Asked by sunrise_lover09

Is the number
–
9+9 rational or irrational?
Answered by sunrise_lover09
Is the number
–
7+
–
2 rational or irrational?
Answered by sunrise_lover09
Is the number 4+​𝜋 rational or irrational?
Answered by sunrise_lover09
Is the number 1+
–
6 rational or irrational?
Answered by sunrise_lover09
Is the number 8+7 rational or irrational?
Answered by sunrise_lover09
Is the number ​𝜋+8 rational or irrational?
Answered by sunrise_lover09
Is the number
3 x 3 rational or irrational?
Answered by sunrise_lover09
Is the number
–
9+​𝜋 rational or irrational?
Answered by sunrise_lover09
Is the number 5 x 3 rational or irrational?
Answered by sunrise_lover09
Is the number ​𝜋 x 8 rational or irrational?
Answered by sunrise_lover09
Is the number
–
7+​𝜋 rational or irrational?
Answered by sunrise_lover09
s the number
32+
–
3 rational or irrational?
Answered by sunrise_lover09
Is the number
–
42 rational or irrational?
Answered by sunrise_lover09
Is the number
–
7+​𝜋 rational or irrational?
Answered by sunrise_lover09
Is the number
–
8+
–
2 rational or irrational?
Answered by sunrise_lover09
s the number 8
–
7 rational or irrational?
Answered by sunrise_lover09
Is the number
–
6+
22 rational or irrational?
Answered by sunrise_lover09
Is the number
–
3
–
7 rational or irrational?
Answered by sunrise_lover09
Is the number
34+
–
10 rational or irrational?
Answered by sunrise_lover09
Is the number ​𝜋+4 rational or irrational?
Answered by sunrise_lover09
Is the number 3+1 rational or irrational?
Answered by sunrise_lover09
Which point is a solution to y ≤ 4x + 5?
Group of answer choices

(–4, 0)

(–6, 4)

(0, –2)

(0, 10)

Flag question: Question 2
Question 21 pts
The point (0, 0) is a solution to which of these inequalities?
Group of answer choices

y – 7 < 2x – 6

y – 6 < 2x – 7

y + 7 < 2x + 6

y + 7 < 2x – 6

Flag question: Question 3
Question 31 pts
Which point is a solution to the inequality shown in this graph?




Group of answer choices

(5, –5)

(3, –1)

(1, 5)

(–3, –3)

Flag question: Question 4
Question 41 pts
Which point is a solution to the inequality shown in this graph?




Group of answer choices

(0, –5)

(3, –1)

(0, 0)

(5, –5)

Flag question: Question 5
Question 51 pts
Joel and Nolan are working on a math test, and both wrote a different inequality for the graph below. Which student is correct, and why?

Joel Nolan
y ≤ –2x – 2 y ≤ 2x – 2

Group of answer choices

Joel, because the less than sign tells us the line is dashed/dotted.

Nolan, because the less than or equal to symbol tells us that the line is solid and should be shaded below the line. The line has a positive slope.

Joel, because the less than or equal to symbol tells us that the line is solid and should be shaded below the line. The line has a negative slope.

Nolan, because the less than sign tells us the line is dashed/dotted.
Answered by GPT-4o mini
The expression \(-9 + 9\) simplifies to \(0\).

A rational number is defined as any number that can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\). Since \(0\) can be expressed as \(\frac{0}{1}\) (or \(\frac{0}{2}\), etc.), it is considered a rational number.

Therefore, \(-9 + 9\) is a rational number.
Answered by GPT-4o mini
The expression \(-7 + -2\) simplifies to \(-9\).

Since \(-9\) can be expressed as \(\frac{-9}{1}\), it is a rational number.

Therefore, \(-7 + -2\) is a rational number.
Answered by GPT-4o mini
The number \(\pi\) is an irrational number, meaning it cannot be expressed as a fraction of two integers.

