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4 years ago

(3x^2+26x+16)/(3x^2-7x-6)×(x^2+2x-15)/2x^2+9x-5) can someone help me solve this step by step please.

Mathematics

1 answer:

const2013 [10]4 years ago

3 0

So firstly, we are going to complete the square for each polynomial. To do this, we need to split the middle term of each polynomial into two terms that add up to the middle term and multiply to the product of the first and third term.

Starting with 3x^2+26x+16, the two terms that fit are 24x and 2x since they add up to 26x and multiply to 48x^2. Now replace 26x with 24x + 2x: $3x^2+24x+2x+16$

Next, you are going to factor 3x^2 + 24x and 2x + 16 separately. Make sure they have the same quantity in the parentheses: $3x(x+8)+2(x+8)$

Next, thanks to distributive property, we can rewrite this as (3x + 2)(x + 8).

The process is going to be the same with the other 3 polynomials, so I'll brush through them real quickly:

$3x^2-7x-6\\ 3x^2-9x+2x-6\\ 3x(x-3)+2(x-3)\\ (3x+2)(x-3)$

$x^2+2x-15\\ x^2-3x+5x-15\\ x(x-3)+5(x-3)\\ (x+5)(x-3)$

$2x^2+9x-5\\ 2x^2+10x-x-5\\ 2x(x+5)-1(x+5)\\ (2x-1)(x+5)$

So right now, just for reminder our fraction looks like this: $\frac{(3x+2)(x+8)(x+5)(x-3)}{(3x+2)(x-3)(2x-1)(x+5)}$

Next, cancel out (x+5), (x-3), and (3x+2) and your answer will be: $\frac{x+8}{2x-1}$

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2 years ago

Is it 7^12 not so sure ._.

Alekssandra [29.7K]

You are correct, it is.

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3 years ago

Which of the following shows 2.736 correctly rounded to the tenths place?

Marysya12 [62]

Answer:

2.7 is the correct answer

Step-by-step explanation:

4 0

3 years ago

Suppose that a researcher is designing a survey to estimate the proportion of adults in your state who oppose a proposed law tha

irinina [24]

Answer:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

The margin of error desired for this case is $ME= \pm 0.02$ equivalent to 2% points

For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is $\hat p =0.5$

In order to find the critical value we need to take in count that we are finding the margin of error for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.96$

Now we have all the values needed and if we replace into equation (b) we got:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

5 0

4 years ago

Imagine you had 40 one-metre sections of fencing.

Darya [45]

Answer: If I’m not mistaken, the largest area is 75 m2 and the smallest is 2 m2

Step-by-step explanation:

For both : since they are asking for the area, you should calculate the perimeter.

So for the largest area, since you know that you have 40 fences, and each are 1 meter long, and they’re also asking for the largest rectangular area, this means that only the opposite sides will have the same length, so in order to divide the rectangle with the 40 one-meter fences, the biggest sides have to be 15 meters long (so for both : 15x2=30 meters). Then you deduct from 40, 30 : 40-30 = 10 which then you can devide by 2 and find 5 + 5 and that means that the 2 smallest sides will be 5 meters long each. Then finally to calculate the perimeter you should do the biggest side multiplied by the smallest side : 15 x 5 and you find 75 m2 (squaremeters), if I’m not mistaken.

And for the smallest area you take the smallest possibilities knowing that only the opposite sides should have the same length and not all of them, so you do 1 x 2 and you find 2 m2.

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4 years ago