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Sedaia [141]
2 years ago
9

7.

Mathematics
1 answer:
Alexxx [7]2 years ago
4 0

Answer:

x = 3

Step-by-step explanation:

Given the 2 equations

x + y = 3 → (1)

2x - y = 6 → (2)

Adding the 2 equations term by term eliminates the y- term, that is

3x = 9 ( divide both sides by 3 )

x = 3

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The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is cl
gladu [14]

Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.

The distances:

  • from perihelion to the sun in terms of ellipse is a-c;
  • from aphelion to the sun in terms of ellipse is a+c.

Then

\left\{\begin{array}{l}a-c=741,000,000\\a+c=817,000,000\end{array}\right.

Add these two equations:

2a=1,558,000,000 \\ \\a=779,000,000

and subtract first equation from the second:

2c=76,000,000 \\ \\c=38,000,000.

Note that b=\sqrt{a^2-c^2}, thus

b=\sqrt{779,000,000^2-38,000,000^2}=\sqrt{605,397,000,000,000,000}.

The equation for the planet's orbit is

\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\Rightarrow \dfrac{x^2}{606,841,000,000,000,000}+\dfrac{y^2}{605,397,000,000,000,000}=1.

7 0
3 years ago
What is the surface area of a square prism with sides that measure 8 units?
V125BC [204]

Answer:

<em>The surface area of square prism = 384 units squared</em>

Step-by-step explanation:

<u><em>Explanation</em></u>:-

<em>Given the square prism side 'a' = 8 units</em>

<em>The surface area of square prism = 2 a² + 4 a h</em>

Given square prism length , width and height also equal identical sides

The surface area of square prism = 2 a² + 4 a h

                                                        = 2(8)² + 4 (8)(8)

                                                        = 2(64) + 4(64)

                                                       = 384 units squared

<u><em>Final answer</em></u>:-

<em>The surface area of square prism = 384 units squared</em>

5 0
2 years ago
89 m<br> 80 m<br> What is the length of the missing leg
sergiy2304 [10]

Answer:

119.67

Step-by-step explanation:

a^2 + b^2 =c^2

6 0
2 years ago
which letter would be the most meaningful variable for the problem situation the weight of a box increase by 5​
Natalija [7]

Answer:i

Step-by-step explanation:

4 0
3 years ago
What is the solution to -x2 + 5x - 3
CaHeK987 [17]

The solution to the equation is x=\frac{5-\sqrt{13}}{2} and x=\frac{5+\sqrt{13}}{2}

Explanation:

Given that the equation is -x^2+5x-3=0

We need to determine the solution of the equation.

The solution of the equation can be determined using the quadratic formula.

The quadratic formula is given by

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Hence, from the equation, we have,

a=-1,\:b=5,\:c=-3

Substituting these values in the quadratic formula, we get,

x=\frac{-5\pm \sqrt{5^2-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}

Simplifying, we get,

x=\frac{-5\pm \sqrt{25-12}}{-2}

Simplifying the terms within the root, we get,

x=\frac{-5\pm \sqrt{13}}{-2}

Thus, the roots of the equation are x=\frac{-5+ \sqrt{13}}{-2} and x=\frac{-5- \sqrt{13}}{-2}

Taking out the negative sign, we get,

x=\frac{-(5- \sqrt{13})}{-2} and x=\frac{-(5+ \sqrt{13})}{-2}

Cancelling the negative sign, we get,

x=\frac{5-\sqrt{13}}{2} and x=\frac{5+\sqrt{13}}{2}

Thus, the solutions of the equation are x=\frac{5-\sqrt{13}}{2} and x=\frac{5+\sqrt{13}}{2}

7 0
3 years ago
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