Finding the Number of Nickels and Dimes To solve the problem of a pile of 55 coins made up of nickels and dimes worth $3.90, we can use a system of equations. Define Variables Let n be the number of nickels. Let d be the number of dimes. Set Up the Equations We can create … Read more
To solve the equation 5x + 13 = 3x + 3, we will follow these steps: Isolate the variable terms: Start by moving the terms that contain x to one side of the equation and the constant terms to the other side. We can subtract 3x from both sides: 5x – 3x + 13 = … Read more
To convert the equation 3x + 5y + 10 = 0 into slope-intercept form, which is typically written as y = mx + b (where m is the slope and b is the y-intercept), we need to isolate y on one side of the equation. Here’s a step-by-step breakdown: Start with the original equation: 3x … Read more
To find an angle that is coterminal with a given angle (in this case, 110 degrees) within the range of 0 to 360 degrees, you can use the concept of adding or subtracting multiples of 360 degrees. Coterminal angles differ by full rotations (360 degrees), meaning that they point in the same direction on the … Read more
The series you’ve provided is composed of two interleaved sequences. Let’s break it down: The first sequence consists of the numbers in the odd positions: 3, 4, 5. This sequence is straightforward: we start at 3 and simply add 1 each time (3 + 1 = 4; 4 + 1 = 5). The second sequence … Read more
The numbering system that exclusively uses the digits 0 and 1 is known as the binary numbering system. In this system, all values are represented using only these two digits, which are essential in various computing and digital applications. Binary is a base-2 numeral system, meaning it operates on two symbols. Each digit in a … Read more
The sum of the interior angles of a polygon can be calculated using the formula: Sum = (n – 2) × 180 Where n is the number of sides in the polygon. Given that the sum of the interior angles is 720 degrees, we can set up the equation: (n – 2) × 180 = … Read more
To find the probability of drawing two marbles of different colors from the bag, we first need to determine the total number of marbles in the bag. The bag contains: 6 Red marbles 4 Blue marbles 7 Green marbles 3 Yellow marbles Adding these together gives us the total number of marbles: Total Marbles = … Read more
Factoring the expression x² + 7x + 8 involves finding two numbers that multiply to the constant term (8) and add up to the linear coefficient (7). Let’s break it down step-by-step: We start with the expression: x² + 7x + 8. Next, we look for two numbers that multiply to 8
To simplify the fraction formed by the numbers 64 and 32, we need to divide both the numerator (64) and the denominator (32) by their greatest common divisor (GCD). 1. **Find the GCD**: The GCD of 64 and 32 is 32, since 32 is the largest number that divides both of these without leaving a … Read more