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2 years ago

Solve by completing the square x^2-6x-4=0

Mathematics

1 answer:

Vesna [10]2 years ago

6 0

Answer:

x = 3 ± $\sqrt{13}$

Step-by-step explanation:

x² - 6x - 4 = 0 ( add 4 to both sides )

x² - 6x = 4

To complete the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 3)x + 9 = 4 + 9

(x - 3)² = 13 ( take square root of both sides )

x - 3 = ± $\sqrt{13}$ ( add 3 to both sides )

x = 3 ± $\sqrt{13}$

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adiocarbon dating of blackened grains from the site of ancient Jericho provides a date of 1315 BC ± 13 years for the fall of the

Zigmanuir [339]

Answer:

$\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659$ and $\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661$

Step-by-step explanation:

The equation of the isotope decay is:

$\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }$

14-Carbon has a half-life of 5568 years, the time constant of the isotope is:

$\tau = \frac{5568\,years}{\ln 2}$

$\tau \approx 8032.926\,years$

The decay time is:

$t = 1315\,years + 2007\,years \pm 13\,years$ (There is no a year 0 in chronology).

$t = 3335 \pm 13\,years$

Lastly, the relative amount is estimated by direct substitution:

$\frac{m(t)}{m_{o}} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\mp\frac{13\,years}{8032.926\,years} }$

$\left(\frac{m(t)}{m_{o}} \right)_{min} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{-\frac{13\,years}{8032.926\,years} }$

$\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659$

$\left(\frac{m(t)}{m_{o}} \right)_{max} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\frac{13\,years}{8032.926\,years} }$

$\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661$

4 0

3 years ago

Error Analysis: Mr. Hasson is buying a new bike for the summer time. The bike originally costs $150 but he sees it's on sale for

evablogger [386]

Answer:

$45

Step-by-step explanation:

30% ÷100 =0.3. 0.3×150= 45

4 0

3 years ago

Combine Like Terms 8 + 19t - 6t A) 8 - 13t B) 21 C) 21t D) 8 + 13t

Hunter-Best [27]

Answer:

8 + 13t

Step-by-step explanation:

Since 19t and 6t have the same variables

4 0

3 years ago

(10-P) Help please, thanks.

Anuta_ua [19.1K]

The formula of linear equation is:
$y1 - y2 = m(x1 - x2)$
Where
x1 and x2: x coordinates(-1 and 3)
y1 and y2: y coordinates(-2 and 10)
m is the slope

We can then choose a point from the line to find the eqaution.

We need to first find the slope:
$\frac{y1 - y2}{x1 - x2}$
In this case:
$\frac{ - 2 - 10}{ - 1 - 3} \\ = \frac{ - 12}{ - 4} \\ = 3$

In this case, as the y2 is given as 1,put (-1,-2) , and the slope(3 )into the eqaution :

y-(-2) = 3(x-(-1))
y+2 = 3(x+1)

Therefore
$y + 2 = 3x + 1$
is the answer.

Hope it helps!

7 0

3 years ago

What are the scores of the students which are less than equal to 25% of the data?

nikitadnepr [17]

Answer:

24/100

Step-by-step explanation:

7 0

3 years ago