You want to fence in a row bed that is adjacent to a deck. the length of your deck is 14ft. you have at most 44 ft of fence. what are the possible widths of the rose bed?

he first step in a problem like this (after sketching the problem out for yourself, which very often helps) is to assign variables.  Let's call the length x, and the width y.

There are two sections that are y long, and one that's x long.  Adding up the total length of the fence, then, gives us x + y + y, or x + 2y, which should be equal to 44, since that's how much fence we have.  Our first equation is thus

x + 2y = 44

Our second equation, since the length is supposed to be twice the width, is x = 2y.

This is enough to solve.  We can substitute this equation for x into the first equation to get

2y + 2y = 44

4y = 44

y = 11

And then x = 2(11) = 22

So the length of the fence is 22, and the width (though they don't actually ask for it) is 11.

Check the  22 + 11 + 11 is 44, as we want, and 22 is twice as great as 11, as we want.  So the answer is valid.

Step-by-step explanation:

Okay so one way you can do this is in a rectangle yard that is 14 by 8 the rose bed can be any where less than 8 ft and still be adjacent to the deck. hope this helps!   :)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.