Area of square = s^2
Area of Rectangle = lw
l = 2s
w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
Answer:
A linear expression is one that has a variable in it. Also, no variable is raised higher than a power of 1 or used as a denominator. So you can't divide by a variable. So if a linear equation is commonly expressed as "y= mx+b", a linear expression would be expressed as mx+b.
Step-by-step explanation:
The nth term can be expressed as 16n-70.
So, if we solve
122=16n-70
we find n=12.
Thus, 122 is the 12th term in the sequence.
Always eliminate the first one before moving on. Remember to drop down monomials, like you would a normal division problem.
2x² + 10x + 18
__________________
x + 3 | 2x³ + 16x² - 12x + 9
-(2x³ + 6x²)
-------------------------------
10x² - 12x
-(10x² - 30x)
-----------------------------
+ 18x + 9
- (18x + 54)
----------------------
-45
2x² + 10x + 18 R: -45/x + 3 is your answer R: = remainder
hope this helps
