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agasfer [191]
3 years ago
7

Solve the quadratic equation (2x-3)^2 = 6(3-2x)

Mathematics
1 answer:
LenKa [72]3 years ago
5 0

Answer:

x=\frac{3\sqrt{2}-3 }{2}

x=-\frac{3\sqrt{2}-3 }{2}

Step-by-step explanation:

Open the brackets first:

4x^2+9=18-12x

Simplify:

4x^2+12x-9=0

It is determined that this can't be factored, so rewrite the equation so you can complete the square.

x^2+3x=\frac{9}{4}

Take the square of 1.5 and add it to both sides:

x^2 + 3x+ \frac{9}{4} =\frac{9}4} +\frac{9}{4}

Factor:

(x+\frac{3}{2})^2=\frac{9}{2}

x+\frac{3}{2} = \frac{3\sqrt{2} }{2 }

or x+\frac{3}{2} =-\frac{3\sqrt{2} }{2}

So x=\frac{3\sqrt{2}-3 }{2}

or x=-\frac{3\sqrt{2}-3 }{2}

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alex41 [277]

If the negative square root is found to be one of your solutions, then that is indicative of a pair of imaginary roots (the imaginary i). According to the conjugate rule, if you have one solution that is imaginary, you will have another but with the opposite sign. For example, if a solution to a quadratic is found to be 2 - i, then its conjugate, 2 + i is also a solution. They will ALWAYS go in pairs. Same thing with radical solutions. If one solution is found to be 3+\sqrt{5}

then 3-\sqrt{5} will also be a solution.

3 0
3 years ago
Help me with these problems please
Scorpion4ik [409]
1. y = 7
2. 0
3. m = -1
4. k = -4
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7 0
3 years ago
Suppose that birth weights are normally distributed with a mean of 3466 grams and a standard deviation of 546 grams. Babies weig
Anon25 [30]

Answer:

3.84% probability that it has a low birth weight

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 3466, \sigma = 546

If we randomly select a baby, what is the probability that it has a low birth weight?

This is the pvalue of Z when X = 2500. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{2500 - 3466}{546}

Z = -1.77

Z = -1.77 has a pvalue of 0.0384

3.84% probability that it has a low birth weight

3 0
3 years ago
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Tema [17]

Answer:

option A

12m/s

Step-by-step explanation:

Given in the question,

mass of object = 11kg

kinetic energy possess by = 792 joules

To find the velocity we use formula

v =  \sqrt{\frac{2KE}{m} }

Plug values in the formula

v = \sqrt{\frac{2(792)}{(11)} }

v = \sqrt{\frac{1584}{11} }

v = \sqrt{144}

v= 12 m/s

3 0
3 years ago
Help meeee!will give brainliest!
meriva
It is (0,-1) hope that helps
8 0
2 years ago
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