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katen-ka-za [31]
3 years ago
7

The mass of the Sun is about 2 × 1027 metric tons, or 2 × 1030 kilograms. How many kilograms are in one metric ton?

Mathematics
1 answer:
Yuri [45]3 years ago
3 0
One metric ton is equal to 1000 Kilograms
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Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 2x – 1 into the quadratic formula below
S_A_V [24]
A= 4 B= 2 C= -1 
follow the formula ax^2 + bx + c= 0.
5 0
4 years ago
Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
nlexa [21]

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\

                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

7 0
2 years ago
The vertices of a rectangle are R(-5, -5), S(-1, -5), T(-1, 1), and U(-5, 1). a translation, R to the point (-4,2). Find the tra
Nikitich [7]
Translation:
R ( - 5, - 5 ) → R` ( - 4, 2 )
- 4  = - 5 + 1,   2 = - 5 + 7;
The translation rule:
( x , y ) → ( x + 1, y + 7 )
Coordinates of the point U are (- 5, 1 )
- 5 + 1 = - 4,  1 + 7 = 8
The image of U is :
U` ( - 4, 8 )
4 0
3 years ago
Elsa uses exactly 60 cubes of ice to build a rectangular ice prism. Each cube has side lengths of 1 unit. Enter the dimensions o
GuDViN [60]

Answer:

2, 5, 6

Step-by-step explanation:

The volume of a rectangular prism is given by V=l\cdot w\cdot h, where all variables to the right are dimensions of the prism.

Therefore, we're looking for three numbers that multiply to be 60.

Since the question stipulates that no side length may be 10, we have:

2\cdot 5\cdot 6=60

3 0
3 years ago
A square floor tile has a diagonal 19 inches long. What is the area of the tile?
Anit [1.1K]

Answer:

C

Step-by-step explanation:

The answer is C because you plugin using the area formula.

3 0
3 years ago
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