Given the function f(x) = 4 – 2x if the domain is [0, 5], find the range.
To find the range of the function f(x) = 4 – 2x over the domain [0, 5], we first need to evaluate the function at the endpoints of the domain. 1. **Calculate f(0):** Substituting x = 0 into the function: f(0) = 4 – 2(0) = 4 2. **Calculate f(5):** Now, substituting x = 5 […]
A password consists of 2 letters followed by 2 digits. How many different passwords can be formed?
To determine how many different passwords can be formed with the structure of 2 letters followed by 2 digits, we need to break down the components. First, consider the letters. The English alphabet has 26 letters. If we are creating a password with 2 letters: The first letter can be any of the 26 letters. […]
How do you simplify the expression 5 log2 k + 8 log2 m + 10 log2 n?
To simplify the expression 5 log2 k + 8 log2 m + 10 log2 n, we can make use of the properties of logarithms. The first step is to factor out the common logarithmic base, which is base 2 in this case. We can rewrite each term using the power rule of logarithms, which states […]
Which of the following conditions makes a pair of triangles congruent?
Two triangles are considered congruent when they are identical in shape and size, which means all corresponding sides and angles are equal. There are several conditions under which this congruence can be established: Side-Side-Side (SSS) Congruence: If all three sides of one triangle are equal to the three sides of another triangle, the triangles are […]
What is the vertex of the quadratic function f(x) = x^2 – 6x?
To find the vertex of the quadratic function f(x) = x^2 – 6x, we can use the vertex formula. The standard form of a quadratic function is given by f(x) = ax^2 + bx + c, where a, b, and c are constants. In this case, we have: a = 1 b = -6 c […]
How do I write the equation in vertex form equivalent to f(x) = x² + x + 1?
To convert the equation f(x) = x² + x + 1 into vertex form, we will complete the square. 1. Start with the original function: f(x) = x² + x + 1 2. Take the coefficient of x, which is 1, divide it by 2, and square it. This gives us: (1/2)² = 1/4. 3. […]
An equation has solutions of m = 5 and m = 9. Which could be the equation?
To find an equation that has solutions of m = 5 and m = 9, we can use the concept of factoring a quadratic equation based on its roots. If m = 5 and m = 9 are the solutions, we can represent the equation in factored form as follows: (m – 5)(m – 9) […]
How do I write the complex number 6 + 5i + 2 + 3i in standard form?
To write the complex number 6 + 5i + 2 + 3i in standard form, we first need to combine the real parts and the imaginary parts separately. The real parts are 6 and 2. When we add these together, we get: 6 + 2 = 8 The imaginary parts are 5i and 3i. Adding […]
How to find vector ab if a = 8i + 6j and b = 4i + 5j?
To find the vector ab, we need to subtract vector a from vector b. In vector notation, this can be expressed as: ab = b – a Given that: a = 8i + 6j b = 4i + 5j Now, we can substitute the values of a and b into the equation: ab = (4i […]
In circle O, AD and BE are diameters. What is MAE?
To find the angle MAE in circle O where AD and BE are diameters, we need to understand the properties of circles and diameters. Since both AD and BE are diameters, we know that they intersect at the center of the circle, point O. In a circle, any angle formed by two diameters is a […]