Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
a) Simplify the expression and explain each step. (2 points)
12
+
3
(
2
y
−
3
)
12+3(2y - 3)
b) Factor the expression completely. (1 point)
18
b
−
12
18b - 12
Why the strange typing, when you end up with the proper version at the end of each question anyway?
Your question fixed:
a) Simplify the expression and explain each step. (2 points)
12+3(2y - 3)
b) Factor the expression completely. (1 point)
18b - 12
a) 12 + 3(2y - 3)
= 12 + 6y - 9
= 6y + 3 , it did not say factor, but you could do it
b) 18b - 12
= 6(3b - 2)
Question
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
∠1
and ∠2
are supplementary angles. m∠1
is 4y+7
, and m∠2
is 9y+4
. Find m∠2
.
Question
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
∠1
and ∠2
are supplementary angles. m∠1
is 4y+7
, and m∠2
is 9y+4
. Find m∠2
.
a) To simplify the expression 12 + 3(2y - 3), we apply the distributive property.
Step 1: Multiply 3 by 2y and -3 separately.
12 + 6y - 9
Step 2: Combine like terms.
6y + 3
Therefore, the simplified expression is 6y + 3.
b) To factor the expression 18b - 12, we can take out the greatest common factor, which is 6.
Step 1: Divide each term by 6.
6(3b - 2)
Therefore, the factored expression is 6(3b - 2).
a) To simplify the expression 12 + 3(2y - 3), we will follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Step 1: Simplify what is inside the parentheses.
Inside the parentheses, we have 2y - 3. This expression cannot be simplified further.
Step 2: Multiply 3 by what is inside the parentheses.
3 multiplied by 2y gives us 6y, and 3 multiplied by -3 gives us -9. Therefore, 3(2y - 3) simplifies to 6y - 9.
Step 3: Add 12 to the simplified expression.
12 + (6y - 9) can be written as 12 + 6y - 9.
Step 4: Combine like terms.
The like terms in this expression are 12 and -9. So, 12 + 6y - 9 simplifies to 3 + 6y.
The simplified expression is 3 + 6y.
b) To factor the expression 18b - 12 completely, we need to look for a common factor, if any.
Step 1: Find the greatest common factor (GCF) of 18 and 12.
The GCF of 18 and 12 is 6.
Step 2: Divide each term by the GCF.
Dividing 18b by 6 gives us 3b, and dividing -12 by 6 gives us -2.
Step 3: Rewrite the expression using the factored terms.
18b - 12 can be written as 6(3b - 2).
The factored expression is 6(3b - 2).