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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

To find the next number in the sequence 3, 6, 4, 8, 6, 12, 10, we first need to analyze the pattern of the sequence. Looking at the numbers, let’s break them down: 3 to 6: This is an increase of 3. 6 to 4: This is a decrease of 2. 4 to 8: This … Read more

To solve the equation x4 + 5×2 – 36 = 0 using factoring, we start by making a substitution to simplify our approach. Let’s set y = x2. This transforms our equation into a quadratic form: y2 + 5y – 36 = 0 Next, we will factor the quadratic equation. We need to find two … Read more

To find the sum of a geometric sequence, we need to use the formula: Sn = a (1 – rn) / (1 – r) Where: Sn is the sum of the first n terms. a is the first term of the sequence. r is the common ratio of the sequence. n is the number of … Read more