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A line that describes volume across the surface of an object or shape is known as a contour line. These lines are used in various fields such as geography, architecture, and design to indicate the elevation or depth of a surface. By connecting points of equal value, contour lines create a visual representation of a … Read more

To find the width of a rectangle, you can use the formula for the perimeter: Perimeter (P) = 2 * (Length (L) + Width (W)) In this scenario, we know the perimeter (P) is 90 cm and the length (L) is 15 cm. We can substitute these values into the formula: 90 cm = 2 … Read more

To solve the equation where ten times the sum of half a number and 6 equals 8, we need to first define the variables and set up the mathematical equation. Let’s denote the unknown number as x. According to the problem, we have: 1. Start with half the number: This is represented as 0.5x. 2. … Read more

To factor the expression 2×3 + 54y3 + 4x + 12y, we can follow these steps: Group the terms: Start by rearranging the terms in pairs for easier factoring. We can group: (2×3 + 4x) + (54y3 + 12y). Factor out the common terms in each group: From the first group (2×3 + 4x), we … Read more

To find the equation of the line with a given slope and a point, you can use the point-slope form of the line’s equation, which is expressed as: y – y1 = m(x – x1) Where: (x1, y1) is a point on the line (in this case, (6, 11)) m is the slope of the … Read more

The range of a set of scores is calculated by subtracting the smallest score from the largest score. This gives you the spread of the scores in that set. In the given set of scores: 5, 7, 9, 15, the smallest score is 5 and the largest score is 15. Now, let’s perform the calculation: … Read more

When the sum of the measures of angle x and angle y equals 90 degrees, it indicates that these two angles are complementary angles. In geometric terms, complementary angles are pairs of angles that, when added together, result in a right angle (90 degrees). This relationship is quite useful in various branches of mathematics, particularly … Read more

To prove the identity tan(2x) = \frac{2tan(x)}{1 – tan^2(x)}, we can start by using the double angle formula for tangent. The double angle formula states: tan(2x) = \frac{2tan(x)}{1 – tan^2(x)} Here’s a step-by-step breakdown of the proof: Recall the definitions: The tangent function can be expressed as the ratio of sine and cosine functions: tan(x) … Read more

To solve the equation x4 + 9×2 + 8 = 0 using u substitution, we can follow these steps: Substitution: Let u = x2. This means that x4 can be expressed as u2. Therefore, we rewrite the original equation in terms of u: u2 + 9u + 8 = 0 Factoring the Quadratic: Next, we … Read more

To solve the system of equations 3x + 2y = 6 and 6x + 4y = 12, we can use either the substitution method or the elimination method. Here, I’ll demonstrate the elimination method. First, let’s write down the equations: Equation 1: 3x + 2y = 6 Equation 2: 6x + 4y = 12 Notice … Read more