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-Dominant- [34]
3 years ago
15

Evaluate each expression if m = 6 and n = 12. m + 5 A) 1 B) 7 C) 11 D) 17

Mathematics
1 answer:
oee [108]3 years ago
5 0

Answer:

Uh where is the question

I don't see it I'm sorry.

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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
Here's some points .
mars1129 [50]

Answer:

thanks mate

Step-by-step explanation:

8 0
3 years ago
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Seventy and six hundred two thousandths as a decimal number
Alex73 [517]
76.002 i think honestly don’t know but have it a try
7 0
3 years ago
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Convert this franction into a percentage 9/12?
kolbaska11 [484]

<span>Hello, Yoloalanis. In order to solve this question that you have just posted, you only have to do a few simple steps. So, We can do this!</span>

<span />Let's start with your fraction. You will first have to change 9/12 into a decimal. In order to do this, you will have to divide the numerator by the denominator. A numerator is also known as the top part of the fraction. A denominator is the bottom part of the fraction. So, when you divide nine by twelve, you get 0.75 as a decimal. Now, you just have to multiply the decimal by 100 or to make it simpler, just move the decimal two places to the right. To sum it all up, you will get 75%.

Hope it helps :)

5 0
4 years ago
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If a sprinkler waters 1 over 8 of a lawn in 1 over 2 hours, how much time will it take to water the entire lawn?
timama [110]

Answer:

4 hours

Step-by-step explanation:

it takes thirty minutes to water 1/8 of a lawn, so you will water 2/8 every hour. 8 divided by 2 is 4.

8 0
3 years ago
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