Solve x² + 4x + 7 = 0 by Completing the Square: What are the Solutions?
To solve the quadratic equation x² + 4x + 7 = 0 by completing the square, we start by rearranging the equation. Our goal is to express the quadratic in the form of a perfect square. First, we need the equation in the standard form: x² + 4x = -7 Next, we complete the square […]
How many 1 cm cubes would it take to construct a cube that is 3 cm on edge?
To find out how many 1 cm cubes are needed to construct a cube that measures 3 cm on each edge, we first need to calculate the volume of the larger cube. The volume of a cube is given by the formula: Volume = side length 3 For our cube with a side length of […]
Which expression is a factor of 3xy + 2x + 18y + 12?
To determine which expression is a factor of the polynomial 3xy + 2x + 18y + 12, we can look for common factors in each term. First, let’s rearrange the polynomial a bit for clarity: (3xy + 18y) + (2x + 12) In the first group (3xy + 18y), we can factor out 3y: 3y(x […]
How Much Less Than 2 is 6?
To determine how much less than 2 is 6, we can set up a simple subtraction problem. We take the number 6 and subtract 2 from it. This will give us the difference between the two numbers. The calculation looks like this: 6 – 2 = 4 So, 6 is 4 units more than 2. […]
What is the factored form of 5x² + 28x + 15?
To factor the quadratic expression 5x² + 28x + 15, we can use the method of grouping or look for two numbers that will help us break it down. First, identify the coefficients: a = 5, b = 28, and c = 15. We need two numbers that multiply to a*c = 5*15 = 75 […]
What are the three whole numbers occurring just before 10001?
The three whole numbers that come just before 10001 are 10000, 9999, and 9998. Whole numbers are non-negative integers, starting from 0 and going upwards without any fractional or decimal parts. To find the numbers just before 10001, we simply subtract one from 10001 repeatedly. – Starting from 10001: 10001 – 1 = 10000 10000 […]
What is the completely factored form of p4 16?
To find the completely factored form of the expression p4 – 16, we start by recognizing that this is a difference of squares. A difference of squares follows the pattern a2 – b2 = (a – b)(a + b). In our case, we can rewrite p4 – 16 as: (p2)2 – (4)2 Applying the difference […]
What is the additive identity of the complex number 14 + 5i?
The additive identity of any number, including complex numbers, is the number that, when added to it, leaves the original number unchanged. For complex numbers, the additive identity is 0. In this case, we are looking at the complex number 14 + 5i. When we add the additive identity, which is 0 (or 0 + […]
2x + 5 = 65: Solve for x
To solve the equation 2x + 5 = 65, we need to isolate the variable x. First, we can eliminate the constant on the left side of the equation by subtracting 5 from both sides: 2x + 5 – 5 = 65 – 5 This simplifies to: 2x = 60 Next, we need to get […]
Find one value of x for which f(x) = 4 and find f(2)
To find one value of x for which f(x) = 4, we first need to know the function f(x) itself. Since the function is not defined here, let’s assume a simple example where f(x) = x + 2. In this case, we set up the equation: x + 2 = 4 Now, solving for x: […]