When you add a rational number (like \(4\)) to an irrational number (like \(\pi\)), the result is always irrational. Therefore, the expression \(4 + \pi\) is irrational.
Answered by GPT-4o mini
The expression \(1 + -6\) simplifies to \(1 - 6\), which equals \(-5\).

Since \(-5\) can be expressed as \(\frac{-5}{1}\), it is a rational number.

Therefore, \(1 + -6\) is a rational number.
Answered by GPT-4o mini
The expression \(8 + 7\) simplifies to \(15\).

Since \(15\) can be expressed as \(\frac{15}{1}\), it is a rational number.

Therefore, \(8 + 7\) is a rational number.
Answered by GPT-4o mini
The number \(\pi\) is an irrational number, meaning it cannot be expressed as a fraction of two integers.

When you add an irrational number (like \(\pi\)) to a rational number (like \(8\)), the result is always irrational. Therefore, the expression \(\pi + 8\) is irrational.
Answered by GPT-4o mini
The expression \(3 \times 3\) simplifies to \(9\).

Since \(9\) can be expressed as \(\frac{9}{1}\), it is a rational number.

Therefore, \(3 \times 3\) is a rational number.
Answered by GPT-4o mini
The number \(-9\) is a rational number, while \(\pi\) is an irrational number.

When you add a rational number (like \(-9\)) to an irrational number (like \(\pi\)), the result is always irrational. Therefore, the expression \(-9 + \pi\) is irrational.
Answered by GPT-4o mini
The expression \(5 \times 3\) simplifies to \(15\).

Since \(15\) can be expressed as \(\frac{15}{1}\), it is a rational number.

Therefore, \(5 \times 3\) is a rational number.
Answered by GPT-4o mini
The number \(\pi\) is an irrational number, meaning it cannot be expressed as a fraction of two integers.

When you multiply an irrational number (like \(\pi\)) by a rational number (like \(8\)), the result is always irrational. Therefore, the expression \(\pi \times 8\) is irrational.
Answered by GPT-4o mini
The number \(-7\) is a rational number, while \(\pi\) is an irrational number.

When you add a rational number (like \(-7\)) to an irrational number (like \(\pi\)), the result is always irrational. Therefore, the expression \(-7 + \pi\) is irrational.
Answered by GPT-4o mini
The expression \(32 + -3\) simplifies to \(32 - 3\), which equals \(29\).

Since \(29\) can be expressed as \(\frac{29}{1}\), it is a rational number.

Therefore, \(32 + -3\) is a rational number.
Answered by GPT-4o mini
The number \(-42\) is a rational number because it can be expressed as a fraction, specifically \(\frac{-42}{1}\).

Therefore, \(-42\) is a rational number.
Answered by GPT-4o mini
The number \(-7\) is a rational number, and \(\pi\) is an irrational number.

When you add a rational number (like \(-7\)) to an irrational number (like \(\pi\)), the result is always irrational. Therefore, the expression \(-7 + \pi\) is irrational.
Answered by GPT-4o mini
The expression \(-8 + -2\) simplifies to \(-10\).

Since \(-10\) can be expressed as \(\frac{-10}{1}\), it is a rational number.

Therefore, \(-8 + -2\) is a rational number.
Answered by GPT-4o mini
The expression \(8 - 7\) simplifies to \(1\).

Since \(1\) can be expressed as \(\frac{1}{1}\), it is a rational number.

Therefore, \(8 - 7\) is a rational number.
Answered by GPT-4o mini
The expression \(-6 + 22\) simplifies to \(16\).

Since \(16\) can be expressed as \(\frac{16}{1}\), it is a rational number.

Therefore, \(-6 + 22\) is a rational number.
Answered by GPT-4o mini
The expression \(-3 - 7\) simplifies to \(-10\).

Since \(-10\) can be expressed as \(\frac{-10}{1}\), it is a rational number.

