Whats the dimensions of a rectangle with area 33cm and perimeter 23cm

5.5 by 6cm

Step-by-step explanation:

P=2x + 2y = 23

x+y= 11.5

y= 11.5 - x

x (11.5-x) =33

11.5x - x^2 = 33

( multiply by 2 to get rid of the decimal?)

23x -2x^2=66

23x-2x^2+66=0

(x-6)(2x - 11) = 0

sub. 6 into y=11.5-x=11.5-6=5.5

sub. 5.5, 5.5=11.5-x, x=11.5 - 5.5= 6

Therefore the dimensions of the rectangle are 6cm by 5.5cm.

hope u get an understanding from this!

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation:

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