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To find the three numbers in arithmetic progression (AP) whose sum is 18, we start by denoting the three numbers as: Let the three numbers be a – d, a, and a + d, where a is the middle term, and d is the common difference. The sum of these three numbers can be expressed … Read more

To solve the equation x + 72 = 36, we need to isolate the variable x. We can do this by performing some basic arithmetic operations. First, we will subtract 72 from both sides of the equation: x + 72 – 72 = 36 – 72 This simplifies to: x = 36 – 72 Now, … Read more

Finding the value of n To solve the equation 2x9yn + 4x2y10 = 8x11y20, we need to simplify and compare the coefficients of both sides of the equation. Step 1: Simplify the equation Firstly, notice that both terms on the left can be factored. Let’s factor out the common term from the left side: 2x9yn … Read more

To simplify the expression 92√3 into its simplest radical form, we need to break down the number 92 and see if it has any perfect square factors. The prime factorization of 92 can be expressed as: 92 = 4 × 23 Here, 4 is a perfect square since √4 = 2. Now, we can rewrite … Read more

To find the value of x in the proportion x/15 = 4x/2 = 35, we can start by breaking down the equation into manageable parts. The given proportion can be simplified as follows: 1. **Set up the equations:** First, we can set up two separate equations from the proportion. According to the proportion: From the … Read more

To determine what 12% of n is, we first need to find the value of n. We know from the problem that 23% of n equals 4. This can be expressed mathematically as: 0.23n = 4 To find n, we can solve the equation by dividing both sides by 0.23: n = 4 / 0.23 … Read more

To solve the system of linear equations represented by: Equation 1: x + 3y = 2 Equation 2: x + 3y = 16 We begin by examining both equations simultaneously. Notice that both equations have the same left-hand side, x + 3y, which implies that they describe parallel lines. 1. From Equation 1, we have: … Read more

To determine the values of b that satisfy the expression 32b = 32 = 36 = b = b = b = …, we need to analyze the expression carefully. It seems like there is a bit of misunderstanding in the question, as the expression does not clearly define a mathematical equation. However, based on … Read more

Finding the Values of tan 135 and cot 135 To calculate the values of tan 135 and cot 135, we can use the properties of trigonometric functions, specifically focusing on the unit circle and the reference angles. Step 1: Understanding the Angle The angle of 135 degrees is located in the second quadrant of the … Read more

To calculate the distance between two points in a Cartesian coordinate system, specifically the points (a, b) and (c, d), we can use the distance formula derived from the Pythagorean theorem. The formula is: Distance = √[(c – a)² + (d – b)²] Here’s a more detailed breakdown of the formula: (c – a): This … Read more