To solve the quadratic equation x² + 6x + 7 = 0 by completing the square, we’ll follow these steps: Rearrange the equation: Start by moving the constant term to the right side of the equation: x² + 6x = -7 Complete the square: To complete the square, we need to turn the left side … Read more
In a 30-60-90 triangle, the sides are in a specific ratio that helps us easily determine the lengths of the sides based on the shortest leg. The ratio of the sides in a 30-60-90 triangle is 1 : √3 : 2. This means: The shortest leg (opposite the 30-degree angle) is 1 part. The longer … Read more
To find the volume of a sphere when given its diameter, we first need to determine the radius. The radius (r) is half of the diameter, so if the diameter of the sphere is 4 centimeters, the radius is: Radius (r) = Diameter / 2 = 4 cm / 2 = 2 cm Next, we … Read more
To solve the inequality 4 × x + 3 × 2 × 2 × x, let’s first clarify it. The expression needs to be correctly phrased as an inequality. For instance, we could be looking at something like 4x + 3 < 2(2x), which is common in solving inequalities. 1. **Combine Like Terms**: First, simplify ... Read more
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