Do you distribute or use exponents first

5.) Simplify the following polynomial. -6x3+5x-3-(2x3+4x2-3x+1)

Vera_Pavlovna [14]

Answer:

-8x3 - 4x2 + 8x - 4

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations alon

melamori03 [73]

Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.

X~ Uniform(0,100)

Then the probability mass function is given as follows.

$f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}$

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows

$D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.$

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable $Y = D(X)$ , $Y$ is a random variable as well, remember that there is a theorem that says that

$E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx$

Where $f(x)$ is the probability mass function of X. Using the information of our problem

$E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75$

3 0

3 years ago

Plot the line that represents the midline of the given periodic function

kirza4 [7]

Answer:6

Step-by-step explanation:

8 0

3 years ago

Consider the diagram and the paragraph proof below.

bonufazy [111]

<span>Given: Right △ABC as shown where CD is an altitude of the triangle. We prove that $a^2 + b^2 = c^2$

Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA.

Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA.

The proportions $\frac{c}{a}$ and $\frac{a}{f}$ are true because they are ratios of corresponding parts of similar triangles.

The two proportions can be rewritten as $a^2 = cf$ and $b^2 = ce$ .

Adding $b^2$ to both sides of first equation, $a^2 = cf$ , results in the equation $a^2 + b^2 = cf + b^2$ .

Because $b^2$ and ce are equal, ce can be substituted into the right side of the equation for $b^2$ , resulting in the equation $a^2 + b^2 = cf + ce$ .

Applying the converse of the distributive property results in the equation $a^2 + b^2 = c(f + e)$ .

The last sentence of the proof is

Because f + e = c, $a^2 + b^2 = c^2$ .</span>

7 0

3 years ago

Find the constant of variation in the direct relation below.

Murljashka [212]

Answer:

A) 5/2

Step-by-step explanation:

It's right. You can trust me.

<3

7 0

2 years ago