To determine the angle between the hour and minute hands of a clock at 2 PM, we can follow a straightforward calculation method based on the positions of the hands. 1. **Position of the Hour Hand:**At 2 PM, the hour hand is pointing directly at the 2 on the clock. Each hour represents a 30-degree … Read more
To find an equivalent expression for the sum of 7a²b, 10a²b², and 14a²b³, we must first factor out any common terms shared by these expressions. Let’s analyze them one at a time: The first term is 7a²b. It consists of the factors 7, a², and b. The second term is 10a²b². Here we have factors … Read more
To solve for the possible values of x in the expression ‘x 12 50’, we first need to clarify the mathematical operation implied by the juxtaposition of ‘x’, ’12’, and ’50’. Typically, expressions like this should include an operator (such as +, -, *, /). Let’s consider two interpretations that commonly arise in such situations: … Read more
To determine the next number in the series 1, 2, 8, 48, 384, let’s first examine the relationships between the numbers. Starting with the given sequence: 1 2 8 48 384 Now, let’s look at how each number is related to its predecessor: From 1 to 2, we can see that 1 is multiplied by … Read more
To determine the value of x to the nearest tenth, you need to follow a few simple steps: Identify the value of x: Start by finding the number that you want to round. For instance, let’s say x = 5.67. Locate the tenths place: The tenths place is the first digit to the right of … Read more
To find the fifth term in the binomial expansion of (x + 1)58, we can use the binomial theorem. The binomial theorem states that: (a + b)n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^{k}, where \binom{n}{k} is a binomial coefficient, which can be calculated as: \binom{n}{k} = \frac{n!}{k!(n-k)!}. In our case, we have: a = x b … Read more
To find the solutions of the quadratic equation x² + 2x + 2 = 0, we can use the quadratic formula, which is given by: x = −b ± √(b² − 4ac) / 2a In this formula: a is the coefficient of x², b is the coefficient of x, c is the constant term. For … Read more
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. To find the explicit formula for the arithmetic sequence given, we need to determine the first term and the common difference. In the sequence 75, 9, 105, 12, let’s identify the terms: First term (a1) = 75 Second … Read more
To determine if an absolute value equation has no solution, we first need to understand the nature of absolute values. An absolute value equation typically looks like this: |ax + b| = c In this equation: ax + b is a linear expression where a and b are constants, c is a non-negative number as … Read more
To find the sine, cosine, and tangent of 3π/4 radians, we can start by analyzing this angle in relation to the unit circle. Location on the Unit Circle: The angle 3π/4 radians is found in the second quadrant, where the sine value is positive and the cosine value is negative. This angle corresponds to 135 … Read more