Solve. -5x^2+9+7x = 0−5x 2 +9+7x=0

Mathematics

1 answer:

Lynna [10]3 years ago

5 0

Answer:

x = $\frac{-7 \frac{+}{} \sqrt{229} }{-10}$ , or x=2.21327 and -0.81327

Step-by-step explanation:

$-5x^2+7x+9 = 0$

see if equation is factor-able:

$\left[\begin{array}{ccc}?&9\\-5x^2&?\\\end{array}\right]$

the two ? must multiply together to $-45x^2$ and add up to 7x

no two integers times x can solve, so we must use quadratic equation

$x = \frac{-b \frac{+}{} \sqrt{b^2-4ac} }{2a}$ , given a quadratic $ax^2 +bx +c$

$x = \frac{-7 \frac{+}{} \sqrt{49+180} }{-10} = \frac{-7 \frac{+}{} \sqrt{229} }{-10}$

You might be interested in

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customer

AlladinOne [14]

Answer:

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

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".

$\bar X=4$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=100 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.326$