Solving system equations by substitution I need help with this asap

vichka [17]

Let's group the cubic function: $h(x)=x^4+2x^3-10x^2-18x+9=(x-3)(x+3)(x^2+2x-1)$ .

The first two roots are $\pm3$ however to find the last two roots we need to solve the square equation:

$x^2+2x-1=0
\\D=b^2-4ac=2^2-4\cdot1\cdot(-1)=8$ . Now we know the discriminator, using the discriminator we're able to find the roots of the equation: $x_{1,2}=\frac{-b\pm\sqrt{D}}{2a}=\frac{-2\pm\sqrt{8}}{2}=\frac{-2\pm2\sqrt{2}}{2}=\frac{2(\sqrt{2}\pm1)}{2}$ . The roots of the square equation are $x_{1}=-1-\sqrt{2}$ and $x_{2}=\sqrt{2}-1$ .

The roots of the cubic function are $\pm3$ , $-1-\sqrt{2}$ and $\sqrt{2}-1$ .

5 0

3 years ago

Read 2 more answers

Only number 17 I need help with plz help this is sooo hard

vaieri [72.5K]

$96 = (((x + 6) + (x)) \div 2)8$
x=9
Base 1=15
Base 2=9

5 0

4 years ago

Add.

kakasveta [241]

To add expressions, you should take note that you can only combine same terms which means they have the same degree of exponents.

-5x^4 + 6x^3 – 43 + 6x^5 – x^2 + 12x + 12

In this expression, you can only combine the constants because they are the only similar terms:

-5x^4 + 6x^3 + 6x^5 – x^2 + 12x + 12 – 43

-5x^4 + 6x^3 + 6x^5 – x^2 + 12x – 31

The standard form starts with the term with the highest exponent so you just have to arrange the terms:

6x^5 - 5x^4 + 6x^3 – x^2 + 12x + 12

5 0

3 years ago

Read 2 more answers

What is the missing angle measure of 112 68 50

serious [3.7K]

It's 130, any quadrilateral's angles add up to 360 and those numbers add up to 230, 360-230 = 130

5 0

3 years ago

Read 2 more answers

As part of their business promotional package, the Milwaukee Chamber of Commerce would like an estimate of the mean cost per mon

Morgarella [4.7K]

Answer:

a) $884-2.426\frac{50}{\sqrt{40}}=864.82$

$884+2.426\frac{50}{\sqrt{40}}=903.179$

So on this case the 98% confidence interval would be given by (864.82;903.179)

b) For this case the upper bound of the confidence interval is lower than 950 so we don't have a significant evidence to conclude that the true mean is 950 per month

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".

$\bar X=884$ represent the sample mean

$\mu$ population mean (variable of interest)

s=50 represent the sample standard deviation

n=40 represent the sample size

Solution to the problem

Part a

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=40-1=39$

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: "=-T.INV(0.01,39)".And we see that $t_{\alpha/2}=2.426$

Now we have everything in order to replace into formula (1):

$884-2.426\frac{50}{\sqrt{40}}=864.82$

$884+2.426\frac{50}{\sqrt{40}}=903.179$

So on this case the 98% confidence interval would be given by (864.82;903.179)

Part b

For this case the upper bound of the confidence interval is lower than 950 so we don't have a significant evidence to conclude that the true mean is 950 per month

3 0

3 years ago

Solving system equations by substitution I need help with this asap​

Solving system equations by substitution I need help with this asap