Find the sum of 4x³ + 2x² + 4x + 3 and 7x³ + 4x² + 7x + 8
To find the sum of the two polynomials, we start by aligning like terms. The given polynomials are: 1. 4x³ + 2x² + 4x + 3 2. 7x³ + 4x² + 7x + 8 Next, we combine the coefficients of each degree of x: For x³
What is the value of x in the equation 42x 12 0?
To solve the equation 42x 12 0, we first need to clarify the equation since it seems to be missing an operator. Assuming it should be written as 42x + 12 = 0, we can solve for x. Here are the steps to find x: First, isolate the term with x: 42x + 12 = […]
Is 0 a Rational or Irrational Number?
0 is a rational number. A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. In this case, 0 can be represented as 0/1, 0/2, or any other fraction where the numerator is 0 and the denominator is a non-zero integer. […]
Use the Zero Product Property to Find the Solutions to the Equation x² – 30x + 12
To solve the equation x² – 30x + 12 = 0 using the Zero Product Property, we need to factor the quadratic expression on the left-hand side. The Zero Product Property states that if the product of two factors equals zero, then at least one of the factors must be zero. First, let’s factor the […]
Which expression is equivalent to 6x² + 19x + 55?
To find an expression equivalent to 6x² + 19x + 55, we can use factoring methods. The expression is a quadratic of the form ax² + bx + c, where a = 6, b = 19, and c = 55. We will look for two numbers that multiply to (a * c) = (6 * […]
What is the solution set of x² – 10 – 30x?
To solve the equation x² – 30x – 10 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In our equation, a = 1, b = -30, and c = -10. Let’s substitute these values into the formula: x = (30 ± √((-30)² […]
When the step function f(x) is graphed, what is the value of f(1)?
The value of f(1) for a step function can be determined by looking at the graph of the function. Step functions are piecewise constant functions that take a constant value within certain intervals. To find f(1), we need to identify the interval that includes x = 1 on the graph. In a typical step function, […]
What is the altitude of a triangle?
The altitude of a triangle is a line segment drawn from a vertex perpendicular to the line containing the opposite side. This segment helps in determining the height of the triangle, which is crucial for calculating its area. More specifically, each triangle has three altitudes, one from each vertex. The length of the altitude can […]
Which number comes next in this series 2 3 4 8 9 10 20 21 22?
To determine the next number in the series 2, 3, 4, 8, 9, 10, 20, 21, 22, let’s first analyze the pattern of the series. The series can be divided into two distinct groups: The first group consists of the numbers: 2, 4, 8, 20. These numbers can be derived by multiplying the previous number […]
Name the types of triangles with lengths of side 80
A triangle with all three sides measuring 80 units is classified as an equilateral triangle. In an equilateral triangle, all three sides are equal in length, and consequently, all three interior angles are also equal, each measuring 60 degrees. This type of triangle is known for its symmetry and is one of the most common […]