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To determine the value that must be added to the expression x² + x to make it a perfect square trinomial, we can follow these steps: Identify the form of a perfect square trinomial. A perfect square trinomial can be expressed as (a + b)² = a² + 2ab + b². In our case, we … Read more

To find the value of y in the system of equations 3x + 5y = 1 and 7x + 4y = 13, we can use either the substitution method or the elimination method. For this explanation, we’ll use the elimination method. Step 1: Align the equations We have the following equations: 1. 3x + 5y … Read more

The sequence presented is intriguing as it appears to be a combination of perfect cubes and perfect squares. To analyze the pattern more closely, we can take a look at these numbers: 1 = 13 (perfect cube) 4 = 22 (perfect square) 27 = 33 (perfect cube) 16 = 42 (perfect square) 125 = 53 … Read more

Converting temperatures from Kelvin to Celsius and Fahrenheit is quite straightforward, and with a few simple formulas, you’ll be able to switch between these temperature scales effortlessly. Conversion Formulas Here are the formulas you need: To convert Kelvin (K) to Celsius (°C): °C = K – 273.15 To convert Kelvin (K) to Fahrenheit (°F): °F … Read more

A composite number is defined as a positive integer that has at least one positive divisor other than one or itself. In simpler terms, a composite number can be divided evenly by numbers other than just 1 and itself, meaning it has more than two factors. Let’s analyze the two examples: 1. The number 7 … Read more

To find the discriminant of the trinomial 3x² + 6x + 5, we first need to recall the formula for the discriminant, which is derived from the quadratic equation in the standard form, ax² + bx + c. The discriminant (D) is given by: D = b² – 4ac In this trinomial, the coefficients are: … Read more

To convert the expression x4 + 3x – 12 into a system of equations, we first need to isolate the variable and create relationships between multiple equations. The expressions can represent a function, and by setting it equal to zero, we can treat it as an equation: 1. First, we start by rewriting the equation: … Read more

To solve the inequality 5 < r < 3, we need to analyze its components and intervals carefully. First, let’s break this down into two parts: 5 < r: This means that r must be greater than 5. r < 3: This means that r must be less than 3. Now, let’s put these two ... Read more

The equation y = 52x represents a direct variation, which means that the value of y varies directly with the value of x. In simpler terms, if you increase x, y increases proportionally to that change, and vice versa. To visualize this, the graph of the equation will be a straight line that passes through … Read more

To prove that if 7n4 is even, then n must be even, we’ll start by analyzing the properties of even and odd numbers. 1. **Understanding Even and Odd Numbers**: A number is even if it is divisible by 2. Conversely, a number is odd if it is not divisible by 2. We know that: If … Read more