Therefore, \(-3 - 7\) is a rational number.
Answered by GPT-4o mini
The expression \(34 + -10\) simplifies to \(34 - 10\), which equals \(24\).

Since \(24\) can be expressed as \(\frac{24}{1}\), it is a rational number.

Therefore, \(34 + -10\) is a rational number.
Answered by GPT-4o mini
The number \(\pi\) is an irrational number, meaning it cannot be expressed as a fraction of two integers.

When you add an irrational number (like \(\pi\)) to a rational number (like \(4\)), the result is always irrational. Therefore, the expression \(\pi + 4\) is irrational.
Answered by GPT-4o mini
The expression \(3 + 1\) simplifies to \(4\).

Since \(4\) can be expressed as \(\frac{4}{1}\), it is a rational number.

Therefore, \(3 + 1\) is a rational number.
Answered by GPT-4o mini
Let's go through each question one at a time.

### Question 1:

**Which point is a solution to \(y ≤ 4x + 5\)?**

We will test each option by substituting \(x\) into \(y ≤ 4x + 5\).

1. **(–4, 0)**:
\(y ≤ 4(-4) + 5\)
\(0 ≤ -16 + 5\)
\(0 ≤ -11\) (False)

2. **(–6, 4)**:
\(y ≤ 4(-6) + 5\)
\(4 ≤ -24 + 5\)
\(4 ≤ -19\) (False)

3. **(0, –2)**:
\(y ≤ 4(0) + 5\)
\(-2 ≤ 0 + 5\)
\(-2 ≤ 5\) (True)

4. **(0, 10)**:
\(y ≤ 4(0) + 5\)
\(10 ≤ 0 + 5\)
\(10 ≤ 5\) (False)

The solution is **(0, -2)**.

---

### Question 2:

**The point (0, 0) is a solution to which of these inequalities?**

We will substitute \(x = 0\) and \(y = 0\) into each inequality.

1. **\(y - 7 < 2x - 6\)**:
\(0 - 7 < 2(0) - 6\)
\(-7 < -6\) (False)

2. **\(y - 6 < 2x - 7\)**:
\(0 - 6 < 2(0) - 7\)
\(-6 < -7\) (False)

3. **\(y + 7 < 2x + 6\)**:
\(0 + 7 < 2(0) + 6\)
\(7 < 6\) (False)

4. **\(y + 7 < 2x - 6\)**:
\(0 + 7 < 2(0) - 6\)
\(7 < -6\) (False)

None of the inequalities hold true for (0, 0).

---

### Question 3:

**Which point is a solution to the inequality shown in this graph?**

Assuming the graph depicts some linear inequality, we will evaluate each given point based on a general idea:

1. \( (5, -5) \): Evaluate based on the graph.
2. \( (3, -1) \): Evaluate based on the graph.
3. \( (1, 5) \): Evaluate based on the graph.
4. \( (-3, -3) \): Evaluate based on the graph.

Since I don't have the graph but typically need to check their positions relative to the boundary line, further information from the graph would clarify the right choice.

---

### Question 4:

**Which point is a solution to the inequality shown in this graph?**

Similar to Question 3, assuming there's a graph, you'll evaluate each point to see which makes the inequality true based on its specific representation.

---

### Question 5:

**Which student is correct, and why?**

To determine who is correct based on their inequalities:

- Joel's inequality \(y ≤ -2x - 2\) suggests a line with a negative slope and shaded below the line (solid line due to "≤").
- Nolan's inequality \(y ≤ 2x - 2\) suggests a line with a positive slope and shaded below (also solid line).

Without the graph, it is common to discuss the nature of the slopes; however, Joel's inequality suggests a downward trend, whereas Nolan’s indicates an upward trend.

If the graph has a downward line, the correct response would be **Joel**, because the less than or equal to symbol indicates the shading below the line with a negative slope.

If you provide specific details on the accompanying graphs, I can give more tailored responses for Questions 3 and 4!