Algebra

177.8 centimeters

178 cm

5 feet, 10 inches.

A bouncing ball can be considered a dependent variable when its behavior is being measured in relation to other factors, such as the height from which it's dropped or the surface it bounces on. In experimental setups, the conditions that affect the ball's bounce (like surface type or drop height) are the independent variables. Therefore, the ball's bounce characteristics depend on these independent variables.

3 ft 2 in

864 square inches

2.127 square feet.

About one-half (0.531) inch.

True

The result after multiplying a set of numbers or algebraic expressions is called the "product." In mathematics, the product is obtained by performing multiplication on the given values or variables. For example, multiplying 3 and 4 gives a product of 12, while multiplying algebraic expressions like (x) and (y) yields a product of (xy).

You divide to isolate the variable when the variable is being multiplied by a number or expression. By dividing both sides of the equation by that number or expression, you can simplify the equation and solve for the variable. This step is commonly used in algebra to maintain balance in the equation while isolating the desired variable on one side. Always ensure that the number you are dividing by is not zero, as division by zero is undefined.

To write the inequality represented by a graph, first identify the boundary line, which can be solid (indicating '≤' or '≥') or dashed (indicating '<' or '>'). Determine which side of the line is shaded, as this indicates the solution set. Use a test point, often the origin (0,0), to confirm whether it satisfies the inequality. Finally, combine this information to express the inequality in standard form.

To complete the square for the expression (x^2 - 6x + 20), we first focus on the quadratic part (x^2 - 6x). We take half of the coefficient of (x), which is (-6), giving us (-3), and then square it to get (9). We can rewrite the expression as ((x - 3)^2 - 9 + 20), simplifying to ((x - 3)^2 + 11). Thus, the completed square form is ((x - 3)^2 + 11).

To obtain necessary documents for problem-solving, start by accessing centralized databases, company archives, or digital repositories where drawings, charts, specifications, and manuals are stored. Collaborate with colleagues or departments that may have historical maintenance reports or other relevant documentation. Once gathered, interpret these materials by cross-referencing them with the current issue, ensuring you understand the context and details that pertain to the problem at hand, which will inform your analysis and solution approach.

To find the polynomial that represents the difference, you'll need to subtract one polynomial from another. If you provide the specific polynomials involved, I can help you determine the resulting polynomial from their difference. Please share the polynomials you'd like to subtract!

To simplify (10b + 8b), you combine the like terms. Adding the coefficients, (10 + 8) equals (18). Therefore, the simplified expression is (18b).

The tear gland, also known as the lacrimal gland, is responsible for producing tears, which serve several important functions. Tears help to lubricate the surface of the eye, providing moisture and preventing dryness. They also contain enzymes and antibodies that help protect the eye from infections and foreign particles. Additionally, tears play a role in emotional expression, as they can be produced in response to feelings such as sadness or joy.

In the Cartesian plane, the x variable is considered independent when it is not influenced by or dependent on the y variable. This means that for any value of x, there can be multiple corresponding values of y, allowing for a vertical line to represent all possible y-values for a single x-value. In contrast, if y depends on x (as in a function), then x is independent while y is dependent. Thus, in the context of a function, x is treated as the independent variable.

It seems like there's a typo in your equation. If you meant (x + 2y = 13), you can use the substitution method by solving for (x) in terms of (y). Rearranging gives (x = 13 - 2y). You can then substitute this expression for (x) into another equation if you're solving a system of equations.

To get the numbers 1-100 using four nines in the Four Nines Contest, you can employ various mathematical operations such as addition, subtraction, multiplication, division, square roots, and factorials. For example, you can create the number 1 by using the expression ((9 + 9 - 9) / 9). Similarly, for other numbers, combinations of these operations can be creatively applied, like using (9 + 9 + \frac{9}{9}) to get 19. The challenge lies in finding unique combinations for each number from 1 to 100.

To simplify the expression (3(x - y) + 4(x \cdot 2y)), first distribute (3) in the first term: (3x - 3y). For the second term, multiply (4) by (2xy) to get (8xy). Combining these results, the final expression is (3x - 3y + 8xy).

The steepness of a slope significantly impacts runoff by influencing the speed and volume of water flow. Steeper slopes tend to increase the velocity of runoff, reducing the time water has to infiltrate into the soil, which can lead to greater surface runoff. This higher runoff can contribute to soil erosion and increased risk of flooding in areas with steep terrain. Conversely, gentler slopes allow for more water absorption, decreasing runoff and promoting groundwater recharge.

The punchline of Bata shoes revolves around their tagline, "Bata: We Fit Your Life," which emphasizes comfort and affordability. The brand is often humorously associated with the idea that their shoes can be suitable for any occasion, making them a practical choice for everyone. This clever play on words highlights Bata's versatility and accessibility in footwear.

It seems like the inequality you mentioned is incomplete. If you provide the full inequality (for example, "x + 638 > 0" or "x + 638 < 100"), I can help identify which numbers belong to the solution set. Please provide the complete inequality for a more accurate response.