 + 4x = -8?

Mathematics

1 answer:

Whitepunk [10]3 years ago

8 0

Answer:

$x=2i-2,\:x=-2i-2$

Step-by-step explanation:

$x^2 + 4x = -8\\\\\mathrm{Solve\:by\:completing\:the\:square}\\\\\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2\\\\\mathrm{Solve\:for\:}a,\:2ax=4x:\quad a=2\\\\\mathrm{Add\:}a^2=2^2\mathrm{\:to\:both\:sides}\\\\x^2+4x+2^2=-8+2^2\\\\\mathrm{Simplify\:}-8+2^2:\quad -4\\x^2+4x+2^2=-4\\\\\mathrm{Complete\:the\:square}\\\left(x+2\right)^2=-4\\\\\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}\\$

$\mathrm{Solve\:}\:x+2=\sqrt{-4}:\quad x=2i-2\\\\\mathrm{Solve\:}\:x+2=-\sqrt{-4}:\quad x=-2i-2\\\\x=2i-2,\:x=-2i-2\\$

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Which one is the larger average rate, -3.142 or -0.5?

SOVA2 [1]

Answer:

-0.5 is the larger average rate

Step-by-step explanation:

-3.142 is less than -0.5

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2 years ago

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const2013 [10]

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2 years ago

Find the difference between points M(6,16) and Z(-1,14) to the nearest tenth.

svlad2 [7]

I'm not sure what you mean by difference, so I am guessing you meant to write "distance". If this is not the case, then feel free to report me. Anyway, to find the distance between two points you would use the distance formula.

Distance Formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ .

Let's substitute our point coordinates into the formula. We'll substitute -1 and 6 for x_2 and x_1, and 14 and 16 for y_2 and y_1. After substituting, your formula will now look like: $d=\sqrt{(-1-6)^2+(14-16)^2}$ .

$d=\sqrt{(-1-6)^2+(14-16)^2}$

Subtract the coordinates.

$d=\sqrt{(-7)^2+(-2)^2}$

Square the subtracted coordinates.

$d=\sqrt{49+4}$

Add 49 and 4.

$d=\sqrt{53}$

Square root 53 and round the answer to the nearest tenth.

7.28 becomes 7.3.

7.3 units is the distance between points M and Z.

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3 years ago

P(×)= x(2x + 1)- 6x-3 <br>Factorize p(×)

kherson [118]

Step-by-step explanation:

P(X)=2x²-5x-3 is in the form ax²+bx+c

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2 years ago

Since the area under the normal curve within two standard deviations of the mean is 0.95, the area under the normal curve that c

alukav5142 [94]

Answer:

$X \sim N (\mu ,\sigma)$

And for this case we know this condition:

$P(\mu-2\sigma$

By the complement rule we know that:

$P(X< \mu -2\sigma \cup X>\mu +2\sigma) = 1-0.95=0.05$

But since the distribution is symmetrical we know that:

$P(X\mu +2\sigma) = 0.025$

So then the statement for this case is FALSE.

b. False

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

For this case if we define the random variable of interest X and we know that this random variable follows a normal distribution:

$X \sim N (\mu ,\sigma)$

And for this case we know this condition:

$P(\mu-2\sigma$

By the complement rule we know that:

$P(X< \mu -2\sigma \cup X>\mu +2\sigma) = 1-0.95=0.05$

But since the distribution is symmetrical we know that:

$P(X\mu +2\sigma) = 0.025$

So then the statement for this case is FALSE.

b. False

5 0

3 years ago