Express the Prime Factorisation of the Numbers in Exponential Form
Prime factorisation is the process of expressing a number as the product of its prime factors. To express this in exponential form, we first need to identify the prime factors of the number and then write them using exponents to indicate how many times each prime factor is used. For example, let’s consider the number […]
What is the equation of a line that passes through the point (2, 1) and has an undefined slope?
The equation of a line that has an undefined slope is a vertical line. Vertical lines go straight up and down, and they are characterized by the fact that they do not change in the horizontal direction regardless of the vertical position. Since the line must pass through the point (2, 1), we can determine […]
A line segment has an endpoint at (4, 6) and the midpoint of the line segment is (1, 5). What are the coordinates of the point at the other end of the line segment?
To find the coordinates of the other endpoint of the line segment, we can use the formula for the midpoint of a line segment. The midpoint, M, of a line segment with endpoints A(x1, y1) and B(x2, y2) is given by: M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) In this case, we […]
Choose the correct simplification of the expression 4x26x 5×2 5
To simplify the expression 4x26x 5×2 5, we should first rewrite it clearly. It looks like there are some missing operators, so we will assume that the expression is meant to be multiplied: So, we rewrite the expression as 4 * 26 * 5 * 2 * 5. Now, let’s break it down step by […]
What is the principal of a loan?
The principal of a loan refers to the original sum of money borrowed or the outstanding balance still owed on a loan, apart from interest and other fees. Essentially, it is the amount that you agreed to pay back when you took out the loan. For example, if you take a loan of $10,000, the […]
How to Simplify 2n² + 4n + 32n + 3 using the Horizontal Method?
To simplify the expression 2n² + 4n + 32n + 3 using the horizontal method, we start by combining like terms. 1. Identify the like terms in the expression. In this case, the like terms are the ones with the variable n. We have: 4n 32n 2. Now, add these two terms together: 4n + […]
What are the solutions to the quadratic equation 3x^2 + 42x + 75?
To find the solutions to the quadratic equation 3×2 + 42x + 75 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b2 – 4ac)) / (2a) In our case, the coefficients are: a = 3 b = 42 c = 75 Now, we first need to calculate […]
Find an explicit rule for the nth term of the sequence 2, 8, 32, 128
To find an explicit rule for the nth term of the sequence 2, 8, 32, 128, we first observe the pattern in the numbers provided. The numbers can be rewritten as follows: 2 = 21 8 = 23 32 = 25 128 = 27 Next, we notice that the exponents form an arithmetic sequence: 1, […]
Find the value of x rounded to the nearest tenth given cos(22°)
To find the value of x where cos(22°), we can use the cosine function in trigonometry. The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse. However, in this case, we are not provided with a specific diagram or lengths of […]
How do you write the equation x² + y² + z² = 16 in spherical coordinates?
The equation given, x² + y² + z² = 16, represents a sphere centered at the origin with a radius of 4. To convert this equation into spherical coordinates, we start by recalling the relationships between Cartesian and spherical coordinates: x = ρ sin(φ) cos(θ) y = ρ sin(φ) sin(θ) z = ρ cos(φ) Here, […]