High School Math Pre-test

The y-intercept of an equation represents the point where the line intersects the y-axis. To find the y-intercept, we set x = 0 in the equation and solve for y. In this case, when x = 0, the equation becomes y + 2(0) = 6, which simplifies to y = 6. Therefore, the y-intercept of the equation y + 2x = 6 is 6.

The slope of a linear equation is the coefficient of the x term. In the given equation, y = -2x + 3, the coefficient of the x term is -2. Therefore, the slope of the equation is -2.

The expression 10 - 2(3) can be simplified by performing the multiplication first. 2(3) equals 6, so the expression becomes 10 - 6. Subtracting 6 from 10 gives us 4. Therefore, the correct answer is 4.

The given system of equations can be solved using the method of substitution. We can solve the second equation for y, which gives us y = 9 - 3x. Substituting this value of y into the first equation, we get 3x - 2(9 - 3x) = 0. Simplifying this equation, we get 3x - 18 + 6x = 0, which further simplifies to 9x - 18 = 0. Solving for x, we get x = 2. Therefore, the value of x in the given system of equations is 2.

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The correct answer is -3 because when you subtract 32 from 6, you get -26. Then, when you divide -26 by 9, you get -3.

The expression (2x3)2 means we have to raise the quantity 2x3 to the power of 2. Simplifying this, we get (2x3)2 = 2^2 * (x^3)^2 = 4 * x^6. Therefore, the correct answer is 4x^6.

The given expression sqrt(200) can be simplified by finding the largest perfect square that divides 200. In this case, the largest perfect square is 100. Therefore, we can rewrite sqrt(200) as sqrt(100 * 2). Taking the square root of 100 gives us 10, and we are left with sqrt(2). Hence, the simplest radical form of sqrt(200) is 10*sqrt(2).

The given equation is a quadratic equation in the form of ax^2 + bx + c = 0. To solve it, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = -1, and c = -2. Plugging these values into the quadratic formula, we get x = (1 ± √(1 - 4(1)(-2))) / 2(1). Simplifying further, x = (1 ± √(1 + 8)) / 2, which becomes x = (1 ± √9) / 2. This gives us two possible solutions: x = (1 + 3) / 2 = 2 and x = (1 - 3) / 2 = -1. Therefore, the answer is x = 2, x = -1, or {2, -1}.

The first step to solving the equation 2k + 3 + 5k = 10 is to substitute values in for k. This means replacing all instances of k in the equation with the given values. Then, the next step is to subtract 5k from both sides of the equation to isolate the variable. Finally, adding 2k to 5k helps to combine like terms and simplify the equation further.

The correct answer is "Distributing the 2 into (m - 3)". This is the first step to solving the equation because it allows us to eliminate the parentheses and simplify the expression. By distributing the 2, we multiply it by both m and -3, resulting in 2m - 6. This step is necessary in order to combine like terms and further simplify the equation. The other options listed are not the first step because they do not address the need to distribute the 2.