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3 years ago

What conclusions can you draw about the roots of the equation x^3+x^2-2x+12=0

Mathematics

1 answer:

nexus9112 [7]3 years ago

4 0

Answer:

x=-3

Step-by-step explanation:

If x=-3, then

x³+x²-2x+12=-27+9+6+12=-27+27=0

If this is true, then x+3 is a factor. So:

x³+x²-2x+12/x+3=x²-2x+4

So the factors of x³+x²-2x+12 are:

(x+3)(x²-2x+4)

((x²-2x+4) has no real roots)........

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3 years ago

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

The equation of the parabola is $\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$
The focus is $\mathbf{Focus = (80, -1760)}$
The directrix is $\mathbf{y = \frac{1}{640}}$
The axis of the symmetry of parabola is: $\mathbf{x = 80}$

From the question, we have:

$\mathbf{Vertex: (h,k) = (80,10)}$

$\mathbf{Origin: (x,y) = (0,0)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

Substitute the values of origin and vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{0 = a(0 - 80)^2 + 10}$

$\mathbf{0 = a(- 80)^2 + 10}$

$\mathbf{0 = 6400a + 10}$

Collect like terms

$\mathbf{6400a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{640}}$

Substitute the values of a and the vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

The focus of a parabola is:

$\mathbf{Focus = (h, \frac{k+1}{4a})}$

Substitute the values of a and the vertex in $\mathbf{Focus = (h, \frac{k+1}{4a})}$

$\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}$

$\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}$

$\mathbf{Focus = (80, -11\times 160)}$

$\mathbf{Focus = (80, -1760)}$

The equation of the directrix is:

$\mathbf{y = -a}$

So, we have:

$\mathbf{y = \frac{1}{640}}$ ----- the directrix

The axis of symmetry is:

$\mathbf{x = -\frac{b}{2a}}$

We have:

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

Expand

$\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}$

Expand

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}$

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }$

A quadratic function is represented as:

$\mathbf{y = ax^2 + bx + c}$

So, we have:

$\mathbf{a = -\frac{1}{640}}$

$\mathbf{b = \frac{1}{4}}$

Recall that:

$\mathbf{x = -\frac{b}{2a}}$

So, we have:

$\mathbf{x = -\frac{1/4}{2 \times -1/640}}$

$\mathbf{x = \frac{1/4}{1/320}}$

This gives

$\mathbf{x = \frac{320}{4}}$

$\mathbf{x = 80}$

Hence, the axis of the symmetry of parabola is: $\mathbf{x = 80}$

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3 years ago

What is 3(x+3)=2(x12) can u help me

Soloha48 [4]

You didn't type the equation correctly.

3 0

3 years ago

The points (4,k) and (5,-8) fall on a line with a slope of -7. what is the value of k?

babunello [35]

Answer:

k= -1

Step-by-step explanation:

To find k, use the points and the m =-7 in the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}\\\\-7=\frac{-8-k}{5-4} \\\\-7 = \frac{-8-k}{1}\\\\-7=-8-k\\\\k = -8+7\\\\k=-1$

4 0

4 years ago

a gas station sells regular gas for $2.10 per gallon and premium gas for $2.90 a gallon. at the end of a business day 280 gallon

insens350 [35]

200 gallons of regular gas and 80 gallons of premium gas were sold.

Let the amount of regular gas sold be x gallons. So, the amount of premium gas sold will be (280 - x).

Now, forming the equation using the given information, to find the amount of each type of gallon.

Equation -

2.10x + 2.90(280 - x) = 652

Performing multiplication with values inside bracket in Left Hand Side

2.10x + 812 - 2.90x = 652

Rewriting the equation -

812 - 652 = 2.90x - 2.10x

Performing subtraction

160 = 0.8x

Rewriting the equation according to x

x = 160÷0.8

Performing division to find the value of x

x = 200

So, 200 gallons of regular gas was sold.

Amount of premium gas sold = 280 - 200

Performing subtraction

Amount of premium gas sold = 80 gallons

Hence, 200 gallons of regular gas and 80 gallons of premium gas was sold.

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4 0

2 years ago

What conclusions can you draw about the roots of the equation x^3+x^2-2x+12=0​

What conclusions can you draw about the roots of the equation x^3+x^2-2x+12=0