Algebra

The square root of 180 is approximately 13.42. The two consecutive integers that this value lies between are 13 and 14.

The growth in language and problem-solving abilities in adulthood typically refers to cognitive development. This phase involves the refinement of critical thinking, reasoning, and communication skills, often influenced by life experiences, education, and social interactions. Adults may develop more sophisticated ways of understanding complex issues and navigating social dynamics, leading to improved decision-making and adaptability. This growth can continue throughout life, influenced by ongoing learning and engagement with diverse perspectives.

Adding a number to both sides of an equation is a strategy used to maintain the equality while transforming the equation into a more manageable form. By making one side a perfect square or a perfect cube, it allows for easier solving, especially when dealing with quadratic or higher-degree equations. This technique preserves the balance of the equation, ensuring that both sides remain equal, while facilitating the process of finding solutions.

In statistics and machine learning, "ŷ" (y hat) represents the predicted value of the dependent variable in a regression model. It is derived from the model's equation and indicates the estimated outcome based on the input variables. The hat notation signifies that this value is an estimate rather than an actual observation from the data.

You misunderstand 'Square metres (m^(2)' (Metric) is a measure of AREA , 'Feet' (Imperial) is s measure of LENGTH'.

Do you mean to convert 'sqare metres (m^(2)' to 'Square feet (sq.ft).

Note the units.

To create an equation of a line, you typically use the slope-intercept form, which is (y = mx + b), where (m) is the slope and (b) is the y-intercept. First, determine the slope by calculating the change in y over the change in x between two points on the line. Next, identify the y-intercept, where the line crosses the y-axis. Finally, substitute these values into the equation to get the line's equation.

To find the height of the building, we can use trigonometry. The angle of elevation (31°20') allows us to calculate the height above point A to the top of the building, while the angle of depression (12°50') helps us find the height from point A to the base of the building. By applying the tangent function for both angles and considering the height of point A (8.2 meters), we can derive the heights from these angles and find the total height of the building.

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Slope orientation refers to the direction that a slope faces, which can significantly influence various environmental factors, such as sunlight exposure, moisture retention, and temperature. For instance, south-facing slopes in the Northern Hemisphere typically receive more sunlight and warmth, promoting different vegetation compared to north-facing slopes. This concept is crucial in fields like agriculture, ecology, and geology, as it affects plant growth, soil erosion, and microclimate conditions. Understanding slope orientation helps in land management and conservation efforts.

Problem-solving as a win-win approach fosters collaboration and understanding, allowing parties to focus on shared interests rather than adversarial positions. By treating conflict as a problem to be solved, it encourages open communication and creative solutions that benefit all involved. This mindset reduces hostility and promotes lasting relationships, as it prioritizes the resolution of issues over the need to "win" the argument. Ultimately, it leads to more sustainable outcomes and a healthier environment for future interactions.

• 999999 x 999999999999 ÷ 99999999999999 ≈ 9999.99

To find the slope of the line through the points (39, y1) and (11, y2), you need both y-coordinates. The slope (m) is calculated using the formula ( m = \frac{y2 - y1}{x2 - x1} ). If you provide the y-coordinates for the points, I can help you calculate the slope.

The absolute value of a number is expressed as the number itself without regard to its sign. It is denoted by vertical bars: for example, the absolute value of ( x ) is written as ( |x| ). If ( x ) is positive or zero, ( |x| = x ); if ( x ) is negative, ( |x| = -x ). Thus, the absolute value represents the distance of a number from zero on the number line.

2 3

To factor the expression ((x + 1)^{1/2} - \frac{1}{3}(x + 1)^{3/2}), we can first factor out the common term ((x + 1)^{1/2}). This gives us ((x + 1)^{1/2} \left(1 - \frac{1}{3}(x + 1)\right)). Simplifying the term inside the parentheses results in ((x + 1)^{1/2} \left(1 - \frac{1}{3}x - \frac{1}{3}\right)), which can be further simplified to ((x + 1)^{1/2} \left(-\frac{1}{3}x + \frac{2}{3}\right)).

An expression that has a value of 0.032 could be ( \frac{32}{1000} ) or ( 0.032 \times 1 ). Another example could be ( 0.064 \div 2 ). Each of these expressions simplifies to 0.032.

To solve a cubic equation, you can use several methods. One common approach is factoring, if the equation can be factored into simpler polynomials. Another method is using the Rational Root Theorem to identify possible rational roots, followed by synthetic division. For more complex cases, one can apply Cardano's formula, or numerical methods such as the Newton-Raphson method for approximate solutions.

7x+10=31x

so 10=31x-7x

or 10 =24x

in which case x=10/24 or 5/12

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The expanded form of 709.104 is 700 + 9 + 0.1 + 0.004. This breaks down the number into its place values, representing each digit based on its position. Here, 700 is the value of the hundreds place, 9 is the value of the units place, 0.1 is the value of the tenths place, and 0.004 is the value of the thousandths place.

The equation ( x - 3 = 0 ) represents a vertical line on a graph. This line is positioned at ( x = 3 ) and extends infinitely in the positive and negative y-directions. Any point on this line will have an x-coordinate of 3, regardless of the y-coordinate.

sqrt(625) = 25

NB

Method

Since 625 ends in '25', it will divide by '25'

Hence

25)625

25)25

=1

Having reduced to '1' , we note that 625 is the product of 25 x 25 = 25^(2) = 625

Hence Inverting the mathematical function.

625 = 25^(2)

25 = 625^(1/2)

The 'power' of '1/2 ' means the square root.

A system of equations has infinite solutions when the equations represent the same line or plane in a geometric sense, meaning they are dependent. This occurs when one equation can be expressed as a multiple or linear combination of the other(s), resulting in an infinite number of points that satisfy all equations simultaneously. In contrast, if the equations are independent and intersect at a single point, there will only be one solution.

The equation you provided seems to be incomplete and a bit unclear. However, if we interpret it as ( x = -2.5(y + 5) ) (assuming you meant ( y + 5 )), the parabola opens to the left since the coefficient of ( y ) is negative. If the equation is different, please provide the correct form for a more accurate determination.