Question
Identify the property that justifies each step asked about in the answer area below.
Line 1: , left parenthesis, 10, x, plus, 3, right parenthesis, plus, 4, x
Line 1: =
(10x+3)+4x
Line 2: , left parenthesis, 3, plus, 10, x, right parenthesis, plus, 4, x
Line 2: =
(3+10x)+4x
Line 3: , 3, plus, left parenthesis, 10, x, plus, 4, x, right parenthesis
Line 3: =
3+(10x+4x)
Line 4: , 3, plus, 14, x
Line 4: =
3+14x
Line 1: , left parenthesis, 10, x, plus, 3, right parenthesis, plus, 4, x
Line 1: =
(10x+3)+4x
Line 2: , left parenthesis, 3, plus, 10, x, right parenthesis, plus, 4, x
Line 2: =
(3+10x)+4x
Line 3: , 3, plus, left parenthesis, 10, x, plus, 4, x, right parenthesis
Line 3: =
3+(10x+4x)
Line 4: , 3, plus, 14, x
Line 4: =
3+14x
Answers
Answer
What is the value of the expression start fraction, left parenthesis, 12, plus, 2, squared, right parenthesis, divided by, 4, squared, end fraction
4
2
(12+2
2
)
4
2
(12+2
2
)
Answer
What is the value of the expression below when z, equals, 9z=9?
7, z, plus, 8
7z+8
7, z, plus, 8
7z+8
Answer
What is the value of the expression below when z, equals, 2z=2 and w, equals, 9w=9?
10, z, plus, 6, w
10z+6w
10, z, plus, 6, w
10z+6w
Answer
Which expression is equivalent to minus, 10, c, minus, 4, minus, c, minus, 9−10c−4−c−9?
Answer
Multiple Choice Answers
minus, 11, c, plus, 5−11c+5
minus, 11, c, minus, 13−11c−13
minus, 24, c−24c
minus, 24−24
Answer
Multiple Choice Answers
minus, 11, c, plus, 5−11c+5
minus, 11, c, minus, 13−11c−13
minus, 24, c−24c
minus, 24−24
Answer
Use the distributive property to write an equivalent expression.
2, left parenthesis, g, plus, 8, right parenthesis
2(g+8)
2, left parenthesis, g, plus, 8, right parenthesis
2(g+8)
Answered by
GPT-4o mini
Here are the properties that justify each step in your lines of work:
- **Line 1 to Line 2:**
- **Property Used:** Commutative Property of Addition
- Justification: The order of addition is changed from \( 10x + 3 \) to \( 3 + 10x \).
- **Line 2 to Line 3:**
- **Property Used:** Associative Property of Addition
- Justification: The grouping of the terms is changed, moving \( 3 \) outside to group with \( (10x + 4x) \).
- **Line 3 to Line 4:**
- **Property Used:** Combining Like Terms
- Justification: The terms \( 10x \) and \( 4x \) are combined to form \( 14x \).
By applying these properties step by step, you successfully transformed the expression into its final form.
- **Line 1 to Line 2:**
- **Property Used:** Commutative Property of Addition
- Justification: The order of addition is changed from \( 10x + 3 \) to \( 3 + 10x \).
- **Line 2 to Line 3:**
- **Property Used:** Associative Property of Addition
- Justification: The grouping of the terms is changed, moving \( 3 \) outside to group with \( (10x + 4x) \).
- **Line 3 to Line 4:**
- **Property Used:** Combining Like Terms
- Justification: The terms \( 10x \) and \( 4x \) are combined to form \( 14x \).
By applying these properties step by step, you successfully transformed the expression into its final form.
Answered by
GPT-4o mini
To evaluate the expression
\[
\frac{(12 + 2^2)}{4^2}
\]
we follow these steps:
1. **Calculate \(2^2\):**
\(2^2 = 4\)
2. **Substitute back into the expression:**
The expression now becomes
\[
\frac{(12 + 4)}{4^2}
\]
3. **Calculate \(12 + 4\):**
\(12 + 4 = 16\)
So we have
\[
\frac{16}{4^2}
\]
4. **Calculate \(4^2\):**
\(4^2 = 16\)
Thus, the expression now is
\[
\frac{16}{16}
\]
5. **Divide:**
\(\frac{16}{16} = 1\)
Therefore, the value of the expression is
\[
\boxed{1}
\]
\[
\frac{(12 + 2^2)}{4^2}
\]
we follow these steps:
1. **Calculate \(2^2\):**
\(2^2 = 4\)
2. **Substitute back into the expression:**
The expression now becomes
\[
\frac{(12 + 4)}{4^2}
\]
3. **Calculate \(12 + 4\):**
\(12 + 4 = 16\)
So we have
\[
\frac{16}{4^2}
\]
4. **Calculate \(4^2\):**
\(4^2 = 16\)
Thus, the expression now is
\[
\frac{16}{16}
\]
5. **Divide:**
\(\frac{16}{16} = 1\)
Therefore, the value of the expression is
\[
\boxed{1}
\]
Answered by
GPT-4o mini
To find the value of the expression \(7z + 8\) when \(z = 9\), we substitute \(9\) for \(z\) in the expression.
