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3 years ago

Please help me with this, and thx in advance

Mathematics

1 answer:

lianna [129]3 years ago

5 0

X + 5 = 20 is the answer

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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

Y varies directly with square root of(x+5) ..<br>. y=4 when x = -1 <br>find y when x=11

velikii [3]

Answer:

y varies as √(x+5)

Step-by-step explanation:

y varies as √(x+5)

y= k√(x+5)

k is a constant connecting the two sides.

therefore

k=y/√(x+5)

k=4/√(-1+5)

k= 4/√4

k=4/2

k=2

Y when x=11

y=k√(x+5)

y=2√(11+5)

y=2√16

y=2*4

y=8

3 0

3 years ago

Diane uses 2 feet of ribbon to decorate each gift she is wrapping. She wraps 7 gifts. How much ribbon does she need?

lakkis [162]

14, because 2x7=14. Every gift box uses 2 feet on ribbon. There are 7 gift boxes, so she needs 2+2+2+2+2+2+2 length of ribbon.

5 0

4 years ago

Please help me find the answer, i will friend you

snow_lady [41]

Ok so what you need to do is first find the area of the circle using π r^2. So π12^2 or π144= 452.389342117 This is the area of the whole circle. To find the area of the sector you have to multiply the total area by 172/360 or 0.47777777777 This will get you 216.141574567 round as necessary but your answer is <span>216.141574567units^2</span>

6 0

3 years ago

5+3/67=<img src="https://tex.z-dn.net/?f=%5Cleq%20%5Csqrt%5Bn%5D%7Bx%7D%20%5Cfrac%7Bx%7D%7By%7D" id="TexFormula1" title="\leq \s

miss Akunina [59]

Answer:

is this a question

Step-by-step explanation:

(　ﾟДﾟ)＜!!

6 0

3 years ago