How do I solve and graph the absolute value inequality 2|x| < 5?
To solve the absolute value inequality 2|x| < 5, we first isolate the absolute value. 1. Divide both sides by 2: |x| < 2.5 2. Now we can rewrite the absolute value inequality as two separate inequalities: -2.5 < x < 2.5 This means that x can take any value between -2.5 and 2.5, not […]
How to Find the Min and Max of a Quadratic Function
To determine the minimum or maximum of a quadratic function, you first need to understand its general form, which is: f(x) = ax² + bx + c In this equation, a, b, and c are constants, and the value of a helps define the shape of the parabola. 1. Identify the Coefficient a: If a […]
How do you express sin 30 in terms of trigonometric functions of theta?
To express sin 30 in terms of trigonometric functions of theta, we first need to recall the value of sin 30 degrees. We know that sin 30° = 1/2. Now, to relate this to the angle theta, we must find a context or a specific scenario where theta can be set such that the sine […]
Which of the following is a factor of the polynomial 2x² + 3x + 5?
To determine which of the options is a factor of the polynomial 2x² + 3x + 5, we need to look at the polynomial and consider the process of factoring. Since we’re not provided with the specific answer choices, we can go through the general approach to finding factors. First, we check if the polynomial […]
Which is a factor of x² + 8x + 48?
To determine a factor of the expression x² + 8x + 48, we can start by trying to factor it into two binomials. The standard approach is to look for two numbers that multiply to the constant term (48) and add to the coefficient of the linear term (8). In this case, we need to […]
What are the solutions of the equation 4x² + 3x – 24 = 0?
To find the solutions of the equation 4x² + 3x – 24 = 0, we can use the quadratic formula. The standard form of a quadratic equation is ax² + bx + c = 0, where a = 4, b = 3, and c = -24. The quadratic formula is given by: x = (-b […]
If a car goes from 20 miles per hour to 10 miles per hour in 5 seconds, find its acceleration
To find the acceleration of the car, we can use the formula for acceleration, which is a = (v_f – v_i) / t where: a is the acceleration v_f is the final velocity v_i is the initial velocity t is the time taken In this case: The initial velocity (v_i) is 20 miles per hour. […]
How do I write the equation 2x + 3y = 6 in slope-intercept form?
To convert the equation 2x + 3y = 6 into slope-intercept form, which is represented as y = mx + b (where m is the slope and b is the y-intercept), we need to isolate y. Starting with the original equation: 2x + 3y = 6 First, we want to move the term with x […]
If a Pentagon is a Regular Pentagon, then What is the Measure of Each Interior Angle?
To find the measure of each interior angle of a regular pentagon, we can use a simple formula: Interior Angle = (n – 2) × 180° / n Where n is the number of sides of the polygon. For a pentagon, n = 5. So, the calculation would be: (5 – 2) × 180° / […]
How to Find an Equation for the nth Term of the Arithmetic Sequence 15, 6, 3, 12?
To find the nth term of the arithmetic sequence 15, 6, 3, 12, we first need to identify the common difference and the first term. The common difference (d) is the difference between consecutive terms. Let’s calculate that: 6 – 15 = -9 3 – 6 = -3 12 – 3 = 9 Here, we […]