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To determine how many zeros the polynomial function f(x) = 7×3 + 12×2 + 16x + 23x + 42 has, we begin by simplifying the function: Combine like terms: f(x) = 7×3 + (12×2 + 16x + 23x) + 42 = 7×3 + 12×2 + 39x + 42 Next, we can analyze the function to … Read more

The geometric sequence given is 400, 200, 100. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant factor, known as the common ratio. To find the common ratio (r), we can divide the second term by the first term: r = second term / first … Read more

To understand the result of multiplying two complex numbers u1 and v1, we can break it down into its constituents. Suppose we have: u1 = a + bi and v1 = c + di, where: a and c are the real parts of u1 and v1, respectively, b and d are the imaginary parts of … Read more

To find the smallest number which, when increased by 17, is exactly divisible by both 520 and 468, we need to follow these steps: Step 1: Determine the Least Common Multiple (LCM) The first step is to find the LCM of 520 and 468. The LCM is the smallest number that is a multiple of … Read more

The conjugate of a complex number is obtained by changing the sign of the imaginary part. For the given complex number, 7i√2, we first identify its components: Real part: 0 (since there is no real component) Imaginary part: 7√2 To find the conjugate, we change the sign of the imaginary part, resulting in: Conjugate: 0 … Read more

To solve this problem, we can set up a couple of equations based on the information given. Let’s denote the amount of money Bill has as B and the amount of money Hanes has as H. From the question, we know two things: The total amount of money they have together is $60. This can … Read more

To find the equation of a line that is perpendicular to another line and passing through a specific point, we can follow these steps: Determine the slope of the original line: The given equation is 8x – 7y + 4 = 0. We can rewrite this equation in slope-intercept form (y = mx + b) … Read more

To find the value of g(3) for the function g(x) = x2 + 2, you need to substitute x with 3 in the function equation. Here are the steps to calculate it: Substituting 3 into the function: g(3) = (32) + 2 Calculating 32: 32 = 9 Adding 2: 9 + 2 = 11 Thus, … Read more

When tossing an unbiased die, each face (including the six) has an equal probability of landing face up. This probability is 1/6, since there are six faces on a standard die. To find the mean number of sixes obtained when the die is tossed 500 times, we can use the formula for expected value, which … Read more

To find the point on the line y = 2x + 3 that is closest to the origin (0, 0), we can use the concept of minimizing the distance from a point to the line. The distance d between a point (x, y) and the origin (0, 0) can be expressed by the following formula: … Read more