All categories

3 years ago

If f(x)=x-6 and g(x)=x^1/2(x+3) what is f(x) times g(x

2 answers:

8 0

$\bf \begin{cases}
f(x)=x-6\\
g(x)=x^{\frac{1}{2}}(x+3)
\end{cases}
\\\\\\
f(x)\cdot g(x)\implies (x-6)\cdot \left[ x^{\frac{1}{2}}(x+3) \right]\implies (x-6)\cdot \left[ \stackrel{distributing}{x^{\frac{3}{2}}+3x^{\frac{1}{2}}} \right]$

$\bf x\left( x^{\frac{3}{2}}+3x^{\frac{1}{2}} \right)-6\left( x^{\frac{3}{2}}+3x^{\frac{1}{2}} \right)
\\\\\\
x^{\frac{5}{2}}+3x^{\frac{3}{2}}~~-~~6x^{\frac{3}{2}}-18x^{\frac{1}{2}}\implies \stackrel{\textit{adding like-terms}}{x^{\frac{5}{2}}-3x^{\frac{3}{2}}-18x^{\frac{1}{2}}}
\\\\\\
\stackrel{\textit{common factoring}}{x^{\frac{1}{2}}\left( x^{\frac{4}{2}}-3x^{\frac{2}{2}}-18 \right)}\implies x^{\frac{1}{2}}(x^2-3x-18)\implies x^{\frac{1}{2}}(x-6)(x+3)$

dimaraw [331]3 years ago

7 0

This is (x - 6)*x^1/2(x + 3)

= x^1/2 (x^2 - 3x - 18)

= x^(5/2) - 3x^(3/2) - 18x^(1/2)

You might be interested in

What’s the simplified principal square root of -36

Musya8 [376]

Answer:

Step-by-step explanation:

because 36 is a perfect square root.

3 0

2 years ago

Which inequality matches the graph?

Papessa [141]

Given:

The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).

Above line is shaded.

To find:

The inequality for the given graph.

Solution:

Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)$

$y+2=\dfrac{10+2}{8}(x-1)$

$y+2=\dfrac{12}{8}(x-1)$

$y+2=\dfrac{3}{2}(x-1)$

Multiply both sides by 2.

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

$2y+4=3x-3$

$2y-3x=-3-4$

$-3x+2y=-7$

Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.

$-3x+2y>-7$

This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.

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

$3x-2y$

Therefore, the correct option is D.

8 0

2 years ago

What is the probability of rolling a pair of dice and not rolling the same number?

Aleksandr [31]

Answer:

5/6

Step-by-step explanation:

The "first" dice can land on any number, so there are 6 choices. The "second" can not be the same number as the first one. So there are 5 choices. We multiply to get 6*5=30 ways to roll a different number. There are 6*6 total ways so the probability is 30/36 which simplifies to 5/6.

4 0

2 years ago

The heights (measured in inches) of men aged 20 to 29 follow approximately the normal distribution with mean 69.3 and standard d

Zolol [24]

Answer:

The middle 92% of all heights fall between 64.4 inches and 74.2 inches.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

$\mu = 69.3, \sigma = 2.8$

Between what two values does that middle 92% of all heights fall?

The middle 92% falls from X when Z has a pvalue of 0.5 - 0.92/2 = 0.04 to X when Z has a pvalue of 0.5 + 0.92/2 = 0.96. So from the 4th percentile to the 96th percentile.

4th percentile

X when $Z = -1.75$