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To solve the compound inequality 6b < 24 or 4b < 12 + 4, we need to solve each part separately. Step 1: Solve the first inequality For the first part: 6b < 24. To isolate b, divide both sides by 6: 6b < 24 b < 4 This means b can be any number … Read more

Finding the Length of Line Segment AC in Triangle ABC To determine the length of line segment AC in triangle ABC, we want to consider the properties of triangles and the numerical values provided: 7, 9, 14, and 18. First, it’s important to visualize the triangle. Typically, the lengths of the sides must abide by … Read more

To find the value of side b in a scalene triangle with a given perimeter, we can use the definition of perimeter. The perimeter of a triangle is the sum of the lengths of all its sides. In this case, we know the perimeter is 546 cm, and we have the lengths of sides a … Read more

To calculate the probability of rolling two fair six-sided dice and getting the same number on both, we start by identifying the total possible outcomes and the favorable outcomes. When rolling two dice, each die can land on one of 6 faces (numbered from 1 to 6). Therefore, the total number of possible outcomes when … Read more

To solve the equation 2×2 + 7x + 9 = 0, I would choose the quadratic formula method. The quadratic formula states that for any quadratic equation of the form ax2 + bx + c = 0, the solutions for x can be found using: x = (-b ± √(b2 – 4ac)) / 2a In … Read more

To express the fractions 34/716 and 5/8 with a common denominator, we first need to determine the least common denominator (LCD) of the two fractions. Step 1: Simplifying 34/716 First, we need to simplify 34/716. We can find the greatest common divisor (GCD) of 34 and 716. 34 can be factored into 2 and 17, … Read more

The metric system, a decimal-based system of measurement, uses prefixes to convey various magnitudes of a unit. These prefixes enhance clarity and precision, making it easier to express both very large and very small quantities. For instance, consider the meter, the base unit for length. When we talk about distances, we might use prefixed units … Read more

To determine whether a set is closed under multiplication, we need to check if the product of any two elements in that set is also an element of the same set. Let’s consider a few common sets: Natural Numbers (N): The natural numbers are 1, 2, 3, and so on. When you multiply any two … Read more

Factoring the Expression 3x² + 10x + 8 To factor the quadratic expression 3x² + 10x + 8, we can make use of the factoring technique that involves finding two numbers that multiply to the product of the leading coefficient (3) and the constant term (8), and also sum to the middle coefficient (10). Identify … Read more

To find the polynomial that has the factors 4×7 and x4, we need to multiply these two expressions together. First, let’s break down what we have: The first factor is 4×7, which means it is the term 4 multiplied by x raised to the power of 7. The second factor is x4, meaning it is … Read more