6x2y^3/3xy Use Laws of exponents. answer is 2xy^2 but I don't know how to get it. My initial answer was 4y^2

Mathematics

1 answer:

allsm [11]3 years ago

4 0

Step-by-step explanation:

$\frac{6x^{2}y^{3}}{3xy}$

If it helps, write as a product of fractions, grouped by variable.

$\frac{6}{3} \frac{x^{2}}{x} \frac{y^{3}}{y}$

Now reduce using exponent rules.

$2xy^{2}$

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Use the table. Make a scatter plot relating the distance of various cities from the metro area to the population of the cities.

Dafna11 [192]

Answer:

Option (A)

Step-by-step explanation:

From the table attached,

Independent variable 'x' is will be represented by the distance from Metro area.

Similarly, dependent variable 'y' will be on y-axis.

Scatter plot relating the distances of various cities from the metro area (x) to the population of the cities (y) will be represented by the ordered pair as (x, y).

Set of ordered pairs to be plotted,

[(1, 300), (5, 275), (10, 208), (15, 135), (20, 108)]

Therefore, graph given in Option (A) will be the answer.

4 0

2 years ago

1/2x + 1/3y = 7

pashok25 [27]

let's multiply both sides in each equation by the LCD of all fractions in it, thus doing away with the denominator.

$\begin{cases} \cfrac{1}{2}x+\cfrac{1}{3}y&=7\\\\ \cfrac{1}{4}x+\cfrac{2}{3}y&=6 \end{cases}\implies \begin{cases} \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{1}{2}x+\cfrac{1}{3}y \right)=6(7)}\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{4}x+\cfrac{2}{3}y\right)=12(6)} \end{cases}\implies \begin{cases} 3x+2y=42\\ 3x+8y=72 \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{using elimination}}{ \begin{array}{llll} 3x+2y=42&\times -1\implies &\begin{matrix} -3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-2y=&-42\\ 3x+8y-72 &&~~\begin{matrix} 3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+8y=&72\\ \cline{3-4}\\ &&~\hfill 6y=&30 \end{array}} \\\\\\ y=\cfrac{30}{6}\implies \blacktriangleright y=5 \blacktriangleleft \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{substituting \underline{y} on the 1st equation}~\hfill }{3x+2(5)=42\implies 3x+10=42}\implies 3x=32 \\\\\\ x=\cfrac{32}{3}\implies \blacktriangleright x=10\frac{2}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(10\frac{2}{3}~~,~~5 \right)~\hfill$