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irga5000 [103]
3 years ago
15

Mars has m moons. The number of moons of Pluto is one more than twice the number of moons of Mars. The number of moons of Neptun

e is one less than 3 times the number of moons of Pluto. Write and interpret a simplified expression that represents the number of moons of Neptune.
Mathematics
1 answer:
tigry1 [53]3 years ago
6 0

Answer:

Neptune has 2 more than 6 times the number of moons on mars

Explanation:

neptune = 6m+2

mars has 'm' moons

pluto has one more than twice that of mars, = 2m+1

neptune is one less than thrice of pluto

= 3(2m+1) -1

= 6m+3 -1

= 6m+2

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VLD [36.1K]

For this case we must solve the following quadratic equation:

x ^ 2 + 2x-6 = 0

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a = 1\\b = 2\\c = -6

The solution is given by:

x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}

Substituting:

x = \frac {-2 \pm \sqrt {2 ^ 2-4 (1) (- 6)}} {2 (1)}\\x = \frac {-2 \pm \sqrt {4 + 24}} {2}\\x = \frac {-2 \pm \sqrt {28}} {2}\\x = \frac {-2 \pm \sqrt {2 ^ 2 * 7}} {2}\\x = \frac {-2 \pm2 \sqrt {7}} {2}\\x = -1 \pm \sqrt {7}

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8 0
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zlopas [31]

We are given with a quadratic equation which represents a Parabola , we need to find the vertex of the parabola , But let's recall that , For any quadratic equation of the form ax² + bx + c = 0 , the vertex of the parabola is given by ;

{\quad \qquad \boxed{\bf{Vertex = \left(\dfrac{-b}{2a},\dfrac{-D}{4a}\right)}}}

Where , D = b² - 4ac (Discriminant)

Now , On comparing the given equation with ax² + bx + c , we have

⇢⇢⇢ <em><u>a = 1 , b = - 10 , c = 2</u></em><em><u>7</u></em>

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{:\implies \quad \sf D=(-10)^{2}-4\times 1\times 27}

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{:\implies \quad \bf \therefore \quad D=-8}

Now , Calculating the vertex ;

{:\implies \quad \sf Vertex =\bigg\{\dfrac{-(-10)}{2\times 1},\dfrac{-(-8)}{4\times 1}\bigg\}}

{:\implies \quad \sf Vertex = \left(\dfrac{10}{2},\dfrac{8}{2}\right)}

{:\implies \quad \bf \therefore \quad Vertex = (5,2)}

Hence , The vertex of the parabola is at (5,2)

Note :- As the Discriminant < 0 . So , the equation will have imaginary roots .

Refer to the attachment for the graph as well .

5 0
3 years ago
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