Middle School Math Strategies

To solve the equation, we need to isolate the variable x on one side of the equation. Subtracting 5 from both sides, we get 3x = 12. Dividing both sides by 3, we find x = 4.

The area of a triangle is given by the formula A = (1/2) * b * h, where b is the base and h is the height. Substituting the given values, we get A = (1/2) * 8 cm * 6 cm = 24 cm^2.

When flipping a coin, there are two possible outcomes: head or tail. Since both outcomes are equally likely, the probability of getting a head is 1/2.

To simplify the expression, we can combine like terms. (x^2 + 2x + 1) - (x^2 - 3x + 2) = x^2 + 2x + 1 - x^2 + 3x - 2 = 5x - 1.

The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height. Substituting the given values, we get V = 10 cm * 5 cm * 3 cm = 150 cm^3.

To solve the inequality, we need to isolate the variable x on one side of the inequality. Adding 5 to both sides, we get 2x < 14. Dividing both sides by 2, we find x < 7.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1). Substituting the given values, we get m = (7 - 3) / (5 - 2) = 4 / 3 = 2.

To simplify the expression, we can use the power of a power rule, which states that (a^m)^n = a^(m * n). Therefore, (3x^2y^3)^2 = 3^(2) * (x^2)^2 * (y^3)^2 = 9x^4y^6.

The area of a circle is given by the formula A = πr^2, where r is the radius. Substituting the given value, we get A = π * (7 cm)^2 = 147π cm^2.

To solve the equation, we need to isolate the variable x on one side of the equation. Distributing the 2, we get 2x + 6 = 10. Subtracting 6 from both sides, we find 2x = 4. Dividing both sides by 2, we get x = 2.

The mean of a set of numbers is the sum of the numbers divided by the number of numbers. In this case, the mean is (5 + 7 + 9 + 11 + 13) / 5 = 45 / 5 = 9.

To simplify the expression, we can use the distributive property. (x - 2)(x + 3) = x(x + 3) - 2(x + 3) = x^2 + 3x - 2x - 6 = x^2 + x - 6.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius. Substituting the given value, we get V = (4/3)π * (5 cm)^3 = 250π cm^3.

To solve the inequality, we need to isolate the variable x on one side of the inequality. Adding 2 to both sides, we get 3x > 10. Dividing both sides by 3, we find x > 10/3. Therefore, x > 3.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting the given values, we get y = -3x + b. To find the value of b, we can use the point (2, 5). Substituting x = 2 and y = 5, we get 5 = -3(2) + b. Solving for b, we find b = 11. Therefore, the equation of the line is y = -3x + 11.