How do you express the area A of a rectangle as a function of the width w if the width of the rectangle is twice its length?
To express the area A of a rectangle as a function of the width w when the width is twice the length, we start by establishing the relationship between the width and length of the rectangle. Let the length of the rectangle be denoted as L. According to the problem, the width (W) is twice […]
What is the area of the figure?
The area of a figure is the amount of space enclosed within its boundaries. To calculate the area, you need to know the shape of the figure, as different shapes have different formulas for area calculation. For instance: Rectangle: Area = length × width Triangle: Area = 1/2 × base × height Circle: Area = […]
Solve for x: 7/8 – 1/x = 3/4
To solve the equation 7/8 – 1/x = 3/4, we need to isolate x. Start by getting rid of the fractions. First, let’s rewrite the equation for clarity: 7/8 – 1/x = 3/4 Next, we can eliminate the fractions by finding a common denominator. The common denominator of 8 and 4 is 8. To make […]
How to Solve the Expression: 3×4 + 2×3 + 1 + 12×4 + x2 + 11?
To solve the expression 3×4 + 2×3 + 1 + 12×4 + x2 + 11, we’ll first look at the like terms and combine them. 1. Identify like terms: 3×4 and 12×4 (which are both terms with x raised to the power of 4) 2×3 (a term with x raised to the power of 3) […]
What are the subtraction property of linear inequalities?
The subtraction property of linear inequalities states that if you subtract the same number from both sides of an inequality, the direction of the inequality remains the same. For example, if you have an inequality like: 4x + 5 > 3 and you subtract 5 from both sides, you get: 4x + 5 – 5 […]
For a population with a mean of 40 and a standard deviation of 8, find the z score corresponding to each of the following samples.
To find the z score for a sample within a population, you can use the z score formula: z = (X – μ) / σ Where: X = the value of the sample μ = the mean of the population σ = the standard deviation of the population In this case, the population mean (μ) […]
Find the Maximum or Minimum Value of the Quadratic Function by Completing the Squares
To find the maximum or minimum value of the given quadratic function, we first need to rewrite the function in the completed square form. The function is: y = 2x² + 4x + 7 1. **Factor out the coefficient of x²** from the first two terms: y = 2(x² + 2x) + 7 2. **Complete […]
What is the solution set of the given system of equations 2y = x + 3 and 5y = x + 7?
To solve the system of equations given by 2y = x + 3 and 5y = x + 7, we will first rewrite both equations to express y in terms of x. From the first equation: 2y = x + 3 can be rewritten as: y = (x + 3)/2 From the second equation: 5y […]
A two dimensional object is called a shape and a three dimensional object is known as a?
A three dimensional object is known as a solid. In geometry, we often categorize objects based on their dimensions. A two-dimensional object exists in a plane and has only two dimensions: length and width. Examples include circles, squares, and triangles. On the other hand, a three-dimensional object has depth in addition to length and width, […]
How much area can water in a canal irrigate in 30 minutes if 8cm of standing water is desired?
To find out how much area the water can irrigate, we need to first calculate the volume of water flowing in the canal and then determine how much area that volume can cover with the desired standing water depth. 1. **Calculate the volume of water flowing per second:** The dimensions of the canal tell us […]