9th Grade Math Review Worksheet with various math problems and a space for answers.

Here's the step-by-step solution to each problem on the 9th Grade Math Worksheet:

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Problem 1: Find x. Round to the nearest tenth.

We have a right triangle with:
- One acute angle = 25°
- Adjacent side to that angle = 15
- Opposite side (to the 25° angle) = x

We use the tangent function:

> tan(θ) = opposite / adjacent
> tan(25°) = x / 15

Multiply both sides by 15:

> x = 15 × tan(25°)

Using a calculator:

> tan(25°) ≈ 0.4663
> x ≈ 15 × 0.4663 ≈ 6.9945

Rounded to the nearest tenth:

✔ Answer: 7.0

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Problem 2: Solve. -4x - 5x < 18

Combine like terms:

> -9x < 18

Divide both sides by -9. Remember: when dividing by a negative number, flip the inequality sign.

> x > -2

✔ Answer: x > -2

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**Problem 3: Simplify. Write each answer in scientific notation.
(2.53 × 10⁻⁵)(4 × 10⁰)**

First, multiply the coefficients:

> 2.53 × 4 = 10.12

Then add the exponents of 10:

> 10⁻⁵ × 10⁰ = 10⁻⁵

So we have:

> 10.12 × 10⁻⁵

But this is not in proper scientific notation because the coefficient must be between 1 and 10.

Convert 10.12 to 1.012 × 10¹:

> 1.012 × 10¹ × 10⁻⁵ = 1.012 × 10⁻⁴

✔ Answer: 1.012 × 10⁻⁴

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**Problem 4: Evaluate each function at the given value.
f(x) = 10 × 2ˣ at x = -4**

Plug in x = -4:

> f(-4) = 10 × 2⁻⁴

Recall: 2⁻⁴ = 1 / 2⁴ = 1 / 16

> f(-4) = 10 × (1/16) = 10/16 = 5/8 = 0.625

✔ Answer: 0.625

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**Problem 5: Simplify the following expression.
(2x³ - x²) - (3x³ - 2x²)**

Distribute the minus sign:

> 2x³ - x² - 3x³ + 2x²

Combine like terms:

- x³ terms: 2x³ - 3x³ = -x³
- x² terms: -x² + 2x² = x²

✔ Answer: -x³ + x²

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✔ Final Answers:

1. 7.0
2. x > -2
3. 1.012 × 10⁻⁴
4. 0.625
5. -x³ + x²

Let me know if you’d like these explained further!