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3 years ago

Factor completely. x 3 + 6x 2 - 4x - 24

Mathematics

1 answer:

Ulleksa [173]3 years ago

5 0

You can factor (x^3 and 6x^2) and (-4x and -24).

So x^2(x+6) - 4(x+6)

(x^2-4)(x+6)

(x-2)(x+2)(x+6)

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The line l passes through the point P = (1,-1,1) and has direction vector d = [2,3,1]. Determine whether l and the plane 4x-y+5z

suter [353]

Hello :
the normal vector of the plane is : d' = [4,-1,5]...(vector perpendicular to the plane)<span>
d </span><span>⊥ d' because : (4)(2)+(-1)(3)+(5)(1)=0
</span>the line is perpendicular to the plane .

3 0

3 years ago

What is the perimeter of this quadrilateral?<br> (5,5)<br> (2, 4)<br> (4, 1)<br> (6, 1)

lbvjy [14]

$~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{4}) ~\hfill AB=\sqrt{[ 2- 5]^2 + [ 4- 5]^2} \\\\\\ AB=\sqrt{(-3)^2+(-1)^2}\implies \boxed{AB=\sqrt{10}} \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) ~\hfill BC=\sqrt{[ 4- 2]^2 + [ 1- 4]^2}$

$BC=\sqrt{2^2+(-3)^2}\implies \boxed{BC=\sqrt{13}} \\\\[-0.35em] ~\dotfill\\\\ C(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) ~\hfill CD=\sqrt{[ 6- 4]^2 + [ 1- 1]^2} \\\\\\ CD=\sqrt{2^2+0^2}\implies \boxed{CD=2} \\\\[-0.35em] ~\dotfill\\\\ D(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad A(\stackrel{x_2}{5}~,~\stackrel{y_2}{5}) ~\hfill DA=\sqrt{[ 5- 6]^2 + [ 5- 1]^2}$

$DA=\sqrt{(-1)^2+4^2}\implies \boxed{DA=\sqrt{17}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{\sqrt{10}~~ + ~~\sqrt{13}~~ + ~~2~~ + ~~\sqrt{17}}~~ \approx ~~ 12.89$

8 0

2 years ago

Three friends collected aluminum cans from the neighborhood to recycle in total they receive 300 cans many collected 90 Jim coll

spin [16.1K]

Given

Total cans = 300

Manny= 90

Jim =100

Bob=110

Now their percentage

Manny percentage

$\begin{gathered} manny=\frac{90}{300}\times100\text{ \%} \\ \\ Manny\text{ percentage=}\frac{90}{3}\text{ \%} \\ \\ Manny\text{ percentage =30 \%} \end{gathered}$

Jim Percentage

$\begin{gathered} Jim=\frac{100}{300}\times100\text{ \%} \\ Jim\text{ percentage=}\frac{1}{3}\times100\text{ \%} \\ Jim\text{ percentage=33.333\%} \end{gathered}$

Bob percentage

$undefined$

6 0

1 year ago

Express the function graphed on the axes below as a piecewise function.

adoni [48]

Answer:

f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

f(x) = x-3 for x ≤ -1

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

y -(-1) = -3(x -5)

y = -3x +15 -1 = -3x +14

The second piece can be written ...

f(x) = -3x +14 for x > 5

<h3>Whole function</h3>

Putting these pieces together, we have ...

$\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}$

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

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2 years ago

Martha measures the big prize wheel on a game show and calculates that it has a circumference of 12.56 yards. What is the prize

trasher [3.6K]

The radius is 2 yards...
Formula for circumference is $\pi r^2$ so divide your circumference by 3.14 or pi and you get 4 the square root of 4 is 2.

Hope this helps!

7 0

3 years ago