Answer:
23
Step-by-step explanation:
To find the Greatest Common Factor, or GCF, we need to factor the first 2 numbers and then find the greatest number that is both present in the prime factorization of both numbers.
253 = 1 * 11 * 23
345 = 3 * 5 * 23
Since 23 is both present in both numbers and is the greatest, the GCF of 253 and 345 is 23.
<h3>Answer:</h3>
Length: 12 yd
Width: 5.5 yd
<h3>Explanation:</h3>
Let x represent the width of the rectangle in yards. Then 2x+1 can represent the length (double the width plus 1 yard). The area is the product of length and width so we have the relation ...
... x(2x+1) = 66
... 2x² +x -66 = 0
This can be solved using any of several methods. One of them is to factor the equation. To do that, we can look for factors of 2·66 = 132 that differ by 1. Since 132 = 11·12, those are the numbers we're looking for. Then ...
... 2x² +12x -11x -66 = 0 . . . . use our found numbers to rewrite the x term
... 2x(x +6) -11(x +6) = 0 . . . . .factor by grouping
... (2x -11)(x +6) = 0
... x = 11/2 or -6 . . . . . values that make the factors zero. Only the positive value is a useful solution.
... The width of the rectangle is 5.5 yards. Its length is 2·5.5+1 = 12 yards,
Answer:
7/20
Step-by-step explanation:
