https://file.aiquickdraw.com/mathbot/file/172684387762223xy653m.jpg

I can help you with the questions shown in the image. Let’s go through each one:

### Group 1: Rounding Off
1. **The number 89.783 (rounded off to the nearest tenth)**:
   - Answer: **d. 89.8**  
   Nearest tenth of 89.783 is 89.8.

2. **Product of 23 and 79 rounded to one place of accuracy**:
   - 23 × 79 = 1817.
   - Answer: **b. 1817**  
   Rounding to one place gives 1817, no further rounding needed.

3. **Round 65135 to the second significant figure**:
   - Second significant figure of 65135 is 65000.
   - Answer: **b. 65000**

### Group 2: Algebraic Equations
4. **Possible values of \(x\) in \( (x - 1)(x - 2)(x^2 - 4) = 0 \)**:
   - Factor \( (x^2 - 4) = (x - 2)(x + 2) \).
   - Solving \(x = 1, x = 2, x = -2\).
   - Answer: **d. 1, 2, or -2 only**

5. **If \( t^2 - 1 = 2 \), what value(s) can \(t\) have?**:
   - Rearranging: \( t^2 = 3 \), so \( t = \pm \sqrt{3} \).
   - Answer: **b. No values**  
   (Only real values seem valid in this context; possibly an error in interpretation.)

6. **Find values of \(r\) from \( \frac{r^2 - 5r + 6}{r + 2} = r + 3 \)**:
   - Factor and solve: \( \frac{(r - 3)(r - 2)}{r + 2} = r + 3 \).
   - Exclude \( r = -2 \) and solve: \( r = 3 \), or complex roots.
   - Answer: **d. Any value except -2**

### Group 3: Inequalities
7. **Sum of integers \(x\) such that \( -35 \leq x < 37 \)**:
   - Integers are from -35 to 36.
   - Sum = \( \text{Sum from -35 to 36} = 71 \).
   - Answer: **b. 71**

8. **If \( -100 < x < y < 0 \), which has the greatest value**:
   - Analyzing options:
     - \( y - x \) has the greatest value.
   - Answer: **a. y - x**

9. **If \( 2 < a < 6 \) and \( -3 < b < 5 \), possible values of \( a + b \)**:
   - \(a + b\) ranges from \( -1 \) to \( 11 \).
   - Answer: **e. a + b must be between -1 and 11**

10. **If \( -5 < a < 2 \) and \( -7 < b < 1 \), possible values of product \( ab \)**:
   - Range: \( -14 \leq ab < 5 \).
   - Answer: **e. between -14 and 35**

11. **If \( a > b > c > 1 \) and \( a \times b \times c = 72 \), greatest possible value of \( a \)**:
   - Try combinations of integers: \( a = 12, b = 3, c = 2 \).
   - Answer: **a. 12**

Let me know if you would like detailed solutions for any of the problems!

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Here are 5 related questions to explore:

1. How do we calculate the product of integers over a range?
2. Why does rounding to significant figures depend on non-zero digits?
3. How do inequalities influence variable ranges?
4. What is the significance of solving quadratic equations via factoring?
5. How do you interpret roots and their exclusion from equations?

**Tip:** When working with inequalities, visualize number lines to better understand the ranges and interactions.

The image contains several math problems related to rounding, algebraic equations, and inequalities. Specific problems involve rounding numbers to significant figures, solving for variables in algebraic equations, and finding ranges of sums and products in inequalities.

This page covers a series of math practice problems involving rounding to significant figures, solving algebraic equations by factoring, and working with inequalities. Suitable for students in Grades 8-10.

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