Question
What is the value of the expression start fraction, left parenthesis, 5, squared, plus, 67, right parenthesis, divided by, 2, squared, end fraction
2
2
(5
2
+67)
?
Answer
2
2
(5
2
+67)
?
Answer
Answers
GPT-4o mini
To evaluate the expression \( \frac{(5^2 + 67)}{2^2} \), we can follow these steps:
1. Calculate \( 5^2 \):
\[
5^2 = 25
\]
2. Add 67 to the result:
\[
25 + 67 = 92
\]
3. Now calculate \( 2^2 \):
\[
2^2 = 4
\]
4. Finally, divide 92 by 4:
\[
\frac{92}{4} = 23
\]
Thus, the value of the expression is \( \boxed{23} \).
1. Calculate \( 5^2 \):
\[
5^2 = 25
\]
2. Add 67 to the result:
\[
25 + 67 = 92
\]
3. Now calculate \( 2^2 \):
\[
2^2 = 4
\]
4. Finally, divide 92 by 4:
\[
\frac{92}{4} = 23
\]
Thus, the value of the expression is \( \boxed{23} \).
bluesanta
What is the value of the expression start fraction, left parenthesis, 2, cubed, plus, 32, right parenthesis, divided by, 2, squared, end fraction
2
2
(2
3
+32)
?
Answer
2
2
(2
3
+32)
?
Answer
GPT-4o mini
To evaluate the expression \( \frac{(2^3 + 32)}{2^2} \), we can follow these steps:
1. Calculate \( 2^3 \):
\[
2^3 = 8
\]
2. Add 32 to the result:
\[
8 + 32 = 40
\]
3. Now calculate \( 2^2 \):
\[
2^2 = 4
\]
4. Finally, divide 40 by 4:
\[
\frac{40}{4} = 10
\]
Thus, the value of the expression is \( \boxed{10} \).
1. Calculate \( 2^3 \):
\[
2^3 = 8
\]
2. Add 32 to the result:
\[
8 + 32 = 40
\]
3. Now calculate \( 2^2 \):
\[
2^2 = 4
\]
4. Finally, divide 40 by 4:
\[
\frac{40}{4} = 10
\]
Thus, the value of the expression is \( \boxed{10} \).
bluesanta
What is the value of the expression below when x, equals, 8x=8 and y, equals, 7y=7?
10, x, minus, 4, y
10x−4y
10, x, minus, 4, y
10x−4y
GPT-4o mini
To find the value of the expression \( 10x - 4y \) when \( x = 8 \) and \( y = 7 \), we can substitute the values of \( x \) and \( y \) into the expression.
1. Substitute \( x = 8 \):
\[
10(8) - 4y
\]
2. Substitute \( y = 7 \):
\[
10(8) - 4(7)
\]
3. Now calculate:
\[
10 \times 8 = 80
\]
\[
4 \times 7 = 28
\]
4. Finally, the expression becomes:
\[
80 - 28
\]
5. Calculate the result:
\[
80 - 28 = 52
\]
Thus, the value of the expression \( 10x - 4y \) is \( \boxed{52} \).
1. Substitute \( x = 8 \):
\[
10(8) - 4y
\]
2. Substitute \( y = 7 \):
\[
10(8) - 4(7)
\]
3. Now calculate:
\[
10 \times 8 = 80
\]
\[
4 \times 7 = 28
\]
4. Finally, the expression becomes:
\[
80 - 28
\]
5. Calculate the result:
\[
80 - 28 = 52
\]
Thus, the value of the expression \( 10x - 4y \) is \( \boxed{52} \).
bluesanta
What is the value of the expression below when w, equals, 6w=6 and x, equals, 10x=10?
5, w, plus, 10, x
5w+10x
5, w, plus, 10, x
5w+10x
GPT-4o mini
To find the value of the expression \( 5w + 10x \) when \( w = 6 \) and \( x = 10 \), we will substitute the values into the expression.
1. Substitute \( w = 6 \):
\[
5(6) + 10x
\]
2. Substitute \( x = 10 \):
\[
5(6) + 10(10)
\]
3. Now calculate:
\[
5 \times 6 = 30
\]
\[
10 \times 10 = 100
\]
4. The expression now becomes:
\[
30 + 100
\]
5. Calculate the result:
\[
30 + 100 = 130
\]
Thus, the value of the expression \( 5w + 10x \) is \( \boxed{130} \).
