How do you solve a diagram

Find all real solutions to the equation (x² − 6x +3)(2x² − 4x − 7) = 0.

Jet001 [13]

Answer:

x = 3 + √6 ; x = 3 - √6 ; $x = \frac{2+3\sqrt{2}}{2}$ ; $x = \frac{2-(3)\sqrt{2}}{2}$

Step-by-step explanation:

Relation given in the question:

(x² − 6x +3)(2x² − 4x − 7) = 0

Now,

for the above relation to be true the following condition must be followed:

Either (x² − 6x +3) = 0 ............(1)

or

(2x² − 4x − 7) = 0 ..........(2)

now considering the equation (1)

(x² − 6x +3) = 0

the roots can be found out as:

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

for the equation ax² + bx + c = 0

thus,

the roots are

$x = \frac{-(-6)\pm\sqrt{(-6)^2-4\times1\times(3)}}{2\times(1)}$

or

$x = \frac{6\pm\sqrt{36-12}}{2}$

or

$x = \frac{6+\sqrt{24}}{2}$ and, x = $x = \frac{6-\sqrt{24}}{2}$

or

$x = \frac{6+2\sqrt{6}}{2}$ and, x = $x = \frac{6-2\sqrt{6}}{2}$

or

x = 3 + √6 and x = 3 - √6

similarly for (2x² − 4x − 7) = 0.

we have

the roots are

$x = \frac{-(-4)\pm\sqrt{(-4)^2-4\times2\times(-7)}}{2\times(2)}$

or

$x = \frac{4\pm\sqrt{16+56}}{4}$

or

$x = \frac{4+\sqrt{72}}{4}$ and, x = $x = \frac{4-\sqrt{72}}{4}$

or

$x = \frac{4+\sqrt{2^2\times3^2\times2}}{2}$ and, x = $x = \frac{4-\sqrt{2^2\times3^2\times2}}{4}$

or

$x = \frac{4+(2\times3)\sqrt{2}}{2}$ and, x = $x = \frac{4-(2\times3)\sqrt{2}}{4}$

or

$x = \frac{2+3\sqrt{2}}{2}$ and, $x = \frac{2-(3)\sqrt{2}}{2}$

Hence, the possible roots are

x = 3 + √6 ; x = 3 - √6 ; $x = \frac{2+3\sqrt{2}}{2}$ ; $x = \frac{2-(3)\sqrt{2}}{2}$

7 0

2 years ago

Consider the given geometric sequence.

Gala2k [10]

F5=(256)f1=16 hope this helps

7 0

3 years ago

Read 2 more answers

Simplify. (x^3 +8 ) / (x+2) <br>show work

Zielflug [23.3K]

Answer:

3x2|9x+18|+8|9x+18|3x2|9x+18|+8|9x+18|

5 0

2 years ago

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.5 parts

Hunter-Best [27]

Answer:

The value of the test statistic is $t = 2.1$

Step-by-step explanation:

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the expected value, $\sigma$ is the standard deviation and n is the size of the sample.

The level of ozone normally found is 7.5 parts/million (ppm).

This means that $\mu = 7.5$

The mean of 24 samples is 7.8 ppm with a standard deviation of 0.7.

This means that $X = 7.8, \sigma = 0.7, n = 24$

Test Statistic:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{7.8 - 7.5}{\frac{0.7}{\sqrt{24}}}$

$t = 2.1$

The value of the test statistic is $t = 2.1$

7 0

3 years ago

A dataset shows that, on average, smokers do not live as long as nonsmokers and heavy smokers do not live as long as light smoke

leva [86]

<span>Given that A dataset shows that, on average, smokers do not live as long as nonsmokers and heavy smokers do not live as long as light smokers.

If you compute the least squares line for y = age at time of death and x = number of packets per day typically smoked, you will notice that as the number of packets per day a person smokes increases, the age at time of death of the person decreases.

Thus, the graph wil have a negative slope.

Therefore, the slope of your regression line will be less than 0.</span>

8 0

3 years ago