Finding Solutions to the Equation To solve the equation sec²(x) = 2tan²(x) within the interval [0, 2π], we start by rewriting the terms using the definitions of secant and tangent: sec(x) = 1/cos(x) tan(x) = sin(x)/cos(x) This allows us to express the equation in terms of sine and cosine: sec²(x) = 1/cos²(x) and tan²(x) = … Read more
To determine which binomial is a factor of the polynomial 9x² + 643x + 8, we first need to factor the expression. Factoring polynomials can often involve finding two numbers that multiply to a specific value, while also adding up to another value. In this case, we’re looking for factors of the form (ax + … Read more
To solve the inequality 2x + 20 < 37 + 62x, we’ll need to follow a series of steps to isolate x: Reorganize the inequality: Start by getting all the terms involving x on one side and the constants on the other. We can subtract 2x from both sides: Subtract 2x from both sides: This ... Read more
Two angles are said to be supplementary when the sum of their measures equals 180 degrees. If we have two angles, let’s call them A and B, both of which are supplementary to the same angle C, we can derive an important conclusion. In this case, since both angle A and angle B satisfy the … Read more
Solving the Equation x² – 24x + 80 by Completing the Square To solve the quadratic equation x² – 24x + 80 = 0 by completing the square, follow these steps: Rearrange the equation: Start with the original equation: x² – 24x + 80 = 0 Move the constant term (80) to the other side: … Read more
To find the exact value of cos(180) multiplied by sin(180), we start by calculating each trigonometric function individually. The value of cos(180) is determined using the unit circle, where the angle 180 degrees corresponds to the point (-1, 0). Therefore: cos(180) = -1 Next, we find sin(180). The angle 180 degrees also corresponds to the … Read more
The equation you provided is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 7, and c = 5. To find the solutions, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a Now, let’s plug in the values: b² … Read more
To determine how many solutions the linear system defined by the equations y = 6x² and y = 12x²y⁴ has, we need to analyze the system step-by-step. 1. **Understanding the equations**: Both equations are nonlinear due to the presence of the variables raised to a power greater than one. The first equation is a simple … Read more
Solving the System of Equations Graphically To solve the system of equations defined by: Equation 1: 2x + y = 3 Equation 2: 4x + 2y = 2 we will follow these steps: Step 1: Rewrite the Equations in Slope-Intercept Form First, we need to express both equations in the slope-intercept form (y = mx … Read more
Understanding the Classification of Numbers To properly classify the numbers 2×4, 8×5, 2×2, and 5, we first need to understand their mathematical forms: 2×4: This represents the multiplication of 2 and 4, which equals 8. 8×5: This indicates the multiplication of 8 and 5, resulting in 40. 2×2: This signifies the multiplication of 2 and … Read more