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3 years ago

X^4 + 4x^3 + 4x^2 = -16x

1 answer:

4 0

x⁴ + 4x³ + 4x² = -16x
 x⁴ + 4x³ + 4x² + 16x = -16x + 16x
 x⁴ + 4x³ + 4x² + 16x = 0
x(x³) + x(4x²) + x(4x) + x(16) = 0
 x(x³ + 4x² + 4x + 16) = 0
x(x²(x) + x²(4) + 4(x) + 4(4)) = 0
 x(x²(x + 4) + 4(x + 4)) = 0
 x(x² + 4)(x + 4) = 0
x = 0 U x² + 4 = 0 U x + 4 = 0
 - 4 - 4 - 4 - 4
 x² = -4 x = -4
 x = +2i
The solution set is equal to {-4, -2i, 0, 2i}.

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Find the vertical asymptotes. 2x2 + 7x + 6 y = 3x2 + 10x - 8 * = [ [?], x=

Llana [10]

Answer:

$-\frac{77}{24}$

Step-by-step explanation:

1. rewrite the equation in standard form: $4\cdot \frac{3}{2}\left(y-\left(-\frac{41}{24}\right)\right)=\left(x-\left(-\frac{3}{2}\right)\right)^2$

2. find (h,k), the vertex. the vertex is $\left(h,\:k\right)=\left(-\frac{3}{2},\:-\frac{41}{24}\right)$

3. find the 'focal length' of the parabola - the focal length is the distance between the vertex and the focus. from the vertex we can see that the focal length, p, = 3/2

4. Parabola is symmetric around the y-axis and so the asymptote is a line parallel to the x-axis, a distance p from the $\left(-\frac{3}{2},\:-\frac{41}{24}\right)$ y coordinate which is at $-\frac{41}{24}\right)$ . Set up the equation:

$y=-\frac{41}{24}-p$

5. substitute and solve:

$y=-\frac{41}{24}-\frac{3}{2}$

$y = -\frac{77}{24}$

hope this helps, ask me questions if you still don't understand.

8 0

3 years ago

Find the equation of the line that passes through (1, -1) and is parallel to

daser333 [38]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

$2x+y-3=0\implies y=\stackrel{\stackrel{m}{\downarrow }}{-2} x+3 \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so we're really looking for the equation of a line with a slope of -2 and that passes through (1 , -1)

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad \qquad \stackrel{slope}{m}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-2}(x-\stackrel{x_1}{1}) \\\\\\ y+1=-2x+2\implies y=-2x+1$

8 0

3 years ago

The health club is raising money through a babysitting fundraiser. On Thursday, they charged $3 per hour plus an initial fee $40

xeze [42]

They need to babysit for 10 hours to have same money each day.

Step-by-step explanation:

On Thursday;

Charges = $3 per hour

Initial fee = $40

let x be the number of hours.

T(x) = 3x+40

On Friday;

Charges = $4 per hour

Initial fee = $30

F(x)= 4x+30

The cost will be same when;

T(x) = F(x)

$3x+40=4x+30\\40-30=4x-3x\\10=x\\x=10$

They need to babysit for 10 hours to have same money each day.

Keywords: functions, addition

Learn more about functions at:

#LearnwithBrainly

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4 years ago

3 turtles walking.

Serggg [28]

Answer:

Divide 250 by 9.4 to get 26.6

Step-by-step explanation:

To calculate her unit rate, 1 minute, we must divide the distance travelled over 9.4 minutes by 9.4 to see how far she travelled in 1 minute.

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3 years ago

The speed of one type of bullet is 200 meters per second. How long would it take the bullet to travel 5,000 meters?

Pie

It would take the bullet 25 seconds to travel 5,000 meters (:

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3 years ago