devyy 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
To express the quadratic function y = 2x² + 8x + 1 in vertex form, we will use the technique of completing the square. The vertex form of a quadratic function is given by: y = a(x – h)² + k Here, (h, k) is the vertex of the parabola. Step 1: Factor out the … Read more
To determine the probability of getting exactly 2 tails when flipping a fair coin 7 times, we can make use of the binomial probability formula. This formula is particularly applicable because we have a fixed number of trials (7 flips), two possible outcomes (heads or tails), and each flip of the coin has the same … Read more
An exponent is a fundamental concept in mathematics that indicates how many times a number, known as the base, is multiplied by itself. For example, in the expression 23, the number 2 is the base, and the exponent is 3. This means that you multiply the base (2) by itself three times: 2 × 2 … Read more
To determine what constant should be added to the expression x² + 6x in order to form a perfect square trinomial, we can follow a systematic approach. A perfect square trinomial can be expressed in the form (a + b)², which expands to a² + 2ab + b². In our case, we need to rewrite … Read more