What is the volume of a cuboid with length of 10cm, width of 5cm, and height of 8cm?
The volume of a cuboid can be calculated using the formula: Volume = Length × Width × Height In this case, we have: Length = 10 cm Width = 5 cm Height = 8 cm Substituting these values into the formula gives us: Volume = 10 cm × 5 cm × 8 cm Calculating that, […]
Where do the lines xy = 0 and 6x + 5y = 22 intersect?
To find the intersection point of the lines represented by the equations xy = 0 and 6x + 5y = 22, we first analyze each equation. The equation xy = 0 describes two lines: one where x = 0 (the y-axis) and one where y = 0 (the x-axis). The second equation, 6x + 5y […]
Find the value of x rounded to the nearest tenth. The diagram is not drawn to scale. The adjacent is 12cm wide and the angle of the hypotenuse is at 35 degrees.
To find the value of x in this right triangle, we can use the cosine function, which relates the adjacent side to the hypotenuse. According to trigonometric principles: cos(θ) = adjacent / hypotenuse Here, θ is 35 degrees, and the length of the adjacent side is 12 cm. We need to find hypotenuse (x). Rearranging […]
What values of c and d make the equation true: 162x^c y^5 = 3x^2 y^6 y^d?
To determine the values of c and d that make the equation 162xcy5 = 3x2y6yd, we first need to simplify the right-hand side. The term y6yd can be combined using the properties of exponents: y6yd = y6 + d. Now, the equation looks like this: 162xcy5 = 3x2y6 + d. Next, we compare the coefficients […]
Find the ordered pair which is a solution of the equation 2xy = 9
To find an ordered pair (x, y) that satisfies the equation 2xy = 9, we need to isolate one of the variables. Let’s solve for y in terms of x: Starting with the equation: 2xy = 9 Now, divide both sides by 2x (assuming x is not zero): y = 9/(2x) This means that for […]
How to Find the Equation of a Line with Two Points
To find the equation of a line given two points, you can follow these steps: Identify the Points: Assume you have two points, (x1, y1) and (x2, y2). Calculate the Slope: The slope (m) of the line through these two points can be calculated using the formula: m = (y2 – y1) / (x2 – […]
If an object travels at five feet per second, how many feet does it travel in one hour?
To find out how many feet an object travels in one hour when it’s moving at five feet per second, we can start by determining how many seconds are in one hour. There are 60 seconds in a minute and 60 minutes in an hour, giving us a total of: 60 seconds/minute × 60 minutes/hour […]
If the line tangent to the graph of the function f at the point 1, 7 also passes through the point 2, 2, then what is the value of f(1)?
To find the value of f(1), we start by using the information that the tangent line at the point (1, 7) also passes through the point (2, 2). First, we need to find the slope of the tangent line. The slope (m) can be calculated using the formula: m = (y2 – y1) / (x2 […]
What is the equation in point slope form of the line passing through (3, 6) and (2, 1)?
To find the equation of the line in point-slope form that passes through the points (3, 6) and (2, 1), we first need to calculate the slope of the line. The slope (m) can be found using the formula: m = (y2 – y1) / (x2 – x1) Here, we will designate (x1, y1) as […]
Identify the 35th term of an arithmetic sequence where a1 is 7 and a18 is 95
To find the 35th term of an arithmetic sequence, we first need to determine the common difference. The general formula for the nth term of an arithmetic sequence is given by: an = a1 + (n – 1) * d where: an is the nth term, a1 is the first term, d is the common […]