Algebra 2 Worksheet Answers 2- 1

Are you a high school student struggling with algebraic equations and expressions? Look no further! In this blog post, we will discuss the importance of worksheets in mastering algebraic concepts and provide you with the answers to the Algebra 2 Worksheet 2-1. Worksheets are an essential tool for students to practice and reinforce their understanding of the subject matter. Let's dive in!

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What is the value of x in the equation 2x + 5 = 17?

The value of x in the equation 2x + 5 = 17 is x = 6.

How can you simplify the expression (3x^2 + 4y^3) - (2x^2 + y^3)?

To simplify the expression (3x^2 + 4y^3) - (2x^2 + y^3), first distribute the negative sign inside the parentheses to get: 3x^2 + 4y^3 - 2x^2 - y^3. Next, combine like terms to simplify further: 3x^2 - 2x^2 + 4y^3 - y^3. This simplifies to x^2 + 3y^3.

Solve the inequality 3(5x - 2) < 12x - 5.

To solve the inequality 3(5x - 2) < 12x - 5, first distribute on the left side to get 15x - 6 < 12x - 5. Next, move all terms involving x to one side by subtracting 12x from both sides to get 3x - 6 < -5. Then, add 6 to both sides to obtain 3x < 1. Finally, divide by 3 to solve for x, which gives x < 1/3. Therefore, the solution to the inequality is x < 1/3.

Factorize the quadratic expression x^2 + 6x + 9.

The expression x^2 + 6x + 9 can be factorized as (x + 3)(x + 3) or (x + 3)^2, representing a perfect square trinomial.

What is the domain of the function f(x) = 1/x?

The domain of the function f(x) = 1/x is all real numbers except for x = 0.

Determine the vertex of the parabola represented by the equation y = x^2 - 4x + 3.

To determine the vertex of the parabola represented by the equation y = x^2 - 4x + 3, we can start by completing the square. By completing the square, we get y = (x - 2)^2 - 1. The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex. Therefore, the vertex of the parabola y = x^2 - 4x + 3 is (2, -1).

Solve the system of equations: 2x + y = 5 and 3x - 2y = -4.

To solve the system of equations, we can first isolate y in the first equation to get y = 5 - 2x. Then we can substitute this expression for y into the second equation: 3x - 2(5 - 2x) = -4. Simplifying this equation, we get 3x - 10 + 4x = -4, which simplifies further to 7x - 10 = -4. Solving for x, we get x = 6/7. Substituting this value back into the expression for y, y = 5 - 2(6/7), we find that y = 23/7. Therefore, the solution to the system of equations is x = 6/7 and y = 23/7.

Find the x-intercept of the graph of the equation 2y = 4x - 8.

To find the x-intercept of the graph of the equation 2y = 4x - 8, we set y equal to zero because the x-intercept is where the line crosses the x-axis. So, we have 2(0) = 4x - 8, which simplifies to 0 = 4x - 8. Adding 8 to both sides gives 8 = 4x, and dividing both sides by 4 yields x = 2. Therefore, the x-intercept of the graph is at the point (2, 0).

Simplify the expression (2/3) * (3/5) * (5/7).

To simplify the expression (2/3) * (3/5) * (5/7), we multiply the numerators and denominators separately. This gives us (2 * 3 * 5) / (3 * 5 * 7), which simplifies to 30/105. Further simplifying by dividing both numerator and denominator by 15, we get the final simplified result of 2/7.

Solve the logarithmic equation log(base 2)(x) = log(base 3)(8).

To solve the equation log(base 2)(x) = log(base 3)(8), you can use the property that if two logarithms with different bases are equal, then their arguments are equal as well. Therefore, we have x = 8, since the logarithms are equal in this case.