7 1/2 - 1 1/4 = 7 2/4 - 1 1/4 = 6 1/4
x^3=54 (Subtract 3 from both sides)
x = 3rd power cube root of 54 (Cube root both sides)
27 = 3^3 (3x3x3) therefore
x = (3) (3rd power cube root of 2)
Answer:
Step-by-step explanation:
Integer factors of 117 include ...
... 117 = 1×117 = 3×39 ≈ 9×13
The last factor pair is two factors that differ by 4. We can take these to be the dimensions of the rectangle.
_____
If you want to write an equation for width (w), it might be ...
... w(w+4) = 117
... w² +4w -117 = 0
The factorization problem for this quadratic is the problem of finding two factors of 117 that differ by 4. That is what we have done, above.
If you want to solve this by completing the square, you can to this:
... w² +4w = 117
... w² +4w +4 = 121 . . . . . add 4 = (4/2)² to complete the square
... (w+2)² = 121
... w + 2 = ±√121 = ±11 . . . . take the square root
... w = -2 ± 11 . . . . . we're only interested in the positive solution
... w = 9, then w+4 = 13 and the dimensions are 9 cm by 13 cm.
25x25+20x25+20x15+15x25=1800 the answer is D.
Answer:
the length of the rectangle is, 21 in.
Step-by-step explanation:
Area of the rectangle(A) is given by:
.....[1]
where,
l is the length of the rectangle
w is the width of the rectangle.
As per the statement:
The width of a rectangle is 9 in. shorter than its length.
⇒
It is also given that:
The area of the rectangle is 252 in².
⇒A = 252 in².
Substitute in [1] we have;
⇒
⇒
Factorize this equation:
Split the middle term;
⇒
⇒
⇒
By zero product property we have;
and 
⇒
and 
Since, length cannot be in negative
⇒
Therefore, the length of the rectangle is, 21 inches.
