To find the inverse of the function y = 2×2 + 2, we need to follow several steps: Start with the original function: Write the equation with y on one side: y = 2×2 + 2 Swap y and x: To find the inverse, we interchange x and y in the equation: x = 2y2 … Read more
To express the fractions 12/316 and 7/8 with a least common denominator (LCD), follow these steps: Step 1: Determine the Denominators The denominators of our fractions are 316 and 8. Step 2: Find the Prime Factorization Next, we need to find the prime factorization of each denominator: 316: It can be factored as follows: 316 … Read more
To find the exact length of the polar curve defined by the equation r = e^(3θ), we can use the formula for the arc length of a polar curve. The arc length L from θ = a to θ = b is given by: L = \int_a^b \sqrt{\left(\frac{dr}{dθ}\right)^2 + r^2} \, dθ. In our case, … Read more
To find the number of which 24 is 60%, we can set up a simple equation. Let's denote the unknown number as X. The relationship can be described mathematically as: 60% of X = 24 We can express 60% as a fraction. So, rewrite the equation: 0.60 * X = 24 To solve for X, … Read more
To find the slope of the line from the equation 3x + 2y = 8, we first need to rearrange it into the slope-intercept form, which is given by: y = mx + b where m represents the slope and b represents the y-intercept. Starting with the original equation: 3x + 2y = 8 We … Read more
To solve the equation 3/(3x) + 1/(x + 4) = 10/(7x), we need to find the value of x. Let’s break down the steps: Find a common denominator: The left side has two fractions, one with a denominator of 3x and the other with x + 4. The least common denominator (LCD) of the left-hand … Read more
A polynomial is considered prime (or irreducible) if it cannot be factored into the product of two non-constant polynomials with coefficients in the same field. Here are some key types of polynomials that qualify as prime: Linear Polynomials: Any polynomial of the form ax + b where a != 0 is prime, as it cannot … Read more
Yes, a triangle with side lengths of 3, 4, and 5 can indeed be classified as a right triangle. To determine this, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of … Read more
To find the exact value of cos 132 degrees, we can follow a few steps using the unit circle and trigonometric identities. First, we can recognize that the angle 132 degrees is located in the second quadrant of the unit circle, where the cosine function takes negative values. We can express 132 degrees in relation … Read more
To simplify the expression √10 * √8, you can use the property of square roots that states √a * √b = √(a * b). 1. **Combine the square roots**: Start by combining the two square roots: √10 * √8 = √(10 * 8) 2. **Perform the multiplication inside the square root**: Calculate the product of … Read more