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3 years ago

Explain how you can find 3x584 using expanded form

Mathematics

1 answer:

Sati [7]3 years ago

3 0

You have to break the number down. (3 x 500) + (3 x 80) + (3 x 4)

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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

1 year ago

I PROMISE I WILL LET EVERYBODY KNOW WHAT GRADE I GET WHEN I KNOW

makkiz [27]

Answer:

are those 3 different question of just one?

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

If someone could explain what i plug into f??

Alexxx [7]

You are correct with part i with what you did so far, but you need to finish it.
What is function f?

i.
$\dfrac{f(9) - f(2)}{9 - 2}$

ii.
$\dfrac{f(1) - f(0)}{1 - 0}$

iii.
$\dfrac{f(9) - f(-7)}{9 - (-7)}$

3 0

2 years ago

The work of a student to solve a set of equations is shown:

Alina [70]

In which step did the student first make an error?

Answer: Step 2

Step 2 should be:

−3y = -45 + 6z

7 0

3 years ago

1. 1.4(x−1.6)=1.6(x−1.4) solve 2. 1.4(x−1.6)=1.6(1.4−x) solve

Bezzdna [24]

1.
$1.4( x - 1.6) = 1.6(x - 1.4) \\ 1.4x - 2 .24 = 1.6x - 2.24 \\ 0.2x = 0 \\ x = 0$
2.
$1.4( x - 1.6) = 1.6(1.4 - x) \\ 1.4x - 2 .24 = 2.24 - 1.6x \\ 3x = 4.48 \\ x = 1.4933333$

5 0

3 years ago