do my math homework problems

Certainly, I’d be happy to help you with your math homework problems! In the space of 1000 words, I’ll address a few math problems and provide explanations for each step. Please provide me with the specific problems you need help with, and I’ll get started.

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Problem 1: Solve for x in the equation 3x + 5 = 17.

To solve for x in this equation, we need to isolate x on one side. First, subtract 5 from both sides: 3x + 5 – 5 = 17 – 5 3x = 12

Now, divide both sides by 3 to solve for x: 3x / 3 = 12 / 3 x = 4

So, the solution to the equation is x = 4.

Problem 2: Simplify the expression (2x^2 – 5x + 3) + (x^2 + 2x – 7).

To simplify the expression, combine like terms: (2x^2 – 5x + 3) + (x^2 + 2x – 7) = 2x^2 + x^2 – 5x + 2x + 3 – 7 = 3x^2 – 3x – 4

The simplified expression is 3x^2 – 3x – 4.

Problem 3: Find the roots of the quadratic equation x^2 – 6x + 9 = 0.

To find the roots, we’ll use the quadratic formula: x = (-b ± √(b^2 – 4ac)) / 2a. In the equation, a = 1, b = -6, and c = 9.

Calculate the discriminant: b^2 – 4ac = (-6)^2 – 4 * 1 * 9 = 36 – 36 = 0.

Since the discriminant is 0, the quadratic equation has a repeated root. Apply the quadratic formula: x = (-(-6) ± √0) / (2 * 1) = (6 ± 0) / 2 = 3.

The repeated root is x = 3.

Problem 4: Evaluate the integral ∫(2x + 5) dx from x = 1 to x = 4.

To evaluate the integral, find the antiderivative of the function 2x + 5 with respect to x: ∫(2x + 5) dx = x^2 + 5x + C, where C is the constant of integration.

Now, evaluate the antiderivative at the upper and lower limits: [x^2 + 5x] from 1 to 4 = (4^2 + 5 * 4) – (1^2 + 5 * 1) = 16 + 20 – 1 – 5 = 30.

The value of the integral is 30.

Problem 5: Solve the inequality 2x – 3 > 9 and express the solution as an interval.

Add 3 to both sides of the inequality: 2x – 3 + 3 > 9 + 3 2x > 12

Divide both sides by 2: 2x / 2 > 12 / 2 x > 6

The solution to the inequality is x > 6. In interval notation, this is (6, ∞), which represents all real numbers greater than 6.

These explanations should help you understand and solve the given math problems. If you have more questions or need further assistance, feel free to ask!

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