Using the Completing the Square Method: Rewrite f(x) = x² + 10x + 7 in Vertex Form
To rewrite the quadratic function f(x) = x² + 10x + 7 in vertex form, we can use the completing the square method. The vertex form of a quadratic equation is given by: f(x) = a(x – h)² + k where (h, k) is the vertex of the parabola. Let’s follow these steps to complete […]
Suppose s and t are mutually exclusive events, find P(s or t) if P(s) = 20 and P(t) = 22
To find the probability of either event s or event t occurring, we can use the formula for mutually exclusive events. When two events are mutually exclusive, the probability of either event occurring is simply the sum of their individual probabilities. The formula can be expressed as: P(s or t) = P(s) + P(t) Given […]
If Bill and Hanes have 60 dollars between them and Hanes has half as much as Bill, how much does Hanes have?
To solve the problem, let’s define the amount of money Bill has as B dollars. Since Hanes has half as much as Bill, we can express Hanes’ amount as H = 0.5B. According to the problem, together they have 60 dollars. We can write this relationship with the equation: B + H = 60 Substituting […]
What is the average rate of change of y = cos(2x) on the interval [0, π/2]?
The average rate of change of a function over an interval is calculated using the formula: Average Rate of Change = (f(b) – f(a)) / (b – a) In this case, we want to find the average rate of change of the function y = cos(2x) over the interval [0, π/2]. Here, a = 0 […]
Which statement about the end behavior of the logarithmic function f(x) = log3(x) is true?
The end behavior of the logarithmic function f(x) = log3(x) demonstrates that as x approaches infinity, the function f(x) also approaches infinity. In other words, the graph of the function continues to rise slowly, but without bound, as you move to the right along the x-axis. Conversely, as x approaches zero from the positive side, […]
What is next in this series 1 4 10 19 31?
To find the next number in the series, let’s examine the pattern between the numbers: The difference between 4 and 1 is 3. The difference between 10 and 4 is 6. The difference between 19 and 10 is 9. The difference between 31 and 19 is 12. The differences we found: 3, 6, 9, 12 […]
Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?
Let’s denote the two numbers as 5x and 3x where x is a common multiplier. Since the numbers are in the ratio of 5:3, we can express them like this: Number 1: 5x Number 2: 3x According to the problem, the difference between these two numbers is 18. Therefore, we can set up the following […]
Which equation results from taking the square root of both sides of x² = 81?
When you take the square root of both sides of the equation x² = 81, you are looking for the values of x that satisfy this equation. The operation of taking the square root introduces both positive and negative solutions. Therefore, you can express the results as: x = ±√81 Since the square root of […]
Choose the Correct Classification of 5x 3×2 7×3 2
To classify the expression 5x + 3x^2 + 7x + 2, we first need to combine like terms. The terms in this expression are: 5x (first degree term) 3x^2 (second degree term) 7x (first degree term) 2 (constant term) Now, let’s combine the like terms: The first degree terms are 5x and 7x. Adding these […]
What is the answer for this: solve for x: x² – 3 – 2x = 7
To solve the equation x² – 3 – 2x = 7, we can start by rearranging it into standard form. First, add 3 to both sides of the equation: x² – 2x – 3 = 7 + 3 Now the equation is: x² – 2x – 3 = 10 Next, subtract 10 from both sides […]