Which shows one way to determine the factors of x³ + 9x² + 5x + 45 by grouping?
To factor the polynomial x³ + 9x² + 5x + 45 by grouping, we can follow these steps: First, we group the terms in pairs: (x³ + 9x²) + (5x + 45). Next, we factor out the greatest common factor from each group: From the first group x³ + 9x², we factor out x², giving […]
If 6k is a solution of the equation 3xy + 22 = 0, then what is the value of k?
To find the value of k when 6k is a solution to the equation 3xy + 22 = 0, we start by substituting 6k for xy in the equation. Substituting, we get: 3(6k) + 22 = 0 This simplifies to: 18k + 22 = 0 Next, we isolate k. Subtract 22 from both sides: 18k […]
Which expression can be used to convert 100 USD to Japanese Yen?
To convert 100 USD to Japanese Yen, you would typically use the following expression: 100 USD * exchange rate (USD to JPY) In this expression, the exchange rate represents how many Japanese Yen are equivalent to one US Dollar. For instance, if the current exchange rate is 110 JPY for 1 USD, the calculation would […]
Which zero pair could be added to the function f(x) = x² + 12x + 6 so that the function can be written in vertex form?
To express the function f(x) = x² + 12x + 6 in vertex form, we need to complete the square. The vertex form of a quadratic function is given by: f(x) = a(x – h)² + k where (h, k) is the vertex of the parabola. Starting with the function: f(x) = x² + 12x […]
Find the value of x in the equation x 5 x 45
To find the value of x, we need to interpret the equation correctly. Assuming the equation is meant to represent multiplication, it should read as: x × 5 × x = 45 We can simplify this equation step by step. Let’s rewrite it: 5x² = 45 Now, to solve for x, we first need to […]
A Takes 3 Hours More Than B to Walk 30 km, But If A Doubles His Pace, He is Ahead of B by 2 Hours. Find Their Speed of Walking.
Let’s denote the speed of A as vA km/h and the speed of B as vB km/h. From the problem, we know that A takes 3 hours more than B to walk 30 km. Therefore, we can set up the following equations based on the formula: time = distance/speed. For A: Time taken by A […]
What is the product of the numbers 20, 1, 2, 19, 1, and 2?
To find the product of the numbers 20, 1, 2, 19, 1, and 2, we multiply them together: First, let’s break it down: 20 * 1 = 20 20 * 2 = 40 40 * 19 = 760 760 * 1 = 760 760 * 2 = 1520 So, the product of the numbers 20, […]
If you triple 4 and subtract 2 each day how many days until you have zero?
To solve this problem, let’s break it down step by step. First, if you triple 4, you get: 3 x 4 = 12 So, you start with 12. Now, every day you subtract 2 from this number. Let’s see how this unfolds over several days: **Day 1:** 12 – 2 = 10 **Day 2:** 10 […]
What is the set of all elements in the universal set that is not in set A called?
The set of all elements in the universal set that is not in set A is called the complement of set A. In set theory, the complement of a set includes everything in the universal set that does not belong to the specified set. If we denote the universal set as U and set A […]
What are all the factors of 16?
The factors of 16 are the numbers that can be multiplied together to produce 16. To find the factors, we can start by determining which whole numbers divide evenly into 16 without leaving a remainder. First, we can start with 1, since 1 is a factor of every number. When we multiply 1 by 16, […]