Complete the statement 36x^3a+45xa^2=9xa

Solve the following inequality for w 8w+8>-10w-5

Vlad [161]

Answer:

Step-by-step explanation:

8w+8 > -10w-5

18w + 8 > -5

18w > -13

w > -13/18

8 0

2 years ago

Cheryl drove 4 hours at a constant rate to travel 160 miles. At what rate did she drive? A. 20 mph B. 35 mph C. 40 mph D. 72 mph

erik [133]

Answer:

40 mph

Step-by-step explanation:

you take your miles 160 and divide them by 4 which is going to be 40

5 0

2 years ago

Read 2 more answers

In the drawer you have 8 black socks and 5 yellow socks, if you pick 2 socks what is the probability that pick out a black sock

Nataliya [291]

Answer:

10/39

Step-by-step explanation:

The chances of picking a black sock on first try are 8/13, and the chances of picking out a yellow sock without replacing the black sock are 5/12. If you multiply 8/13 and 5/12, you get 40/156, and if you simplify, you will get 10/39 as your answer.

7 0

2 years ago

A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The u

OverLord2011 [107]

Answer:

The volume of the ball with the drilled hole is:

$\displaystyle\frac{8000\pi\sqrt{2}}{3}$

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

$x^2+y^2=15^2\to y=\sqrt{225-x^2}$

Then we set the integral for the volume by using shell method:

$\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx$

That can be solved by substitution:

$u=225-x^2\to du=-2xdx$

The limits of integration also change:

For x=5: $u=225-5^2=200$

For x=15: $u=225-15^2=0$

So the integral becomes:

$\displaystyle -\int_{200}^{0}\pi \sqrt{u}du$

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

$\displaystyle \int_{0}^{200}\pi u^{1/2}du$

Then applying the basic rule we get:

$\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}$

Since that is just half of the solid, we multiply by 2 to get the complete volume:

$\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}$

$=\displaystyle\frac{8000\pi\sqrt{2}}{3}$

5 0

3 years ago

How do you solve an absolute value equation?

Mkey [24]

The distance between two real numbers $x,y$ is the absolute value of their difference, $|x-y|$ . So the statement "all $x$ that are 1/4 away from -6" is captured in the equation

$|x-(-6)|=\dfrac14$

or

$|x+6|=\dfrac14$

To solve, you can use the definition of absolute value: if $x$ is not negative, then $|x|=x$ ; otherwise, $|x|=-x$ .

So there are two cases to consider:

1. Suppose $x+6\ge0$ . Then $|x+6|=x+6$ , and the equation reduces to

$x+6=\dfrac14\implies x=-\dfrac{23}4$

2. Suppose $x+6$ . Then $|x+6|=-(x+6)=-x-6$ and

$-x-6=\dfrac14\implies x=-\dfrac{25}4$

$-6=-\dfrac{24}4$ , so the two solutions we found are correct because both $-\dfrac{23}4$ and $-\dfrac{25}4$ are indeed 1/4 away from -6.

- - -

For the question regarding inequality, you know that the absolute value must return a non-negative number. In other words, there is no $x$ such that $|x|$ .

6 0

2 years ago