Solve 3(4y + 6) greater equal to -2(3-6y) show work pls

Semenov [28]

$\large \boxed{(f + g)(x) = f(x) + g(x)}$

The property above is distribution property where we distribute x-term in the function.

Substitute both f(x) and g(x) in.

$\large{ \begin{cases} f(x) = 2 {x}^{2} - x - 6 \\ g(x) = 4 - x \end{cases}} \\ \large{f(x) + g(x) = (2 {x}^{2} - x - 6) + (4 - x)} \\ \large{f(x) + g(x) = 2 {x}^{2} - x - 6 + 4 - x}$

Évaluate/Combine like terms.

$\large{f(x) + g(x) = 2 {x}^{2} - 2x - 2}$

The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)

$\large{(f + g)(x) = 2 {x}^{2} -2x -2}$

Alternative

$\large{(f + g)(x) = 2({x}^{2} -x - 1)}$

Answer

(f+g)(x) = 2x²-2x-2
(f+g)(x) = 2(x²-x-1)

Both answers work. The second answer is in factored form.

Let me know if you have any doubts!

8 0

3 years ago

When rounding 72.631 to the hundredths place, Jack rounded to 72.64 and Tamar rounded to 72.63. Who is correct? EXPLAIN YOUR ANS

Mrrafil [7]

Answer:

Tamar

Step-by-step explanation:

Since we're rounding to the hundredths place, we need to see if the thousandths place is greater or equal to 5. Since it is less than 5, we round down to 72.63.

3 0

4 years ago

Read 2 more answers

a) A large hotel in Miami has 900 rooms (all rooms are equivalent). During Christmas, the hotel is usually fully booked. However

Olegator [25]

Answer:

14.69% probability that this happens

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$