All categories

3 years ago

How to solve 3p^2-2p-5 step by step without splitting the middle term

1 answer:

3 0

$3p^2-2p-5= \\\\ a=3 \\ b=-2 \\ c=-5 \\\\ \Delta=(-2)^2-4*3*(-5) =4+60\to\boxed{64} \\\\ x_1;x_2=\frac{-(-2) +/- \sqrt{64}}{2*3} \\\\ x_1;x_2=\frac{2 +/-8}{6} \\\\ x_1=\frac{2+8}{6}=\frac{10}{6}\to\boxed{\frac{5}{3}} \\\\ x_2=\frac{2-8}{6}=\frac{-6}{6}\to\boxed{-1} \\\\ 3p^2-2p-5=(x-\frac{5}{3})(x+1)$

You might be interested in

The train travels 558 miles in 3 hours. At this rate, how far does the train travel?

tresset_1 [31]

Answer:

186 mph

Step-by-step explanation:

Miles per hour means miles divided by hour(s), so 558/3 is 186 miles per hour.

5 0

3 years ago

Read 2 more answers

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 lower than in the first

Artyom0805 [142]

Answer:

Let x = the charge in 1st city before taxes

Let y = the charge in 2nd city before taxes

Set up equation before taxes.

y = x - 1500 eq1

Set up equation for total tax paid.

0.065x + 0.06y = 378.75 eq2

Substitute eq1 into eq2.

0.065x + 0.06(x - 1500) = 378.75

0.065x + 0.06x - 90 = 378.75

0.125x - 90 = 378.75

0.125x = 468.75

x = 3750

Substitute this value of x into eq1.

y = 3750 - 1500

y = 2250

The hotel charge in city one is $3750 and the hotel charge in city two is $2250

3 0

3 years ago

My brother wants to estimate the proportion of Canadians who own their house.What sample size should be obtained if he wants the

AVprozaik [17]

Answer:

a) $n=\frac{0.675(1-0.675)}{(\frac{0.02}{1.64})^2}=1475.07$

And rounded up we have that n=1476

b) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.64})^2}=1681$

And rounded up we have that n=1681

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

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

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)

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by: