6z^2-3z=-220 complete the square

All zeros of polynomial function 3x^4 +14x^2 -5

Marizza181 [45]

Answer:

Correct answer: x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3

Step-by-step explanation:

Given:

3 x⁴ + 14 x² - 5 = 0 biquadratic equation

this equation is solved by a shift x² = t and get:

3 t² + 14 t - 5 = 0

t₁₂ = (-14 ± √14² - 4 · 3 · 5) / 2 · 3 = (-14 ± √196 + 60) / 6

t₁₂ = (-14 ± √256) / 6 = (-14 ± 16) / 6

t₁ = -5 or t₂ = 1 / 3

the solution t₁ = -5 is not accepted because it cannot be x² = -5

we accepted t₂ = 1 / 3

x² = 1 / 3 ⇒

x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3

God is with you!!!

5 0

3 years ago

Find the function value.

MArishka [77]

Hey!! here is your answer --

1) tan30° = √3/3

2) cot30° = √3

3) sec30° = (2√3)/3

★ hope you like it ★

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6 0

3 years ago

Read 2 more answers

Hong needs to memorize words on a vocabulary list for Russian class. He has 14 words to memorize, and he is one-half done. How m

GREYUIT [131]

Step-by-step explanation:

He has done one half = ½

Finding ½ of 14

½ × 14

7

Hence, Hong has memorized 7 words

5 0

2 years ago

A realtor would like to create a 95% confidence interval for the average price of a house in Franklin County, Ohio. To accomplis

VMariaS [17]

Answer:

$320128-1.96\frac{50324}{\sqrt{529}}=315839.52$

$320128+1.96\frac{50324}{\sqrt{529}}=324416.48$

So on this case the 95% confidence interval would be given by (315839.52;324416.48)

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".

$\bar X=320128$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=50324$ represent the population standard deviation

n=529 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 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$