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To determine how many solutions exist for the equation 3×10 = 6 + 3×12, we first need to rearrange it into a standard form where one side equals zero. Start by subtracting 3×12 from both sides: 3×10 – 3×12 – 6 = 0 Next, factor out 3 from the left-hand side: 3(x10 – x12 – … Read more

To find the approximate solutions of the equation 4x² + 2x – 17 = 0, we can use the quadratic formula given by: x = (-b ± √(b² – 4ac)) / 2a In our case, the coefficients are: a = 4 b = 2 c = -17 First, let’s calculate the discriminant: b² – 4ac … Read more

To convert the quadratic function f(x) = x² + 12x + 6 into vertex form, we need to identify a suitable zero pair. The vertex form of a quadratic function is typically written as: f(x) = a(x – h)² + k Where (h, k) is the vertex of the parabola. To achieve this, we can … Read more

Converting Cartesian Coordinates to Polar Form To convert an equation from Cartesian coordinates (in terms of x and y) to polar coordinates (in terms of r and θ), we use the following relationships: x = r * cos(θ) y = r * sin(θ) r = sqrt(x² + y²) θ = atan2(y, x) Let’s go through … Read more

To find the difference between the polynomials 7y², 6xy, 2xy, and 3, we first need to identify which polynomials we are comparing and how to express this difference mathematically. Let’s break this down step-by-step: Identify the Polynomials: Polynomial 1: 7y² Polynomial 2: 6xy Polynomial 3: 2xy Polynomial 4: 3 Organize the Polynomials: If we are … Read more

Solving the Equation \( \frac{2}{3} x + 4 = 2x \) To solve the equation \( \frac{2}{3} x + 4 = 2x \), we will follow a series of steps to isolate the variable \( x \). Step 1: Eliminate the Fraction To make calculations easier, we can eliminate the fraction by multiplying every term … Read more

To solve this problem, we need to set up equations based on the given information. Let B’s walking speed be v km/h. Therefore, the time taken by B to walk 30 km can be expressed as: Time taken by B = Distance / Speed = 30 / v According to the problem, A takes 3 … Read more

To find the product of the numbers 20, 1, 2, 19, 1, and 2, we need to multiply all of these numbers together. The calculation goes as follows: Start with 20. Multiply by 1: 20 x 1 = 20. Multiply by 2: 20 x 2 = 40. Multiply by 19: 40 x 19 = 760. … Read more

The set of all elements in the universal set that are not included in set A is known as the complement of set A. In set theory, the universal set (often denoted as U) contains all possible elements under consideration for a particular discussion or problem. Set A is a specific collection of some of … Read more

To find the z-score for a given value, you can use the following formula: z = (X – μ) / σ In this formula: X is the value for which you want to calculate the z-score (in this case, 62). μ is the mean of the data set (here, it is 79). σ is the … Read more