the length of the flower garden is 3 times as great as the width. what are the dimensions of the flower garden

1 answer:

5 0

Without any more information we can't find the actual numerical representation of the length and width but we can give an expression that will allow us to find them...

We let the width equal x, so the length is 3x. That would be the dimensions...

length = 3x
width = x

So to find perimeter the expression would be

2(3x) + 2(x) =
6x + 2x =
8x

For the area it would be

a= length × width
a = 3x × x
a = 3x^2

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Find the average rate of change of the function defined by the following table. x y -2 -5 2 35 6 75 10 115

Pani-rosa [81]

By definition we have that the average rate of change of the function is:

$AVR = \frac{f(x2) - f(x1)}{x2 - x1}$

Evaluating the function for the complete interval we have that the AVR is given by:

$AVR = \frac{115 - (-5)}{10 - (-2)}$

Rewriting we have:

$AVR = \frac{115+5}{10+2}$

Simplifying the expression we have:

$AVR = \frac{120}{12}$

$AVR = 10$

Answer:

the average rate of change of the function defined by the table is:

$AVR = 10$

6 0

2 years ago

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:

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

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

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