How do i factor this with grouping?<br> x^3+x^2+2x+2

PLEASE HELP ME IM BEGGING

RideAnS [48]

Answer:

$\frac{4}{25}$

Step-by-step explanation:

there are a total of 20 marbles and the chance that it is blue is 8/20 so multy that by itself and the answer is 4/25

3 0

3 years ago

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For a certain bathtub, it takes the hot water faucet

Valentin [98]

So, we know both faucets open, can do the whole job in 6minutes

ok, how much has the faster cold water faucet done in 1minute then?

well, let's say the the rate of speed of the cold water faucet is "c", so in 1minute it has done 1/c of the whole work

now, we know the hot water faucet is slower, it takes it 3 times as long, that means is 1/3 the speed of the cold water faucet, so, how much does the hot water faucet do in 1min? well, we know is 1/3 fast as the cold one, the cold one is 1/c, what's 1/3 of 1/c? well, 1/3 * 1/c

now, we know they both added together, can do the whole job in 6 minutes, so in 1minute, they've done 1/6 of the job then

thus

$\bf \begin{array}{cccccclllllll}
\cfrac{1}{c}&+&\left( \cfrac{1}{3}\cdot \cfrac{1}{c} \right)&=&\cfrac{1}{6}\\\\
\cfrac{1}{c}&+&\cfrac{1}{3c}&=&\cfrac{1}{6}\\\\
\uparrow &&\uparrow &&\uparrow \\
\textit{cold water rate}&&\textit{hot water rate}&&\textit{total done by both}
\end{array}\\\\
-----------------------------\\\\$

$\bf \cfrac{3+1}{3c}=\cfrac{1}{6}\implies 24=3c\implies \cfrac{24}{3}=c\implies \boxed{8=c}
\\\\\\
\textit{now, if the cold water faucet can do it in 8 minutes by itself}\\\\
\textit{then the hot water faucet can do it in 3 times as long}
\\\\\\
3\cdot 8\implies \boxed{24}$

4 0

3 years ago

A discrete sample space is one in which outcomes are counted.<br> True<br> False

icang [17]

The answer to your question is True.

4 0

3 years ago

What is 1.8 divided by 12.06 equal

aalyn [17]

Your answer rounded to the nearest hundredths is 0.15.
You can find this by converting the decimals into fractions, then multiplying by the reciprocal of the second fraction. Finally, convert it to decimal form.

8 0

3 years ago

Find the longer leg of the triangle.

Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship $\sin{\theta} < \cos{\theta}$ holds for all acute angles? (That is, $0^{\circ} < \theta$ ?) It turns out that:

$\sin{\theta} < \cos{\theta}$ if $0^{\circ} < \theta$ ;
$\sin{\theta} > \cos{\theta}$ if $45^{\circ} < \theta$ ;
$\sin{\theta} = \cos{\theta}$ if $\theta = 45^{\circ}$ .

4 0

3 years ago

Read 2 more answers

How do i factor this with grouping? x^3+x^2+2x+2