If 5x + 13 = 3x + 3, what is the value of x?
To find the value of x in the equation 5x + 13 = 3x + 3, we need to isolate x. First, we can rearrange the equation to get all the x terms on one side. We start by subtracting 3x from both sides: 5x – 3x + 13 = 3 This simplifies to: 2x […]
How do you find the surface area of a rectangular prism?
To find the surface area of a rectangular prism, you can use the formula: Surface Area = 2lw + 2lh + 2wh Where: l = length w = width h = height This formula accounts for all six rectangular faces of the prism. Essentially, you calculate the area of each pair of opposite faces and […]
How do you write the equation x² + y² + z² = 49 in spherical coordinates?
To convert the equation x² + y² + z² = 49 into spherical coordinates, we need to recall the relationships between Cartesian and spherical coordinates. In spherical coordinates, the variables are defined as follows: x = ρ sin(φ) cos(θ) y = ρ sin(φ) sin(θ) z = ρ cos(φ) Here, ρ represents the radial distance from […]
How do you write an equation in slope-intercept form when given a slope and a point?
To write an equation in slope-intercept form, which is expressed as y = mx + b, you need to follow these steps when provided with a slope (m) and a point (x, y). For example, let’s say the slope (m) is 2 and the point given is (3, 4). Use the point-slope formula: We can […]
Find the slope of the tangent line to the parabola y = 4x – x² at the point (1, 3)
To find the slope of the tangent line to the given parabola at the specified point, we need to follow these steps: Start with the equation of the parabola: y = 4x – x². Differentiate the equation with respect to x to find the derivative (dy/dx). This derivative represents the slope of the tangent line […]
Find the Number of Winners if Number of Participants is 63
To find the number of winners when the number of participants is 63, we first need to determine the context of the event. In many competitions, the number of winners can vary depending on the rules set for that particular event. For instance, in a raffle or lottery, there could be one grand prize winner, […]
How Many Female Members Are There in a Book Club with 415 Male Members?
To find the number of female members in the book club, we start with the total number of members and subtract the number of male members from it. The total number of members in the book club is 315, and we know that 415 of them are male. However, this doesn’t quite add up since […]
How do you find all the zeros of the function and write the polynomial as a product of linear factors for f(x) = x² – 25?
To find the zeros of the function f(x) = x² – 25, we start by setting the function equal to zero: f(x) = 0x² – 25 = 0 Next, we can solve for x by adding 25 to both sides: x² = 25 Now, we take the square root of both sides. Remember that taking […]
What is the solution of log3x 4125 3?
To find the solution for the equation log3(x) = 4125, we need to understand what this logarithmic expression means. The logarithm tells us the power to which the base (in this case, 3) must be raised to obtain a certain number (x). In simpler terms, if we have log3(x) = 4125, we can rewrite it […]
Find the first four terms of the sequence a1, a4, a1
To find the first four terms of the sequence defined by a1, a4, and a1 (which seems to suggest that a1 is repeated), we first need to clarify what the sequence actually looks like. If we assume that an refers to a sequence defined by a rule or a function, we need some form of […]