Work for determining system for log base radical 2 of e

F(x)=9 x^{3} +2x^2-5x+4 and g(x)=5x^3-7x+4. What is f(x)-g(x)? Show all of your steps and write your finial answer in factored f

olasank [31]

Answer:

{ -0.5 - √2, 0, -.5 + √2 }

Step-by-step explanation:

Let's rewrite these two functions in a vertical column:

f(x)=9 x^{3} +2x^2-5x+4

-g(x)=5x^3-7x+4

Now combine (through subtraction) like terms, in order of descending powers of x:

f(x) - g(x) = 4x^ 3 + 2x^2 + 2x

Let's do some preliminary factoring here. Factor 2x out of each term, obtaining

f(x) - g(x) = 2x(2x^2 + x + 1)

First setting 2x = 0, we find that x = 0 is one solution.

Applying the quadratic formula to 2x^2 + x + 1, we see that a = 2, b = 1 and c = 1. Then the two roots of this quadratic are:

-1 plus or minus √(1^2 - 4(2)(1) ) -1 ± √(8)

x = ----------------------------------------------- = ---------------

2(1) 2

This simplifies to:

-1 plus or minus √(1^2 - 4(2)(1) ) -1 ± 2√(2)

x = ----------------------------------------------- = ---------------

2(1) 2

Thus, the roots of f(x) - g(x) are { -0.5 - √2, 0, -.5 + √2 }

7 0

4 years ago

The temperature was 12 degrees below zero then dropped another 14 degrees find the new temperature

kotykmax [81]

Answer:

26 degrees below zero

Step-by-step explanation:

add the two numbers together and since 12 below zero would be -12 and it drops 14 more it would be -12 - 14 which would lead to -26 because since both are negative its basically adding then putting the negative sign in front.

7 0

3 years ago

Footballs sell for $27.99 each at Dicks Sporting Goods and $21.59 each at Big 5. If the coach buys a dozen footballs, how much c

klasskru [66]

Answer:

The money he can save by buying them at Big 5 is $76.80.

Step-by-step explanation:

Given:

Footballs sell for $27.99 each at Sporting Goods.

Footballs sell for $21.59 each at Big 5.

The coach buys a dozen footballs.

Now, to find the amount he save by buying them at Big 5.

So, first we find the cost of footballs at Sporting Goods and at Big 5.

1 Dozen = 12 pieces.

Thus, the cost of footballs at Sporting Goods =

$\$27.99\times 12 =\$335.88$

And, the cost of footballs at Big 5 =

$\$21.59\times 12=\$259.08.$

Now, to get the amount coach can save by buying them at Big 5, we subtract both the cost as the cost of Sporting Goods is more than the Cost of Big 5:

The amount coach can save by buying them at Big 5 =

$\$335.88-\$259.08=\$76.80.$

Therefore, the amount he can save by buying them at Big 5 is $76.80.

7 0

3 years ago

The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20 hours, standard deviation of 6:

This means that $\mu = 20, \sigma = 6$

Sample of 150:

This means that $n = 150, s = \frac{6}{\sqrt{150}}$

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}$

$Z = 2.04$

$Z = 2.04$ has a p-value of 0.9793

X = 19.5

$Z = \frac{X - \mu}{s}$

$Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}$

$Z = -1.02$

$Z = -1.02$ has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

3 0

3 years ago

What are two equivalent forms for 15xyz+10xy+5x

7nadin3 [17]

We can express this number in the standard form, which is simply 15xyz+10xy+5x. Alternatively, we can factor a 5 or an x out, receiving 5(3xyz+2xy+x) or x(15yz+10y+5). However, the most effective factorization is to factor out 5x, for a result of 5x(3yz+2y+1).

3 0

3 years ago

Work for determining system for log base radical 2 of e​

Work for determining system for log base radical 2 of e