How can x + 4 = 3x + 12 be set up as a system of equations?
To set up the equation x + 4 = 3x + 12 as a system of equations, we first need to rearrange this equation to express it in a standard form. We start by moving all terms involving x to one side and constants to the other side. Here’s the step-by-step process: Subtract x from […]
What is the sum of the roots of the equation 3x² + 11x + 4 = 0?
To find the sum of the roots of the quadratic equation 3x² + 11x + 4 = 0, we can use the formula derived from Vieta’s formulas. For a quadratic equation of the form ax² + bx + c = 0, the sum of the roots (r₁ + r₂) can be calculated using the formula: […]
What is the solution of log2x 5 25 2?
To solve the expression log2x 5 25 2, we first need to clarify what operation we are performing. It looks like a logarithm is involved, specifically with base 2. Let’s break it down: 1. **Identify the Logarithmic Expression**: The expression log2(5 + 25 – 2) translates to: calculate the logarithm base 2 of the sum […]
How do you factor the expression 48x² + 26x + 3?
To factor the expression 48x² + 26x + 3, we start by looking for two numbers that multiply to the product of the coefficient of x² (48) and the constant term (3), which is 144, and add up to the coefficient of x (26). After examining the factors of 144, we find that 18 and […]
What is the 8th term of the sequence given by an = 3n + 5?
To find the 8th term of the sequence defined by the formula an = 3n + 5, we will substitute n with 8. Let’s do the calculation: a8 = 3(8) + 5 Now, multiply: 3(8) = 24 Adding 5 gives: 24 + 5 = 29 Thus, the 8th term of the sequence is 29.
How to Solve the Equation 9x + 1 = 17?
To solve the equation 9x + 1 = 17, we will isolate the variable x. Here are the steps: Start by subtracting 1 from both sides of the equation to eliminate the constant on the left side: 9x + 1 – 1 = 17 – 1 This simplifies to: 9x = 16 Next, divide both […]
What should be the next number in the following series 3 6 4 7 5 8?
The next number in the series is 6. To understand why, let’s analyze the pattern in the series: The first number is 3. The second number is 6, which is obtained by adding 3 to the first number. The third number is 4, which is 6 minus 2. The fourth number is 7, which is […]
Use Synthetic Division to Solve x³ + 1x + 1: What is the Quotient?
Synthetic division is a shorthand method of dividing a polynomial by a linear factor. In this case, we are looking to divide the polynomial x³ + 1x + 1 by a factor that we’ll determine as we start the process. First, we need to express our polynomial in standard form, which gives us: x³ + […]
What is the 25th term of this arithmetic sequence 3, 9, 15, 21, 27?
To find the 25th term of the arithmetic sequence given (3, 9, 15, 21, 27), we first need to identify the common difference and then use the formula for the nth term of an arithmetic sequence. The first term (a) of the sequence is 3. The common difference (d) can be calculated as follows: 9 […]
Factor x^2 + 7x + 8
To factor the quadratic expression x2 + 7x + 8, we need to find two numbers that multiply to the constant term (8) and add up to the linear coefficient (7). The numbers that meet these criteria are 1 and 8 because: 1 × 8 = 8 1 + 8 = 9 So, we can […]