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2 years ago

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:

The surface area of square prism = 384 units squared

Step-by-step explanation:

Explanation:-

Given the square prism side 'a' = 8 units

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

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

Final answer:-

The surface area of square prism = 384 units squared

5 0

2 years ago

89 m 80 m 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