1. Substitute \( w = 6 \):
\[
5(6) + 10x
\]
2. Substitute \( x = 10 \):
\[
5(6) + 10(10)
\]
3. Now calculate:
\[
5 \times 6 = 30
\]
\[
10 \times 10 = 100
\]
4. The expression now becomes:
\[
30 + 100
\]
5. Calculate the result:
\[
30 + 100 = 130
\]
Thus, the value of the expression \( 5w + 10x \) is \( \boxed{130} \).
bluesanta
Click and drag like terms onto each other to simplify fully.
minus, x, squared−x
2
plus, 2, y, squared+2y
2
minus, 4, y, cubed−4y
3
minus, 2, x, cubed−2x
3
minus, 7, y, squared−7y
2
minus, 6, y, cubed−6y
3
minus, 4, x, cubed−4x
3
minus, x, squared−x
2
plus, 2, y, squared+2y
2
minus, 4, y, cubed−4y
3
minus, 2, x, cubed−2x
3
minus, 7, y, squared−7y
2
minus, 6, y, cubed−6y
3
minus, 4, x, cubed−4x
3
GPT-4o mini
To simplify the expression by combining like terms, let's group and combine the coefficients of each type of term present:
1. **Identify like terms**:
- **\( x^2 \) terms**: \( -x^2 \)
- **\( x^3 \) terms**: \( -2x^3, -4x^3, -2x^3 \)
- **\( y^2 \) terms**: \( 2y^2, -7y^2 \)
- **\( y^3 \) terms**: \( 2y^3, -4y^3, -6y^3 \)
2. **Combine the coefficients of like terms**:
- **For \( x^2 \)**:
- Only \( -x^2 \) remains.
- **For \( x^3 \)**:
- \( -2x^3 - 4x^3 - 2x^3 = -8x^3 \)
- **For \( y^2 \)**:
- \( 2y^2 - 7y^2 = -5y^2 \)
- **For \( y^3 \)**:
- \( 2y^3 - 4y^3 - 6y^3 = -8y^3 \)
3. **Write the simplified expression**:
\[
-8x^3 - x^2 - 5y^2 - 8y^3
\]
Thus, the fully simplified expression is:
\[
\boxed{-8x^3 - x^2 - 5y^2 - 8y^3}
\]
1. **Identify like terms**:
- **\( x^2 \) terms**: \( -x^2 \)
- **\( x^3 \) terms**: \( -2x^3, -4x^3, -2x^3 \)
- **\( y^2 \) terms**: \( 2y^2, -7y^2 \)
- **\( y^3 \) terms**: \( 2y^3, -4y^3, -6y^3 \)
2. **Combine the coefficients of like terms**:
- **For \( x^2 \)**:
- Only \( -x^2 \) remains.
- **For \( x^3 \)**:
- \( -2x^3 - 4x^3 - 2x^3 = -8x^3 \)
- **For \( y^2 \)**:
- \( 2y^2 - 7y^2 = -5y^2 \)
- **For \( y^3 \)**:
- \( 2y^3 - 4y^3 - 6y^3 = -8y^3 \)
3. **Write the simplified expression**:
\[
-8x^3 - x^2 - 5y^2 - 8y^3
\]
Thus, the fully simplified expression is:
\[
\boxed{-8x^3 - x^2 - 5y^2 - 8y^3}
\]
bluesanta
no it wants you to put it in a spicific order
GPT-4o mini
I apologize for any confusion! To arrange the expression in a specific order, we typically organize the terms by degree, starting with the highest degree down to the lowest, and then by variable. Here’s how to arrange the original terms and then combine them with the specified order in mind:
### Given Terms:
- \(-x^2\)
- \(-2x^3\)
- \(-4x^3\)
- \(-2x^3\)
- \(2y^2\)
- \(-7y^2\)
- \(2y^3\)
- \(-4y^3\)
- \(-6y^3\)
### Combine like terms:
1. **For \(x^3\)**:
- \(-2x^3 - 4x^3 - 2x^3 = -8x^3\)
2. **For \(x^2\)**:
- \(-x^2\)
3. **For \(y^2\)**:
- \(2y^2 - 7y^2 = -5y^2\)
4. **For \(y^3\)**:
- \(2y^3 - 4y^3 - 6y^3 = -8y^3\)
### Assembling into ordered format:
Now we put it all together in the order of decreasing powers of \(x\) first (highest degree first), followed by \(y\):
\[
-8x^3 - x^2 - 8y^3 - 5y^2
\]
### Final Ordered Expression:
\[
\boxed{-8x^3 - x^2 - 8y^3 - 5y^2}
\]
If you have a particular order in mind (e.g., by degree, or grouping specific variables together first), please let me know!
### Given Terms:
- \(-x^2\)
- \(-2x^3\)
- \(-4x^3\)
- \(-2x^3\)
- \(2y^2\)
- \(-7y^2\)
- \(2y^3\)
- \(-4y^3\)
- \(-6y^3\)
### Combine like terms:
1. **For \(x^3\)**:
- \(-2x^3 - 4x^3 - 2x^3 = -8x^3\)
2. **For \(x^2\)**:
- \(-x^2\)
3. **For \(y^2\)**:
- \(2y^2 - 7y^2 = -5y^2\)
4. **For \(y^3\)**:
- \(2y^3 - 4y^3 - 6y^3 = -8y^3\)
### Assembling into ordered format:
Now we put it all together in the order of decreasing powers of \(x\) first (highest degree first), followed by \(y\):
\[
-8x^3 - x^2 - 8y^3 - 5y^2
\]
### Final Ordered Expression:
\[
\boxed{-8x^3 - x^2 - 8y^3 - 5y^2}
\]
If you have a particular order in mind (e.g., by degree, or grouping specific variables together first), please let me know!