What are two solutions of the equation x * y = 7?
To find two solutions for the equation x * y = 7, we need to choose values for one variable and then calculate the other. Here are two simple examples: Solution 1: Let's take x = 1. If we substitute this value into the equation, we have: 1 * y = 7 This simplifies to […]
Which One of the Following Statements is True of Parallel Lines?
Parallel lines are lines in a plane that never meet; they are always the same distance apart and have the same slope. A true statement about parallel lines is that they never intersect, regardless of how far they are extended in either direction. This means that no matter what, there is always a consistent distance […]
Factor 15x³ + 5x² + 6x² by Grouping: What is the Resulting Expression?
To factor the expression 15x³ + 5x² + 6x² by grouping, we start by rearranging and combining like terms. Notice that the second and third terms can be combined: 15x³ + (5x² + 6x²) = 15x³ + 11x² Next, we will group the terms: (15x³) + (11x²) Now, we can factor out the greatest common […]
Find the Cube Roots of 27cos 279° i sin 279°
What is the solution to the system of equations y = 5x + 6 and y = 3x + 4?
To find the solution to the system of equations given by y = 5x + 6 and y = 3x + 4, we need to set the two equations equal to each other since they both equal y: 5x + 6 = 3x + 4 Now, we will solve for x. First, let’s get all […]
How to Find the Domain and Range of a Parabola
To find the domain and range of a parabola, you first need to understand its general form and characteristics. Domain The domain of a parabola is the set of all possible x-values that the function can take. Since a parabola extends indefinitely in both the left and right directions, the domain is always all real […]
A circle has its center at (2, 5) and a radius of 4 units. What is the equation of the circle?
The standard form of the equation of a circle is given by the formula: (x – h)² + (y – k)² = r² where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is at (2, 5), so h = 2 and k […]
Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply and explain.
A regular pentagon has several properties that make it unique when it comes to symmetry. It has 5 lines of symmetry. Each line of symmetry passes through a vertex and the midpoint of the opposite side. The lines of symmetry divide the pentagon into congruent halves. To explain: A regular pentagon has equal-length sides and […]
What is the solution to the system of equations y = 3x + 8 and y = 5x + 2?
To find the solution to the system of equations, we need to set the two equations equal to each other since both are equal to y: Equation 1: y = 3x + 8 Equation 2: y = 5x + 2 Setting the equations equal gives us: 3x + 8 = 5x + 2 Now, we […]
What is the value of x to the nearest tenth?
To find the value of x to the nearest tenth, we first need to have an equation or information about x. Let’s assume we have a simple linear equation such as 2x + 3 = 11. To solve for x, we can follow these steps: Subtract 3 from both sides: 2x = 11 – 3 […]