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3 years ago

How to solve the problem 12w-3(4w-2)

Mathematics

1 answer:

kati45 [8]3 years ago

5 0

The answer is 6. Check photo for steps and please mark me as brainliest!

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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

2 years ago

If I earn $15/hour and work for 20 hours/week, how much would I earn in one

choli [55]

Answer:

$1,200

Step-by-step explanation:

$15 x 20 = $300/week; $300 x 4 weeks = $1,200

6 0

1 year ago

Read 2 more answers

4 Gears A and B turn together. Gear A turns 20 times when

aleksandr82 [10.1K]

Answer:

90 turns

Step-by-step explanation:

<u>Ratio of turns</u>

A/B = 20/30 = 2/3

<u>If A = 60 then the ratio is</u>

60/B = 2/3 ⇒ B = 60*3/2 = 90

5 0

2 years ago

One of my cats, Apollo, drives a cat car. He used 6/8 of a tank of gas to visit his friends for the weekend, and another 1 half

Arlecino [84]

Answer:

Total gas used = 3/2 of a tank of gas

Step-by-step explanation:

Visit to friend = 6/8 of a tank of gas

Commute to work = 1/2 of a tank of gas

Weekend trip = 1/4 of a tank of gas

Total gas used = Visit to friend + Commute to work + Weekend trip

= 6/8 + 1/2 + 1/4

= 6+4+2/8

= 12/8

= 3/2

Total gas used = 3/2 of a tank of gas

7 0

3 years ago

The Martinez family went to play and paid $13 for 1 adult and 4 children. The Hernandez family went to the same place and paid $

andrey2020 [161]

Answer: the price for an adult ticket is $3

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one child ticket.

The Martinez family went to play and paid $13 for 1 adult and 4 children. This means that

x + 4y = 13 - - - - - - - - - - -1

The Hernandez family went to the same place and paid $14 for 3 adults and 2 children. This means that

3x + 2y = 14 - - - -- - - - - - - -2

Multiplying equation 1 by 3 and equation 3 by 1, it becomes

3x + 12y = 39

3x + 2y = 14

Subtracting, it becomes

10y = 25

y = 25/10 = 2.5

Substituting y = 2.5 into equation 1, it becomes

x + 4 × 2.5 = 13

x + 10 = 13

x = 13 - 10

x = 3

6 0

3 years ago