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3 years ago

Factor the quadratic expression 3xsquared+4x-4

Mathematics

1 answer:

Schach [20]3 years ago

5 0

Answer:

(3x − 2) (x + 2)

Step-by-step explanation:

For a quadratic ax² + bx + c, you can factor using the AC method.

1. First, multiply a and c.

2. Next, find factors of ac that add up to b.

3. Divide the factors by a. Reduce if possible.

4. The numerator of the fraction becomes the constant. The denominator of the fraction becomes the coefficient.

3x² + 4x − 4

In this case, a = 3, b = 4, and c = -4.

1. 3 × -4 = -12

2. Factors of -12 that add up to 4 are -2 and +6

3. Divide by 3 and reduce: -2/3, 6/3 = 2/1

4. The factors are 3x − 2 and x + 2

3x² + 4x − 4 = (3x − 2) (x + 2)

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What is the product of (X4/3)(X2/3) ?

katrin [286]

Hi, the answer to this would be x6/9. I'm assuming the x4/3 and x2/3 are fractions and the x's aren't exponents. Now how I got x6/9 is shown here.

1st Step: Started off by regrouping the terms
1/3x3 x^4x^2

2nd Step: we can easily simplify 3x3 to just 9. And now we're left with 1/9x^4x^2

3rd Step: Now we can simplify the 1/9 to just x^4x^2/9

4th Step: Now we can use the product rule which is simple. So We add the exponents and simplify it to just one exponent. So x4+2=6 that simplifies to just x^6.

Final Answer: x^6/9.
Hope this helped you :)

7 0

3 years ago

Slope of -1,0 and 10,18

steposvetlana [31]

You should find the slope using (y2 - y1) / (x2 - x1) = m

m = (18 - 0) / (10 - (-1))

m= 18 / 11

Therefore the slope is 18/11

6 0

3 years ago

Read 2 more answers

Jamie is x years old. His friend Ana is the same age.

SSSSS [86.1K]

<h3>Answer: 2x</h3>

Explanation:

Each person is x years old. Adding those unknown ages gets us x+x = 2x

We can think of it like x being one box, so x+x represents having two boxes which shortens to 2x.

6 0

2 years ago

Solving Exponential and Logarithmic Equations In Exercise, solve for x. 100(1.21)x = 110

SVETLANKA909090 [29]

Answer:X=110/121

Step-by-step explanation:

Multiply 100 by 1.21 then by x

121x=110

Divide both side by 121

X=110/121

X=0.91

8 0

3 years ago

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of

iris [78.8K]

Answer:

The probability that the mean battery life would be greater than 533.2 minutes (in a sample of 75 batteries) is $\\ P(z>0.48) = P(x>533.2) = 0.3156$

Step-by-step explanation:

The main thing we have to take into account in this question is that we are about to find the probability of a sample mean. The distribution for sample means follows a normal distribution with mean $\\ \mu$ and standard deviation $\\ \frac{\sigma}{\sqrt{n}}$ . Mathematically

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

For values of the sample $\\ n \ge 30$ , no matter the distribution the data come from.

And the variable z follows a standard normal distribution, and, as we can remember, this distribution has a mean = 0 and a standard deviation = 1. Mathematically

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

That is

$\\ z \sim N(0, 1)$

We have a variance of 3364. That is, a standard deviation of

$\\ \sigma^2 = 3364; \sigma = \sqrt{3364} = 58$

The population mean is

$\\ \mu = 530$

The sample size is $\\ n = 75$

The sample mean is $\\ \overline{x} = 533.2$

With all this information, we can solve the question

The probability that the mean battery life would be greater than 533.2 minutes

Using equation [1]

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{533.2 - 530}{\frac{58}{\sqrt{75}}}$

$\\ z = \frac{3.2}{\frac{58}{8.66025}}$

$\\ z = \frac{3.2}{6.69726}$

$\\ z = 0.47780$

With this value of z we can consult a cumulative standard normal table (or use some statistic program) to find the cumulative probability for z (and remember that this variable follows a standard normal distribution).

Most standard normal tables have values for z for only two decimals, so we can round the previous value for z as z = 0.48.

Then

$\\ P(z$

However, in the question we are asked for $\\ P(z>0.48) = P(x>533.2)$ . As well as all normal distributions, the standard normal distribution is symmetrical around the mean, and we have

$\\ P(z>0.48) = 1 - P(z$

Thus

$\\ P(z>0.48) = 1 - 0.68439$

$\\ P(z>0.48) = 0.31561$

Rounding to four decimal places, we have

$\\ P(z>0.48) = 0.3156$

So, the probability that the mean battery life would be greater than 533.2 minutes is (in a sample of 75 batteries) $\\ P(z>0.48) = P(x>533.2) = 0.3156$ .

5 0

3 years ago