Alex is drawing rectangles with different areas on a centimetre grid he can draw 3 different rectangles with an area of 12cmsquared a) How many different rectangles could alex draw with an area of 11cmsquared? B)Give a reason for ur anwser

Alex can only draw a rectangle with an area of 11 cm²

The reason for the answer is that 11 is a prime number

Step-by-step explanation:

We are told that Alex is drawing rectangles with different areas on a centimeter grid, and he can draw 3 different rectangles with an area of 12 cm²

We have the minimum grid length of centimeters = 1 cm, since we assume that only integers can be used.

That is to say:

12 = 1 x 12

12 = 2 x 6

12 = 3 x 4

These are the 3 different rectangles with an area of 12 cm²

Now we have to find how many rectangles Alex could draw with an area of 11 cm²

11 = 1 x 11

Therefore, only one factorization is possible. Which means that you can only draw a rectangle with an area of 11 cm²

The reason for the answer is that 11 is a prime number, which means only the common factor of 1 and the number itself, that is, 11.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!