To find the three consecutive multiples of 8 whose sum is 888, we can start by defining the multiples. Let the first multiple of 8 be represented as x. The next two consecutive multiples can be expressed as x + 8 and x + 16. Now, we can write an equation representing the sum of … Read more
To simplify the expression 4 over y to the power of negative 3, we start with the original expression: 4 / y-3 According to the rules of exponents, any term with a negative exponent can be rewritten by taking it to the opposite side of the fraction. This means that we can move y-3 from … Read more
An acre is a unit of area commonly used in the United States and other countries, and it plays a vital role in land measurement, particularly in agriculture and real estate. To understand how many feet are in an acre, we start with the basic definition: One acre is defined as a tract of land … Read more
To find the equation of a line given the y-intercept and slope, we can use the slope-intercept form of a linear equation, which is: y = mx + b In this equation: y represents the dependent variable (output), x represents the independent variable (input), m is the slope of the line, and b is the … Read more
To determine the angle between the two vectors u and v, you can use the dot product formula along with the magnitudes of the vectors. The dot product formula is given by: u · v = |u| |v| cos(θ) Where: u · v is the dot product of the vectors u and v. |u| and … Read more
To determine how many integers in the range from 1 to 140 are multiples of 2, 5, or 7, we can use the principle of inclusion-exclusion. First, let’s calculate the number of multiples for each individual number: Multiples of 2: The largest multiple of 2 within 140 is 140. To find how many multiples of … Read more
To derive a Cartesian equation from the given polar equations r = 4 tan(θ) and r = sec(θ), we start by utilizing the relationships between polar and Cartesian coordinates. In polar coordinates, r is the distance from the origin, and (x, y) are the Cartesian coordinates, which relate as follows: x = r cos(θ) y … Read more
The general equation of a circle in the Cartesian coordinate system can be expressed as: (x – h)² + (y – k)² = r² In this equation: (h, k) is the center of the circle. r is the radius. Given that the center of the circle is at the point (2, 1) and the radius … Read more
To determine the length of the line segment HJ in triangle GHJ, we first need to know some essential details about the triangle. Typically, this includes the lengths of its sides or the coordinates of its vertices if it’s plotted on a coordinate plane. If you have the lengths of the other two sides (let’s … Read more
The functions g(x) = x² and h(x) = x² represent the same mathematical expression. Here are some statements that can be evaluated for their truthfulness: They are both quadratic functions: True. Both functions can be classified as quadratic functions, as they can be expressed in the standard form f(x) = ax² + bx + c, … Read more