Understanding the Expression To determine which expression is a factor of 3xy + 2x + 18y + 12, we first need to simplify and analyze the terms of the provided expression. The expression can be rearranged to facilitate factoring. Rearranging the Expression The expression can be grouped as follows: 3xy + 18y + 2x + … Read more
The prime factorization of a number involves breaking it down into the simplest factors that are prime numbers. To find the prime factorization of 50, we start by identifying the smallest prime number that divides 50. First, we notice that 50 is an even number, so we can divide it by 2: 50 ÷ 2 … Read more
To find the volume of a right triangular prism, you can use the following formula: Volume = Base Area × Height 1. **Calculate the Base Area**: Since the base of the prism is a right triangle, you need to determine the area of the triangle first. The area of a triangle can be calculated using … Read more
To analyze the expression 3 + 4i + 5 + 6i + 3 + 5 + 4i + 6i, we need to identify which property of addition is being displayed. The property that applies here is the Commutative Property of Addition. The Commutative Property states that the order in which two numbers are added does … Read more
To simplify the rational expression \( \frac{t^2}{6t^2 + 9} \), we’ll start by factoring the denominator. The expression in the denominator, \( 6t^2 + 9 \), can be factored by taking out the greatest common factor: Factoring out a 3: \( 6t^2 + 9 = 3(2t^2 + 3) \) Now the original expression can be … Read more
To find the area of the shaded sector when the measure of central angle ABC is θ = p2 radians, we can use the formula for the area of a sector of a circle: Area of Sector = 0.5 × r2 × θ Where: r is the radius of the circle. θ is the angle … Read more
To find the x-intercept of the graph of the equation y = x² + 4x + 4, we need to determine the points where the graph intersects the x-axis. This occurs when y = 0. Here are the steps to find the x-intercept: Set the equation to zero: Replace y by 0 in the equation: … Read more
The provided sequence is: 14 5 18 24 15 28 34 To find the next number in the sequence, let’s analyze the pattern: First, we will separate the sequence into two different parts. If we observe the positions, we have: Odd indices: 14, 18, 15, 34 Even indices: 5, 24, 28 Now, let’s look at … Read more
To find the measure of angle PQR when the measure of arc QR is 100 degrees, we can apply the concept of inscribed angles in a circle. In circle geometry, the measure of an inscribed angle is always half the measure of the intercepted arc. Therefore, the formula to calculate the measure of angle PQR … Read more
To calculate the future value of an investment, we can use the formula: Future Value (FV) = Present Value (PV) x (1 + r) Where: FV = Future Value PV = Present Value (the amount you are investing now) r = interest rate (expressed as a decimal) In this case: PV = $500 r = … Read more