Question

select all of the true statements below.
(9b + 5) is written as a sum of three terms.
in 9b, 9 is a coefficient.
4 is a factor.
in (9b + 5), 9b is a constant.
3 and 8 are like terms.
none of these are true.

Explanation:

Step1: Analyze each statement

• Statement 1: \((9b + 5)\) has two terms (\(9b\) and \(5\)), not three. So this is false.
• Statement 2: In \(9b\), the number multiplying the variable \(b\) is \(9\), so \(9\) is a coefficient. This is true.
• Statement 3: The problem doesn't show an expression where \(4\) is a factor (no context about a product involving \(4\)). So this is false.
• Statement 4: \(9b\) has a variable, so it's not a constant (constants have no variables). This is false.
• Statement 5: \(3\) and \(8\) are both constants (like terms are terms with the same variable part; constants have the same "variable part" (none), so they are like terms). This is true.
• Statement 6: Since some statements are true, this is false.

Step2: Identify true statements

From the analysis, "In \(9b\), \(9\) is a coefficient" and "3 and 8 are like terms" are true. But let's check the options again (maybe I missed context, but based on standard definitions):
Wait, maybe the original problem had a typo or missing context, but based on the given options:
Wait, the first statement: \((9b + 5)\) has two terms, so false.
Second: coefficient definition: number in front of variable, so true.
Third: "4 is a factor" – no expression given with 4, so false.
Fourth: \(9b\) has a variable, so not constant, false.
Fifth: 3 and 8 are constants, so like terms (since like terms can be constants), true.
So the true statements are "In \(9b\), \(9\) is a coefficient" and "3 and 8 are like terms". But let's check the options as presented. Wait, maybe the user's problem had a previous part, but based on the given:

Wait, the options are checkboxes. Let's re-express:

1. \((9b + 5)\) is sum of three terms: false.
2. In \(9b\), 9 is coefficient: true.
3. 4 is a factor: false (no expression with 4).
4. In \((9b + 5)\), \(9b\) is constant: false (has variable).
5. 3 and 8 are like terms: true (both constants, so like terms).
6. None of these: false.

So the true statements are the second and fifth checkboxes. But let's confirm the options:

The checkboxes are:

• \((9b + 5)\) is written as a sum of three terms: false.
• In \(9b\), 9 is a coefficient: true.
• 4 is a factor: false (no context).
• In \((9b + 5)\), \(9b\) is a constant: false.
• 3 and 8 are like terms: true.
• None of these are true: false.

So the true ones are "In \(9b\), 9 is a coefficient" and "3 and 8 are like terms". But maybe the problem had a different context, but based on standard math definitions, those two are true. However, let's check again:

Wait, maybe the "4 is a factor" is from a previous problem, but since it's not here, we can't assume. So based on the given:

The true statements are:

• In \(9b\), 9 is a coefficient.
• 3 and 8 are like terms.

But let's check the options as presented. The user's image shows the checkboxes, so the correct checkboxes to select are "In \(9b\), 9 is a coefficient" and "3 and 8 are like terms". But maybe I made a mistake. Wait, 3 and 8: like terms are terms that can be combined, and constants are like terms. So yes, 3 and 8 are like terms. And 9 is a coefficient of \(9b\).

Answer:

The true statements are:

• In \(9b\), 9 is a coefficient.
• 3 and 8 are like terms.

(So the checkboxes to select are the second and fifth ones, assuming the fifth is "3 and 8 are like terms" and the second is "In \(9b\), 9 is a coefficient".)