9 x 10 to the power of 2 how many times as much as 3 x 10 to the -2 power

Mathematics

1 answer:

hjlf2 years ago

6 0

Answer:

3×10^4

Step-by-step explanation:

The desired factor is found by calculating the ratio of the two numbers:

k = (9×10^2)/(3×10^-2) = (9/3)×10^(2 -(-2)) = 3×10^4

The first number is 3×10^4 = 30,000 times as much as the second number.

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3. How many solutions does the system of equations have? 2x=-10y+ 6 and x+5y=3

ozzi

Answer:

<h2>3. Infinitely many</h2>

Step-by-step explanation:

$\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right\\\\(1)\\\text{if}\ a=d,\ b=e,\ c=f,\ \text{then the system of equations has infinitely many solutions}\\Example:\\\left\{\begin{array}{ccc}2x-3y=5\\2x-3y=5\end{array}\right\\(2)\\\text{if}\ a=d,\ b=e,\ c\neq f,\ \text{then the system of equations has no solution}\\Example:\\\left\{\begin{array}{ccc}2x-3y=5\\2x-3y=-5\end{array}\right$

$(3)\\\text{if}\ a\neq d\ \text{or}\ b\neq e,\ \text{then the system of equations has infinitely many solutions}\\Example:\\\left\{\begin{array}{ccc}x-3y=5\\2x-3y=5\end{array}\right$

$\text{We have:}\\\\\left\{\begin{array}{ccc}2x=-10y+6&\text{add 10y to both sides}\\x+5y=3\end{array}\right\\\left\{\begin{array}{ccc}2x+10y=6&\text{divide both sides by 2}\\x+5y=3\end{array}\right\\\left\{\begin{array}{ccc}x+5y=3\\x+5y=3\end{array}\right$