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klio [65]
2 years ago
11

Simplify the fraction (9x² - 12x +4/ 3x²+ x - 2) ÷ (12x² - 5x - 2 / 4x²+5x + 1)

Mathematics
1 answer:
solmaris [256]2 years ago
5 0
When simplified, the answer is 1
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Sarah deposits $600 in a savings account that pays 2.5% per year. What is the minimum number of years it would take for the amou
shutvik [7]
Here is the compound interest formula solved for years:
<span>Years = {log(total) -log(Principal)} ÷ log(1 + rate)
</span>Years = {log(800) - log(600)} <span>÷ log(1.025)
</span><span>Years = {2.903089987 -2.7781512504} / 0.010723865392
</span>Years = { <span> <span> <span> 0.1249387366 } / </span></span></span><span><span><span>0.010723865392
</span> </span> </span> Years = <span> <span> <span> 11.6505319708 </span> </span> </span>
That's how many years it takes for the $600 to become exactly $800.00
The question specifically asks how long for the money to be MORE than $800.00?

So, if we enter 800.01 into the equation, then the answer is
Years = {log(800.01) - log(600)} <span>÷ log(1.025)
</span><span>Years = {2.9030954156 -2.7781512504} / 0.010723865392
</span>Years = <span> <span> <span> 0.1249441652 </span> </span> </span> / 0.010723865392
<span> <span> <span> Years = 11.6510381875 </span> </span> </span>
<span><span> </span></span>












6 0
3 years ago
PLEASE HELP ME LINK IS BELOW
n200080 [17]

Answer:

55

Step-by-step explanation:

Since there is a right angle at the bottom, we know that x and angle 35 degrees form a right angle so 90 minus 35 is 55.

8 0
3 years ago
Read 2 more answers
If PQ = QR, find x. NEED HELP.
max2010maxim [7]

Answer:

x=-3,5

Step-by-step explanation:

4 0
2 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
1 year ago
*<br> 30 35 40<br> 45 50 55 60<br> 65 70 75<br> 80<br><br><br> c. Determine the median
tester [92]

Answer:

median is 55

Step-by-step explanation:

6 0
2 years ago
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