devyy To simplify the expression 2n² + 4n + 32n + 3 using the horizontal method, let’s follow these steps: Combine Like Terms: First, we identify and combine the like terms in the expression. Here, we have: The quadratic term: 2n² The linear terms: 4n and 32n The constant term: 3 Now, let’s combine the linear … Read more
To find the solutions to the quadratic equation 3x² + 42x + 75 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In this equation, the coefficients are: a = 3 b = 42 c = 75 First, we need to calculate the … Read more
To find the exact trigonometric ratios for the angle x whose radian measure is 3π/4, we first need to determine the position of this angle on the unit circle. 1. **Locate the Angle**: The angle 3π/4 is in the second quadrant. It is equivalent to 180° – 45°, or 135° in degrees. 2. **Reference Angle**: … Read more
To find the x-intercept of the linear equation 3y + 4x = 8, we need to determine the point where the line intersects the x-axis. At the x-axis, the value of y is always 0. 1. Start by substituting 0 for y in the equation: 3(0) + 4x = 8 2. This simplifies to: 4x … Read more
The value of the numbers 817, 12, 28, and 2 can depend on what you are asking. If you’re looking for the sum of these numbers, we can simply add them together: Calculation: 817 + 12 + 28 + 2 Performing this addition gives us: 817 + 12 = 829 829 + 28 = 857 … Read more
To find the explicit rule for the nth term of the sequence 2, 8, 32, 128, we first need to analyze the relationship between consecutive terms. The given sequence is: a1 = 2 a2 = 8 a3 = 32 a4 = 128 Next, let’s examine how each term relates to the previous one: a2 = … Read more
To determine whether the given differential equation is exact, we start by expressing it in the standard form: M(x, y) dx + N(x, y) dy = 0 where: M(x, y) = 5x + 4y N(x, y) = 4x + 8y3 A differential equation is said to be exact if the following condition holds: ∂M/∂y = … Read more
To analyze the given logarithmic functions represented in the equations, let’s break them down one by one: 1. Logarithmic Function: fx = log₅(x) This function indicates the logarithm of x with base 5. In simpler terms, it’s the power to which 5 must be raised to obtain the value of x. For example, if x … Read more
To find the correct sum of the polynomials 4x³ + 2x + 9 and 2x³ + 5x + 3, we need to combine like terms. Let’s break it down step by step: 1. **Identify the like terms:** The first polynomial is: 4x³ + 2x + 9 The second polynomial is: 2x³ + 5x + 3 … Read more