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To determine the number of solutions for the given system of equations, we can manipulate the equations and analyze their relationships. The system of equations is: Equation 1: x + 2y = 24 Equation 2: 3x – 6y = 72 First, let’s simplify Equation 2. We can divide every term by 3: 3x – 6y … Read more

To simplify the expression 6x2y2y23, we will follow the steps of combining like terms and performing multiplication. 1. **First, write the expression clearly:** This can be expressed as: 6 * x2 * y2 * y2 * 3 2. **Now let’s group the coefficients and the variable parts:** The coefficients are 6 and 3, which can … Read more

The base of a natural logarithm, denoted as ln, is the mathematical constant e. This constant is approximately equal to 2.71828. The natural logarithm is defined as the logarithm to the base e. In simpler terms, if you have an equation in the form of y = e^x, then the natural logarithm ln(y) will give … Read more

Finding the Equation of a Line To find the equation of a line, we can use the point-slope form of a linear equation, which is given by: y – y1 = m(x – x1) In this equation: m is the slope of the line. (x1, y1) is a specific point on the line. Given that … Read more

Finding the Third Number To find the third number when the highest common factor (HCF) of 3240, 3600, and this number is 36, and the least common multiple (LCM) is 2435520, follow these steps: Step 1: Understanding HCF and LCM The HCF of a set of numbers is the largest integer that divides each of … Read more

To determine how many solutions the linear system has, we need to analyze the two equations: Equation 1: y = 2x + 5 Equation 2: 8x – 4y = 20 First, let’s rearrange Equation 2 to express it in slope-intercept form (y = mx + b) similar to Equation 1. We want to isolate y: … Read more

To calculate the slope of a line that passes through two points, you can use the slope formula: slope (m) = (y2 – y1) / (x2 – x1) Here, (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we have: Point 1: (2, 5) – So, x1 = 2 … Read more

To find the quotient of dividing the polynomial x^3 + 5x^2 + 3x + 8 by x + 3, we can use polynomial long division. 1. **Set up the long division**: Write x^3 + 5x^2 + 3x + 8 under the long division bar and x + 3 outside. 2. **Divide the first term**: Divide … Read more

Solving the Equation: 4 log12(2) + log12(x) + log12(96) To solve the equation 4 log12(2) + log12(x) + log12(96) = 0, we will follow a step-by-step approach. Step 1: Simplify the logs First, let’s break down the individual logarithmic components: Calculate 4 log12(2): Using the property of logarithms that states k logb(a) = logb(ak), we … Read more

The equation of a circle can be derived from its center coordinates and radius. In general, the standard form of the equation of a circle is given by: (x – h)2 + (y – k)2 = r2 Here, (h, k) represents the coordinates of the center of the circle, and r represents the radius. Given … Read more