devyy To find the length of the hypotenuse of a right triangle when the lengths of the two legs are known, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of … Read more
The basic unit of volume in the metric system is c) liter. The liter is widely used to measure liquids and is a fundamental unit within the metric system, which is based on powers of ten. A liter is equivalent to 1,000 cubic centimeters (cm³) and can be thought of as the volume occupied by … Read more
The formulas for 1 + cos(2x) and 1 – cos(2x) can be derived using trigonometric identities. Firstly, let’s consider 1 + cos(2x). This expression can be simplified using the half-angle identity. The cosine double angle formula states: cos(2x) = 2cos²(x) – 1 Using this identity, we replace cos(2x) in our formula: 1 + cos(2x) = … Read more
To find the remainder when the expression 32 + 32 + 32 is divided by 7, we can first simplify the expression. 1. **Calculate the Total:** When we add 32, 32, and 32 together, we get: 32 + 32 + 32 = 96 2. **Divide by 7:** Now we need to find the remainder when … Read more
To find the measure of angle WRS in the diagram, we first need to identify the relevant angles or lines associated with this angle. Depending on the context, WRS may involve relationships such as complementary angles, supplementary angles, or angles formed by intersecting lines. If WRS specifically represents the angle formed by two intersecting lines, … Read more
The expression 2x^3 + 4x^2 + x can be factored by first identifying the common factors in each term. In this case, we see that each term has a factor of x, and we can also factor out 2 from the first two terms. Here’s how to approach it step-by-step: Identify the common factors: Each … Read more
The shape with six sides is known as a hexagon. This name is derived from the Greek word ‘hex’, which means six, paired with ‘gonia’, meaning angle. Thus, hexagons are polygons that consist of six straight sides and six angles. Hexagons can be found in various forms and structures in both nature and human-made designs. … Read more
To determine how many tickets the stadium sells, we need to calculate three-fourths of its total seating capacity. The total seating capacity of the stadium is 1600 seats. We can calculate three-fourths of this number using the following steps: Start with the total number of seats: 1600. Identify what three-fourths means. Mathematically, three-fourths can be … Read more
The primary difference between a histogram and a stem-and-leaf plot lies in the way they represent data distribution visually. A histogram is a graphical representation of the frequency distribution of numerical data. It consists of bars where each bar represents the frequency of data points that fall within a specific range, known as a ‘bin’. … Read more
To solve the system of linear equations given by: 1. 3x + 2y = 14 2. 5x + y = 32 we can use the substitution or elimination methods. Here, we’ll utilize the elimination method for clarity. Step 1: Align the equations We first write the equations clearly: 3x + 2y = 14 (1) 5x … Read more