Which point is an x-intercept of the quadratic function f(x) = x^2 – 8x + 9?
To find the x-intercepts of the quadratic function, we need to set the function equal to zero and solve for x. The function given is: f(x) = x^2 – 8x + 9 Setting f(x) to zero: 0 = x^2 – 8x + 9 This is a standard form of a quadratic equation. To solve for […]
The Sum or Product of a Non-Zero Rational Number and an Irrational Number is Always?
The sum or product of a non-zero rational number and an irrational number is always irrational. To understand why this is the case, let’s first define our terms. A rational number is any number that can be expressed as the quotient of two integers (where the denominator is not zero), such as 1/2 or -3. […]
What are the solutions of the equation x^4 + 5x^2 – 14 = 0? Use factoring to solve.
To solve the equation x4 + 5×2 – 14 = 0 by factoring, we can start by making a substitution to simplify the expression. Let y = x2. This transforms the equation into a quadratic form: y2 + 5y – 14 = 0 Next, we will factor this quadratic equation. We are looking for two […]
What is the mass of a solid cylinder with a radius of 2 cm, a length of 7 cm, and a density of 31 g/cm³?
To determine the mass of the solid cylinder, we can use the formula: Mass = Volume × Density First, we need to calculate the volume of the cylinder. The formula for the volume of a cylinder is: Volume = π × r² × h Where: π (pi) is approximately 3.14, r is the radius, and […]
How do you solve the system of equations 9x + 2y = 5 and y = 2x + 3?
To solve the system of equations algebraically, we have the following equations: 9x + 2y = 5 y = 2x + 3 We can use substitution to solve this system. Since the second equation already expresses y in terms of x, we can substitute that expression into the first equation. Substituting y from the second […]
Write Five Rational Numbers Greater Than 2
Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. To find rational numbers greater than 2, we can simply add a decimal or fraction to 2 or consider integers greater than 2. Here are five examples of rational numbers greater than 2: 2.1 2.5 […]
What is the general form of the equation of a circle with center at a, b and radius of length m?
The general form of the equation of a circle with center at the point (a, b) and radius m is given by the formula: (x – a)² + (y – b)² = m² In this equation: (x, y) represents any point on the circle. (a, b) is the center of the circle. m is the […]
A model of a car is 4 inches long; if the actual car is 8 feet long, find the scale of the model?
To find the scale of the model car to the actual car, we first need to convert the lengths to the same unit. The model car is 4 inches long, and the actual car is 8 feet long. Since there are 12 inches in a foot, we convert 8 feet to inches: 8 feet × […]
How many lines can pass through one given point and two given points?
When considering how many lines can pass through one given point, it’s essential to differentiate between the two scenarios: one point alone versus two points. For one given point, an infinite number of lines can pass through it. This is because you can draw a line at any angle around that point, and there is […]
What is the equation that represents the line that passes through the point (2, 2) and is parallel to y = (1/2)x + 8?
To find the equation of the line that passes through the point (2, 2) and is parallel to the line given by the equation y = (1/2)x + 8, we first need to determine the slope of the original line. The equation is in slope-intercept form, y = mx + b, where m represents the […]