What is the completely factored form of 9x² – 24x + 16?
To find the completely factored form of the quadratic expression 9x² – 24x + 16, we can start by searching for two numbers that multiply to 9 times 16 = 144 (the product of the coefficient of x² and the constant term) and add up to -24 (the coefficient of x). The two numbers that […]
Which ordered pair makes both inequalities true y < x + 1 and y < x + 3?
To determine which ordered pair satisfies both inequalities, we need to analyze each pair given: (5, 2), (2, 1), (3, 0), and (1, 3). The first inequality is y < x + 1. Rearranged, it predicts that for any x value, y must be less than that value plus one. The second inequality is y […]
What type of number has an odd number of factors?
Numbers that have an odd number of factors are perfect squares. This might seem a bit surprising at first, but let’s break it down. Every number has factors that typically come in pairs. For instance, if you take the number 12, its factors are 1, 2, 3, 4, 6, and 12. These can be paired […]
What is the product of the complex numbers 3i and 4?
To find the product of the complex numbers 3i and 4, we simply multiply them together. Since 4 is a real number, the multiplication is straightforward: 3i × 4 = 12i The result, 12i, is also a complex number, where the real part is 0 and the imaginary part is 12. Therefore, the product of […]
What number is a common multiple of 5 and 9?
To find a common multiple of 5 and 9, we need to look for multiples of each number and identify the smallest one that they share. The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, … The multiples of 9 are: 9, 18, 27, 36, 45, 54, … From these […]
Which expression is equivalent to 2x² + 2x + 7?
To find an expression that is equivalent to 2x² + 2x + 7, we can factor or simplify depending on what we want to do with the expression. In this case, we can factor out the common term. First, notice the terms: 2x² is a quadratic term. 2x is a linear term. 7 is a […]
How many solutions exist for the given equation 3x 10 6 3x 12?
To determine how many solutions exist for the equation 3x + 10 = 6 + 3x + 12, we first rearrange the equation to isolate x. Starting with the original equation: 3x + 10 = 6 + 3x + 12 We can simplify the right side: 6 + 12 = 18 Now the equation looks […]
What Does It Mean to Say That lim x→∞ 8?
When we say that lim x→∞ 8, we are discussing the concept of limits in calculus. In this case, we are examining what happens to the value of a constant as x approaches infinity. The limit of a constant value, such as 8, as x approaches infinity is simply the constant itself. This is because […]
Find the degree measure of an angle of 3π/5 radians
To convert radians to degrees, we use the conversion factor that states 180 degrees is equivalent to π radians. Therefore, to convert an angle in radians to degrees, we multiply by the fraction 180/π. For the angle of 3π/5 radians, the conversion to degrees can be done as follows: Degrees = (3π/5) * (180/π) In […]
What number should come next in the sequence: 6, 18, 20, 10, 30, 32, 16?
To find the next number in this sequence, let’s first analyze the pattern of the numbers provided. Starting with the sequence: 6, 18, 20, 10, 30, 32, 16. 1. Looking at the first two numbers, 6 and 18, we can deduce that 18 is 3 times 6. 2. Next, we move to 18 and 20. […]