To find the value of x given the equations 12y = 210 and 6y = 90, we can solve for y in both equations and then relate them to x. First, let’s start with the first equation: 1. Solve for y from the first equation: Given: 12y = 210 To isolate y, divide both sides … Read more
Finding the square root of a number and finding the cube root of a number are two different mathematical operations that serve distinct purposes and yield different results. Square Root: The square root of a number x is a value y such that when y is multiplied by itself (i.e., y × y), it equals … Read more
To convert the improper fraction 17/7 into a mixed number, you will follow these steps: Divide the numerator by the denominator: Start by dividing the top number (17) by the bottom number (7). Perform the division: When you divide 17 by 7, the result is 2 because 7 goes into 17 two times. This gives … Read more
To find the value of the expression 36x × 8y² when x = 3 and y = 6, we need to substitute the values of x and y into the expression. First, we substitute x = 3: 36 × 3 × 8y² Next, we will deal with the y part by substituting y = 6: … Read more
To factor the quadratic expression x² + 2x + 8, we first need to analyze the coefficients and the constant term. In this case, the expression is in the standard form of a quadratic, which is: ax² + bx + c Here, a = 1, b = 2, and c = 8. Next, we look … Read more
To solve the expression 3 – 3 * 6 + 2, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). 1. **Calculate the multiplication first:** 3 * 6 = 18 2. **Now substitute back … Read more
The next number in the sequence is 19. This sequence consists of prime numbers, which are numbers greater than 1 that have no divisors other than 1 and themselves. To clarify, the prime numbers included in the sequence so far are: 2 – the only even prime number 3 – the first odd prime number … Read more
The circumference of a circle can be calculated using the formula: C = 2 × π × r, where C represents the circumference, π (pi) is approximately 3.14, and r is the radius of the circle. In this case, the radius r is given as 7 inches. Plugging this value into the formula: C = … Read more
The equation of a line can often be expressed in standard form as Ax + By = C, where A, B, and C are integers, and A should be non-negative. Let’s analyze the equation you’ve given: 2x + 3y = 6. To clarify further, the standard form of the line can be derived and rearranged … Read more
Finding the Minimum and Maximum of a Quadratic Function A quadratic function is typically expressed in the standard form: f(x) = ax² + bx + c, where a, b, and c are constants. The shape of the graph of a quadratic function is a parabola. To find the minimum or maximum value of this function, … Read more