Question
Answer questions 1–19 in your test book. You may NOT use a calculator. 1. Which shows a number that is not equivalent to 23}} 8? 햠 3}} 28햡 8}} 23햢 20.375 햣 2 3} 82. Which expressions are equivalent to 12x 2 6? Select all that apply. -6(2x-1) 6(2x-1) 6x(2-1) -6x(2x-1) -6(-2x+1) 6(-2x+1)
Answers
GPT-4o mini
1. To determine which number is not equivalent to \(\frac{23}{8}\), we first convert \(\frac{23}{8}\) to a decimal form.
Calculating \(\frac{23}{8}\):
\[
23 \div 8 = 2.875
\]
Now, let's examine the options given:
- \(\frac{3}{28} \approx 0.107\), which is not equivalent to \(2.875\).
- \(\frac{8}{23} \approx 0.348\), which is not equivalent to \(2.875\).
- \(20.375\), which is not equivalent to \(2.875\).
- \(\frac{2}{3} \approx 0.667\), which is also not equivalent to \(2.875\).
All the options listed appear to be not equivalent to \(\frac{23}{8}\).
However, if we were to further clarify that all of them are fewer than \(2.875\) as well. If the expectation is to find one that exactly matches \(\frac{23}{8}\):
The answer is that all of the provided options are not equivalent.
---
2. To determine which expressions are equivalent to \(12x^2 - 6\), we can factor the expression and check the given options.
Starting with \(12x^2 - 6\):
\[
12x^2 - 6 = 6(2x^2 - 1)
\]
Now, we can apply the difference of squares:
\[
2x^2 - 1 = (2x - 1)(2x + 1)
\]
Therefore,
\[
12x^2 - 6 = 6(2x - 1)(2x + 1)
\]
Now let’s check the given options:
1. \(-6(2x-1)\): Not equivalent.
2. \(6(2x-1)\): This can work as it’s a factor.
3. \(6x(2-1)\): Not equivalent.
4. \(-6x(2x-1)\): Not equivalent.
5. \(-6(-2x+1)\): Simplifies to \(6(2x-1)\), which is equivalent.
6. \(6(-2x+1)\): Simplifies to \(-6(2x-1)\), which is not equivalent.
The equivalent expressions from the list are:
- \(6(2x-1)\)
- \(-6(-2x+1)\)
**Final Answers:**
1. All options are not equivalent to \(\frac{23}{8}\).
2. The expressions equivalent to \(12x^2 - 6\) are \(6(2x-1)\) and \(-6(-2x+1)\).
Calculating \(\frac{23}{8}\):
\[
23 \div 8 = 2.875
\]
Now, let's examine the options given:
- \(\frac{3}{28} \approx 0.107\), which is not equivalent to \(2.875\).
- \(\frac{8}{23} \approx 0.348\), which is not equivalent to \(2.875\).
- \(20.375\), which is not equivalent to \(2.875\).
- \(\frac{2}{3} \approx 0.667\), which is also not equivalent to \(2.875\).
All the options listed appear to be not equivalent to \(\frac{23}{8}\).
However, if we were to further clarify that all of them are fewer than \(2.875\) as well. If the expectation is to find one that exactly matches \(\frac{23}{8}\):
The answer is that all of the provided options are not equivalent.
---
2. To determine which expressions are equivalent to \(12x^2 - 6\), we can factor the expression and check the given options.
Starting with \(12x^2 - 6\):
\[
12x^2 - 6 = 6(2x^2 - 1)
\]
Now, we can apply the difference of squares:
\[
2x^2 - 1 = (2x - 1)(2x + 1)
\]
Therefore,
\[
12x^2 - 6 = 6(2x - 1)(2x + 1)
\]
Now let’s check the given options:
1. \(-6(2x-1)\): Not equivalent.
2. \(6(2x-1)\): This can work as it’s a factor.
3. \(6x(2-1)\): Not equivalent.
4. \(-6x(2x-1)\): Not equivalent.
5. \(-6(-2x+1)\): Simplifies to \(6(2x-1)\), which is equivalent.
6. \(6(-2x+1)\): Simplifies to \(-6(2x-1)\), which is not equivalent.
The equivalent expressions from the list are:
- \(6(2x-1)\)
- \(-6(-2x+1)\)
**Final Answers:**
1. All options are not equivalent to \(\frac{23}{8}\).
2. The expressions equivalent to \(12x^2 - 6\) are \(6(2x-1)\) and \(-6(-2x+1)\).