The Power of Open-Ended Play Quiz

To solve the equation, subtract 3 from both sides to obtain x = 7 - 3, which equals 4. This basic linear equation tests simple algebraic manipulation.

Calculating 10% of a number involves multiplying it by 0.1. Multiplying 200 by 0.1 gives 20, demonstrating a fundamental percentage calculation.

2 raised to the 4th power means multiplying 2 by itself four times: 2 x 2 x 2 x 2 equals 16. This reinforces the concept of exponents.

Dividing 12 by 3 results in 4. This question checks the student's ability to perform basic division.

Following the order of operations, multiply 2 by 3 to get 6, and then add 5, resulting in 11. This question emphasizes the importance of PEMDAS/BODMAS.

By adding 5 to both sides, the equation becomes 2x = 8, and dividing both sides by 2 gives x = 4. This problem reinforces basic solving of linear equations.

The quadratic factors into (x + 2)(x + 3) because 2 and 3 multiply to 6 and add up to 5. Recognizing these factor pairs is crucial for solving quadratic expressions.

Dividing the equation 2y = 6x - 4 by 2 gives y = 3x - 2, where the slope is the coefficient of x, which is 3. This tests understanding of converting equations to slope-intercept form.

Substitute x = 5 into the function to get f(5) = 2(5) + 1, which equals 11. This direct substitution reinforces the concept of evaluating functions.

The area of a triangle is given by the formula ½ à - base à - height. Substituting in the given values, we get ½ à - 10 à - 6 = 30.

Dividing both sides by 3 yields y - 2 = 3, and then adding 2 to both sides gives y = 5. This is a standard approach to solving linear equations involving a distributive property.

Subtract 4 from both sides to obtain 3x = 15, and then divide by 3 to get x = 5. This reinforces the method of isolating the variable.

First, calculate 3² to get 9, then multiply by 2 to obtain 18, and finally subtract 4 to reach 14. This problem emphasizes following the correct order of operations.

Distribute 4 across (x + 3) to get 4x + 12, then subtract 2x to simplify the expression to 2x + 12. This question tests the distributive property and combining like terms.

Arranging the set in order gives {1, 3, 5, 7, 9}, where the middle number is 5. The median is the value that lies in the center of a sorted data set.

The quadratic factors as (x - 2)(x - 3) = 0, which implies that the solutions are x = 2 and x = 3. Factoring is a fundamental technique for solving quadratic equations.

The perimeter of a rectangle is given by 2(length + width). Setting up the equation 2(10 + width) = 30 leads to 10 + width = 15, so the width is 5 units. This problem integrates algebra with geometric formulas.

Using the area formula A = πr², set πr² equal to 50π, which simplifies to r² = 50. Taking the square root gives r = √50, which simplifies to 5√2.

Expanding both sides gives 3x - 6 = 2x + 8 + 1, which simplifies to 3x - 6 = 2x + 9. Subtracting 2x and adding 6 leads to x = 15. This problem involves careful use of the distributive property and combining like terms.

The x-coordinate of the vertex is given by -b/(2a). Here, -(-4)/(2*1) equals 2, and substituting x = 2 into the function yields y = -1. This vertex (2, -1) represents the minimum point of the parabola.