Find the GCF of 18j + 27
To find the greatest common factor (GCF) of 18j and 27, we can find the prime factors of both numbers.
18j: The prime factorization of 18 is 2 * 3 * 3. Since there is a "j" attached to the number, it means that "j" is a factor. Therefore, the prime factorization of 18j is 2 * 3 * 3 * j.
27: The prime factorization of 27 is 3 * 3 * 3.
Now, let's compare the prime factorizations of 18j and 27:
18j: 2 * 3 * 3 * j
27: 3 * 3 * 3
To find the GCF, we only consider the common prime factors with the lowest exponent. In this case, the common prime factor is 3 and its exponent is 2 (from 3 * 3). Therefore, the GCF of 18j and 27 is 3^2, which is equal to 9.
Use properties of operations to factor 8w + 16 using GCF.(1 point)
Responses
4(2w + 4)
4(2w + 4)
2(4w + 8)
2(4w + 8)
6(2w + 10)
6(2w + 10)
8(w + 2)
To factor 8w + 16 using the greatest common factor (GCF), we need to find the largest number that evenly divides both terms. The GCF of 8w and 16 is 8.
We can then factor out 8 from both terms:
8w + 16 = 8(w + 2)
Therefore, the factored form of 8w + 16 using GCF is 8(w + 2).
Factor -27h + 6 using the GCF.(1 point)
Responses
3(-9h - 2)
3(-9h - 2)
3(9h + 2)
3(9h + 2)
3(-9h +2)
3(-9h +2)
3(-9h - 2)
To factor -27h + 6 using the greatest common factor (GCF), we need to find the largest number that evenly divides both terms. The GCF of -27h and 6 is 3.
We can then factor out 3 from both terms:
-27h + 6 = 3(-9h + 2)
Therefore, the factored form of -27h + 6 using GCF is 3(-9h + 2).
−5(−3−11g)(1 point)
Responses
55g + 15
55g + 15
-55g + 15
-55g + 15
55g - 15
55g - 15
-55g - 15
To simplify -5(-3 - 11g), we need to distribute the -5 to both terms within the parentheses.
-5(-3 - 11g) = (-5)(-3) + (-5)(-11g)
= 15 + 55g
Therefore, the simplified form of -5(-3 - 11g) is 15 + 55g.
2/8x+3/10y−5/8x+4/10y(1 point)
Responses
−3/8x+7/10ynegative 3 eighths x plus 7 tenths y
14/18xy14 over 18 x y
4/18xy4 over 18 x y
7/10x+7/8y
To simplify 2/8x + 3/10y - 5/8x + 4/10y, we can first combine like terms with the same variable.
2/8x - 5/8x can be simplified to (2 - 5)/8x = -3/8x.
3/10y + 4/10y can be simplified to (3 + 4)/10y = 7/10y.
Therefore, the simplified form of 2/8x + 3/10y - 5/8x + 4/10y is -3/8x + 7/10y.
Evaluate when a = 9, b = 6.
a−b/3(1 point)
Responses
6
6
3
3
1
1
9
To evaluate the expression a - b/3 when a = 9 and b = 6, we substitute these values into the expression:
9 - 6/3
First, we divide 6 by 3:
9 - (6/3) = 9 - 2
Then, we subtract 2 from 9:
9 - 2 = 7
Therefore, when a = 9 and b = 6, the value of a - b/3 is 7.
You are saving for a skateboard. Your aunt gives you $45 to start and you save $3 each week. The expression 45 + 3w gives the amount of money you save after w weeks. How much will you have saved after 4 weeks?(1 point)
Responses
$57
$57
$33
$33
$576
$576
$42
To determine how much money you will have saved after 4 weeks, we can substitute w = 4 into the expression 45 + 3w:
45 + 3(4) = 45 + 12 = 57
Therefore, after 4 weeks, you will have saved $57.
Evaluate when a = 9, b=6.
a-b/3
Responses
6
6
9
9
1
1
3
Simplify by combining like terms. 2/8x+3/10y−5/8x+4/10y
Factor 18m - 24 in using the GCF
Find the GCF of 42m - 28n.(1 point)
Responses
14
14
2
2
7
7
84
To find the greatest common factor (GCF) of 42m and -28n, we can first simplify the expression by factoring out the common factors:
42m - 28n
We can factor out 14, which is the greatest common factor of both 42 and 28:
14(3m - 2n)
So, the GCF of 42m - 28n is 14.