Which letter in the word happy has an order 2 rotational symmetry?
In the word happy, the letter that exhibits order 2 rotational symmetry is h. This means that if you rotate the letter h by 180 degrees (or half a turn), it looks the same as it did before the rotation. To further elaborate, order 2 symmetry allows an object to map onto itself in two […]
What is the solution set of the inequality 15y – 9 < 36y - 95 + 95y - 3y - 3?
To solve the inequality 15y – 9 < 36y - 95 + 95y - 3y - 3, we first simplify the right-hand side. Combining like terms on the right side gives us: 36y – 3y + 95y = (36 – 3 + 95)y = 128y -95 – 3 = -98 So the inequality becomes: 15y […]
How to Tell if a Function is Increasing or Decreasing by Calculus
To determine whether a function is increasing or decreasing using calculus, you should follow these steps: Find the derivative: Start by computing the derivative of the function, denoted as f'(x). The derivative measures the rate of change of the function. Set the derivative to zero: Solve the equation f'(x) = 0. The solutions will give […]
What is the inverse of the function f(x) = 2x + 1?
To find the inverse of the function f(x) = 2x + 1, we need to follow a few steps: Replace f(x) with y: We start by rewriting the function as: y = 2x + 1 Swap x and y: Next, we exchange the variables x and y: x = 2y + 1 Solve for y: […]
Which Shows One Way to Determine the Factors of 12x^3 2x^2 18x^3 by Grouping?
To determine the factors of the expression 12×3 + 2×2 + 18×3 by grouping, we first rearrange the terms: 12×3 + 18×3 + 2×2 Next, we can group the first two terms and the last term: (12×3 + 18×3) + (2×2) Now, factor out the common factors from each group: 6×3(2 + 3) + 2×2 […]
The vertex angle of an isosceles triangle measures 84; what is the measure of the base angle?
In an isosceles triangle, the two base angles are equal. To find the measure of the base angles when you know the vertex angle, you can use the fact that the sum of all angles in a triangle is always 180 degrees. Given that the vertex angle is 84 degrees, we can first subtract this […]
What is the measure of angle K in kite JKL-M?
To find the measure of angle K in kite JKL-M, we start by recalling some properties of kites. A kite has two pairs of adjacent sides that are equal and one pair of opposite angles that are equal. In this case, we can use the fact that the sum of the angles in any quadrilateral […]
What is the output of the function fp 3p 2 when the input is 2?
To determine the output of the function fp 3p 2 when the input is 2, we first need to analyze what the function ‘fp’ means. In many programming contexts, f often refers to a function and p can stand for parameters passed to that function. Given fp 3p 2, we can assume that this represents […]
Using Synthetic Division What is the Quotient of 2x³ + 3x + 10x²?
To perform synthetic division on the polynomial 2x³ + 10x² + 3x, we must first identify what we are dividing by. For this example, let’s assume we are dividing by (x – 1). The first step is to write down the coefficients of the polynomial: 2 (for x³) 10 (for x²) 3 (for x) 0 […]
Which equation has the solutions x² + 2x + 4 = 0?
To find the equation that has the solutions for x² + 2x + 4 = 0, we first need to consider what it means to solve a quadratic equation. The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants. In this case, we […]