1. Substitute \(z = 9\):
\[
7(9) + 8
\]
2. Calculate \(7 \times 9\):
\[
7 \times 9 = 63
\]
3. Add \(8\):
\[
63 + 8 = 71
\]
Therefore, the value of the expression \(7z + 8\) when \(z = 9\) is
\[
\boxed{71}
\]
1. Substitute \(z = 9\):
\[
7(9) + 8
\]
2. Calculate \(7 \times 9\):
\[
7 \times 9 = 63
\]
3. Add \(8\):
\[
63 + 8 = 71
\]
Therefore, the value of the expression \(7z + 8\) when \(z = 9\) is
\[
\boxed{71}
\]
Answered by
GPT-4o mini
To find the value of the expression \(10z + 6w\) when \(z = 2\) and \(w = 9\), we will substitute these values into the expression:
1. Substitute \(z = 2\) and \(w = 9\):
\[
10(2) + 6(9)
\]
2. Calculate \(10(2)\):
\[
10 \times 2 = 20
\]
3. Calculate \(6(9)\):
\[
6 \times 9 = 54
\]
4. Add the results from steps 2 and 3:
\[
20 + 54 = 74
\]
Therefore, the value of the expression \(10z + 6w\) when \(z = 2\) and \(w = 9\) is
\[
\boxed{74}
\]
1. Substitute \(z = 2\) and \(w = 9\):
\[
10(2) + 6(9)
\]
2. Calculate \(10(2)\):
\[
10 \times 2 = 20
\]
3. Calculate \(6(9)\):
\[
6 \times 9 = 54
\]
4. Add the results from steps 2 and 3:
\[
20 + 54 = 74
\]
Therefore, the value of the expression \(10z + 6w\) when \(z = 2\) and \(w = 9\) is
\[
\boxed{74}
\]
Answered by
GPT-4o mini
To simplify the expression \(-10c - 4 - c - 9\), we can follow these steps:
1. **Combine like terms (\(c\) terms):**
- The \(c\) terms: \(-10c - c = -11c\)
2. **Combine the constant terms:**
- The constant terms: \(-4 - 9 = -13\)
Putting it all together, we get:
\[
-10c - 4 - c - 9 = -11c - 13
\]
Now we can compare this simplified expression to the multiple choice answers:
1. \(-11c + 5\) (No match)
2. \(-11c - 13\) (This is a match!)
3. \(-24c\) (No match)
4. \(-24\) (No match)
Therefore, the equivalent expression is:
\[
\boxed{-11c - 13}
\]
1. **Combine like terms (\(c\) terms):**
- The \(c\) terms: \(-10c - c = -11c\)
2. **Combine the constant terms:**
- The constant terms: \(-4 - 9 = -13\)
Putting it all together, we get:
\[
-10c - 4 - c - 9 = -11c - 13
\]
Now we can compare this simplified expression to the multiple choice answers:
1. \(-11c + 5\) (No match)
2. \(-11c - 13\) (This is a match!)
3. \(-24c\) (No match)
4. \(-24\) (No match)
Therefore, the equivalent expression is:
\[
\boxed{-11c - 13}
\]
Answered by
GPT-4o mini
To use the distributive property on the expression \(2(g + 8)\), we distribute the \(2\) to both terms inside the parentheses.
Here's the step-by-step application of the distributive property:
1. **Apply the distributive property:**
\[
2(g + 8) = 2 \cdot g + 2 \cdot 8
\]
2. **Calculate each term:**
- \(2 \cdot g = 2g\)
- \(2 \cdot 8 = 16\)
3. **Combine the results:**
\[
2(g + 8) = 2g + 16
\]
Thus, the equivalent expression is
\[
\boxed{2g + 16}
\]
Here's the step-by-step application of the distributive property:
1. **Apply the distributive property:**
\[
2(g + 8) = 2 \cdot g + 2 \cdot 8
\]
2. **Calculate each term:**
- \(2 \cdot g = 2g\)
- \(2 \cdot 8 = 16\)
3. **Combine the results:**
\[
2(g + 8) = 2g + 16
\]
Thus, the equivalent expression is
\[
\boxed{2g + 16}
\]
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