Factor out completely
45x - 18y + 36
To factor out completely, we need to find the greatest common factor (GCF) among all the terms.
For the given expression, the GCF is 9 because it is the largest number that divides evenly into all the coefficients (45, -18, and 36).
So, we can factor out 9 from each term:
45x can be written as 9 * 5x
-18y can be written as 9 * (-2y)
36 can be written as 9 * 4
Therefore, the completely factored expression is:
9(5x - 2y + 4)
So D?
Yes, that is correct. The factored expression is 9(5x - 2y + 4).
A board 6 1/8 feet in length is shortened by having 2 1/12 feet cut off one end. The length of the shortened board is Responses A 3 1/4 feet. B 3 5/24 C 4 1/24 feet D 4 5/24 feet E 4 9/24 feet.
To find the length of the shortened board, we need to subtract the amount that was cut off from the original length.
The original length is 6 1/8 feet, and 2 1/12 feet was cut off.
To subtract these mixed numbers, we can convert them to improper fractions:
6 1/8 = 49/8
2 1/12 = 25/12
Now, we can subtract the fractions:
49/8 - 25/12
To subtract fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 8 and 12 is 24.
49/8 = 49/8 * 3/3 = 147/24
25/12 = 25/12 * 2/2 = 50/24
Now, we can subtract:
147/24 - 50/24 = 97/24
Therefore, the shortened length of the board is 97/24 feet.
This fraction can be simplified to a mixed number:
97 ÷ 24 = 4 remainder 1
So, the final result is 4 1/24 feet.
Therefore, the correct answer is C) 4 1/24 feet.
To factor out completely, we need to find the greatest common factor (GCF) of all the terms. In this case, we can start by looking for any common factors among the coefficients (numbers): 45, -18, and 36.
The GCF of 45, -18, and 36 is 9 (the largest factor that divides evenly into all three numbers). We can now factor out 9 from each term:
45x = 9 * 5x
-18y = 9 * (-2y)
36 = 9 * 4
Now we can rewrite the expression with the factored terms:
45x - 18y + 36 = 9 * 5x - 9 * 2y + 9 * 4
Next, we can further simplify this expression by factoring out the common factor of 9:
45x - 18y + 36 = 9(5x - 2y + 4)
So the completely factored form of the expression 45x - 18y + 36 is 9(5x - 2y + 4).