What is a simpler form of the radical expression 4 √(1296 x^16 y^12)?
To simplify the radical expression 4 √(1296 x16 y12), we can break it down step by step. First, let’s look at the term inside the square root, √(1296 x16 y12): Finding the square root of 1296: The number 1296 is a perfect square. Its square root is 36 because 36 × 36 = 1296. Finding […]
Find the area of the green sector if m∠APB = 6° and the circle has a radius of 10 inches
To find the area of the green sector, we can use the formula for the area of a sector in a circle, which is given by: Area of sector = (m∠/360) × π × r² where: m∠ is the measure of the angle of the sector in degrees, π is approximately 3.14, and r is […]
Draw the graph of 15x + 5y = 30
To draw the graph of the equation 15x + 5y = 30, we first need to rearrange it in the format y = mx + b, where m is the slope and b is the y-intercept. 1. **Rearranging the Equation**: We start with the original equation: 15x + 5y = 30 Subtract 15x from both […]
How to find the function h(x) = f(x) + g(x) if f(x) = 3x and g(x) = 32x + 3x?
To find the function h(x), we first need to substitute the given functions f(x) and g(x) into the equation h(x) = f(x) + g(x). We know that: f(x) = 3x g(x) = 32x + 3x First, let’s simplify g(x): g(x) = 32x + 3x = 35x Now, we can substitute these results into the function […]
What is the equation in point slope form of the line passing through (2, 0) and (2, 8)?
To find the equation in point slope form of the line passing through the points (2, 0) and (2, 8), we first need to determine the slope of the line. The slope (m) is calculated using the formula: m = (y2 – y1) / (x2 – x1) Substituting our points (2, 0) as (x1, y1) […]
What are the zeros of the function and what are their multiplicities?
To find the zeros of the function defined by f(x) = 4x^4 + 4x^3 + 3x^2, we first set the function equal to zero: 4x^4 + 4x^3 + 3x^2 = 0 Next, we can factor out the common term, which is x^2: x^2(4x^2 + 4x + 3) = 0 This gives us one zero immediately, […]
Which of the following is a polynomial with roots 5, 4i, and -4i?
To find a polynomial with given roots, we can use the fact that if a number is a root of a polynomial, then the polynomial can be expressed in factored form using that root. In this case, the roots are 5, 4i, and -4i. The corresponding factors of the polynomial will be: (x – 5) […]
How to Solve the Expression x² + 8x + 20?
To solve the expression x² + 8x + 20, we first need to find the values of x that will satisfy the equation. This expression is a quadratic equation in the form of ax² + bx + c, where: a = 1 b = 8 c = 20 We can use the quadratic formula to […]
Given the point (4, 5) and the slope of 6, find y when x = 24
To find the value of y when x = 24, we can use the point-slope form of the equation of a line. The point-slope form is given by: (y – y1) = m(x – x1) where (x1, y1) is a point on the line and m is the slope. Here, we have the point (4, […]
What is the slope of the line that contains the points 15 and 32?
To find the slope of the line that contains the points 15 and 32, we first need to clarify what we mean by ‘points 15 and 32’. If we assume these represent points on a coordinate plane, we can interpret them as two points: (x1, y1) = (1, 5) and (x2, y2) = (3, 2) […]