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When faced with a true or false test that contains 9 questions, each question offers 2 possible answers: true or false. To determine the total number of different ways to answer the test, we can utilize the principle of multiplication. For each of the 9 questions, you have 2 choices (true or false). This can … Read more

To find the value of tan(2x) given that sin(x) = 35 and x is in the third quadrant, we first need to clarify that the sine of an angle cannot exceed 1. In the context of the unit circle, the sine of any angle represents the y-coordinate of a point on the unit circle. Therefore, … Read more

To convert the Cartesian equation 2x + 3y = 6 into polar coordinates, we first recall the relationships between Cartesian coordinates (x, y) and polar coordinates (r, θ): x = r * cos(θ) y = r * sin(θ) 1. **Substituting for x and y:** Using these relationships, we can substitute for x and y in … Read more

Finding the Zeros of the Polynomial Function The function we want to analyze is given by: \[ f(x) = 4x^3 + 13x^2 + 37x + 10 \] To find the zeros of this polynomial, we need to determine the values of \( x \) for which \( f(x) = 0 \). Step 1: Applying the … Read more

To solve the problem, we need to break it down into two parts: calculating the sum of 22 and 9, and finding the quotient of 18 and 2. 1. **Calculate the sum:** We start with adding 22 and 9: 22 + 9 = 31 2. **Calculate the quotient:** Next, we find the quotient of 18 … Read more

To determine the length of line segment AC using the equation sin(40), we can apply the basic principles of trigonometry. Here’s how it works: 1. **Understanding the Context**: First, we need to understand that the sin function relates the angle to the ratios of the sides of a right triangle. In this case, we have … Read more

To solve for the value of x when the difference between x and 6 is 5, we can set up the equation based on the information provided. The difference between x and 6 can be expressed mathematically as: |x – 6| = 5 This absolute value equation can be split into two separate cases: Case … Read more

To graph the equation 3x + 5y = 15, follow these steps: Step 1: Rearrange the Equation First, it helps to rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. To do this, solve for y: 5y = -3x + 15 y = … Read more

To find the three quartiles in the given data set (4, 5, 8, 7, 11, 9, 9), we first need to organize the data in ascending order: Sorted Data Set: 4, 5, 7, 8, 9, 9, 11 Next, we will determine the quartiles: First Quartile (Q1): This is the median of the first half of … Read more