To determine whether the line y = 3x + 7 is parallel or perpendicular to the line 3x + 9y = 9, we first need to put both equations into the slope-intercept form, which is y = mx + b, where m indicates the slope of the line. Step 1: Identify the slope of the … Read more
To solve the quadratic equation x² + 12x + 6 = 0 using the method of completing the square, we will follow these steps: Move the constant to the other side: Start by isolating the x terms. We can do this by subtracting 6 from both sides: x² + 12x = -6 Complete the square: … Read more
To determine the equation that models the relationship between the variables y, w, x, and z, we start by understanding the principle of joint and inverse variation. When we say that y varies jointly with w and x, it means that y is proportional to the product of w and x. Additionally, since y varies … Read more
To rewrite the equation of the sphere in standard form, we start with the given equation: 2×2 + 2y2 + 2z2 – 8x – 24z + 1 = 0 First, we can simplify the equation by dividing everything by 2: x2 + y2 + z2 – 4x – 12z + rac{1}{2} = 0 Next, we … Read more
To find the ratio of the volumes of two cylinders, we can use the formula for the volume V of a cylinder, which is given by: V = πr2h Where: r = radius of the cylinder h = height of the cylinder π ≈ 3.14 (or you can use the greater precision of π as … Read more
Converting to Vertex Form The standard form of a quadratic function is given by: y = ax² + bx + c In this case, we have: y = x² + 2x + 5 To convert this to vertex form, which is: y = a(x – h)² + k where (h, k) is the vertex of … Read more
To find the lateral surface area of a hexagonal prism, we first need to understand the components involved in the formula. A hexagonal prism consists of two hexagonal bases connected by rectangular faces. The lateral surface area (LSA) refers specifically to the area of these rectangular faces, not including the bases. Here is a step-by-step … Read more
Finding the x-Intercepts To find the x-intercepts of the function f(x) = x² + 4x – 12, we need to determine the values of x where the graph of the function crosses the x-axis. This occurs where the function equals zero, so we set up the equation: x² + 4x – 12 = 0 Step … Read more
To find the length of an arc in a circle, you can use the formula: Arc Length = rac{ heta}{360} imes 2 ext{π}r Where: heta = angle of the arc in degrees r = radius of the circle π (Pi) ≈ 3.14159 In this case: The radius (r) is 8. The angle ( heta) is … Read more
To find the inverse function of f(x) = 2x + 6, we need to follow a few logical steps. The first step is to replace f(x) with y: Step 1: Rewrite the function: y = 2x + 6 Step 2: Swap x and y: x = 2y + 6 Step 3: Solve for y. To … Read more