Algebra

When you solve a linear equation, the solution represents the value(s) of the variable that make the equation true, meaning both sides of the equation are equal when substituted with that value. In a practical context, this solution often corresponds to a specific quantity or condition, such as the point of intersection of two lines in a graph. For example, in a real-world problem, it could indicate the amount of resources needed to achieve a balance between two competing demands.

YES!!!

A number raised to the power of '2', is said to be 'squared'

A number raised to the power of '3' , is said to be 'cubed'.

There is no corresponding , name/number for hight powers. It is just raised to the fourth power.

NO!!!!

Four cubed means 4^(3) = 4x4x4 = 64

Four to the fourth power means 4^(4) = 4x4x4x4 = 16 x 16 = 256

It's like saying '64' times another '4' ; 64 x 4 = 256

To find the slope of the line that goes through the points (0, 0) and (5, 1), use the formula for slope ( m = \frac{y_2 - y_1}{x_2 - x_1} ). Here, ( (x_1, y_1) = (0, 0) ) and ( (x_2, y_2) = (5, 1) ). Plugging in the values, we get ( m = \frac{1 - 0}{5 - 0} = \frac{1}{5} ). Thus, the slope of the line is ( \frac{1}{5} ).

10 to the power of 0.5 is equivalent to the square root of 10. This can be expressed mathematically as √10. The approximate value of √10 is about 3.16.

When a bus covers long distances at high speeds, the tires heat up as the rubber expands with each revolution. This regular flexing generates internal friction, which produces heat within the tyre. As the temperature rises, the air trapped within expands and causes the tyre pressure to rise considerably. High load, long journey time, and road resistance increase stress, pushing temperatures even higher. If not monitored, this can accelerate tyre wear or reduce performance. These factors highlight why proper inflation and maintenance are essential for long-route operations, as seen in the Truck & Bus Bias tyres offered by Birla Tyre.

The independent variable in an experiment involving soapy water could be the concentration of soap in the solution. This variable is manipulated to observe its effect on a dependent variable, such as the size of soap bubbles, surface tension, or cleaning effectiveness. By changing the amount of soap while keeping other factors constant, researchers can draw conclusions about the relationship between soap concentration and the observed outcomes.

To find the line of best fit for the given data, typically a linear regression analysis is performed, resulting in an equation of the form ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Once the equation is determined, you can substitute ( x = 3.8 ) into this equation to predict the corresponding value of ( y ). If you provide the specific data from the table, I can help you calculate the line of best fit and the prediction.

The periosteum is a dense layer of connective tissue that encases bones, providing a protective covering and serving as an attachment point for muscles and tendons. It contains osteoblasts, which are essential for bone growth and repair, and plays a crucial role in the nourishment of bone tissue through its blood supply. Additionally, the periosteum helps in the healing process after fractures and contributes to the overall structural integrity of the skeleton.

A point is considered a solution to an equation if, when the coordinates of that point are substituted into the equation, the equation holds true (i.e., both sides are equal). For example, in a linear equation, if the coordinates of a point satisfy the equation’s conditions, it lies on the graph of that equation. Essentially, the point represents a specific value or combination of values that fulfills the equation's requirements.

The expression ( x^4 - 3x + 2 ) contains three terms: ( x^4 ), ( -3x ), and ( 2 ). The degree of a polynomial is determined by the highest power of the variable ( x ) present in the expression. In this case, the term ( x^4 ) has the highest degree, which is 4. Therefore, the degree of the polynomial ( x^4 - 3x + 2 ) is 4.

Progressives were a diverse group of reformers in the late 19th and early 20th centuries in the United States, advocating for social, political, and economic reforms. They sought to address issues such as industrialization, urbanization, and corruption in government, aiming to improve living conditions, labor rights, and women's suffrage. Progressives aimed to reduce the power of monopolies and address issues like poverty, education, and public health, promoting greater equality and democratic participation. Their efforts led to significant changes, including various legislative reforms and the establishment of social programs.

The domain of the absolute value parent function, ( f(x) = |x| ), is all real numbers, expressed as ( (-\infty, \infty) ). The range of the function is all non-negative real numbers, starting from zero, which can be expressed as ( [0, \infty) ). This means the function can take any real input and outputs values that are zero or greater.

The square root of three hundred sixty-one (361) is 19. This is because 19 multiplied by itself (19 × 19) equals 361. Therefore, the square root of 361 is 19.

Yes, all terms are also expressions, but not all expressions are terms. A term is a single mathematical entity, which can be a number, variable, or the product of numbers and variables. An expression, on the other hand, can consist of one or more terms combined using operations like addition or subtraction. Therefore, while every term qualifies as an expression, expressions can be more complex and include multiple terms.

The domain of an exponential function, typically expressed as ( f(x) = a^x ) (where ( a > 0 )), is all real numbers, represented as ( (-\infty, \infty) ). The range, however, is limited to positive real numbers, given by ( (0, \infty) ), since the output of an exponential function never reaches zero or negative values.

To write the equation (5x + 2y = 3) in slope-intercept form (y = mx + b), first isolate (y). Subtract (5x) from both sides to get (2y = -5x + 3). Then, divide each term by 2 to solve for (y): (y = -\frac{5}{2}x + \frac{3}{2}). Thus, the equation in slope-intercept form is (y = -\frac{5}{2}x + \frac{3}{2}).

The OMR, or Optical Mark Recognition, is a technology used to scan and interpret marked data from forms, such as multiple-choice tests, surveys, and ballots. It detects the presence or absence of marks made in designated areas, converting them into digital data for analysis. OMR is widely used for its efficiency and accuracy in processing large volumes of responses quickly. Overall, it streamlines data collection and enhances the speed of information retrieval and processing.

FHS, or Functional Health Systems, operates by integrating various health-related services and resources to promote comprehensive patient care. It emphasizes collaboration among healthcare providers, utilizing technology and data to streamline communication and improve patient outcomes. By focusing on preventive care, education, and personalized treatment plans, FHS aims to enhance overall health and well-being within communities.

To provide an answer, I need the specific system of equations you're referring to. Please provide the equations, and I'll help you find the solution in the requested format.

The sum of three consecutive integers starting with ( n ) can be expressed as ( n + (n + 1) + (n + 2) ). Simplifying this expression gives ( 3n + 3 ). Therefore, the sum of the three consecutive integers is ( 3n + 3 ) or ( 3(n + 1) ).

Use Pythagoras .

d^(2) = l^(2) + w^(2)

Substituting

d^(2) = 24^(2) + 10^(2)

d&(2) = 576 + 100

d^(2) = 676

Square root both sides

d = sqrt)676_

d = 26 cm

When you choose a variable and decide what it represents, it is called "variable definition" or "variable assignment." This process involves specifying the meaning and context of the variable within a particular study or mathematical model, ensuring clarity in interpretation and analysis. Properly defining variables is crucial for effective communication and accurate results in research and data analysis.

Eleven squared in exponent notation is written as ( 11^2 ). This means eleven multiplied by itself, which equals 121. So, ( 11^2 = 121 ).

To solve the equation, we first express it mathematically: ( 10 \left( \frac{x}{2} + 5 \right) = 7 ). Simplifying this gives ( \frac{x}{2} + 5 = \frac{7}{10} ). Subtracting 5 from both sides results in ( \frac{x}{2} = \frac{7}{10} - 5 ), which simplifies to ( \frac{x}{2} = \frac{7}{10} - \frac{50}{10} = -\frac{43}{10} ). Multiplying by 2, we find ( x = -\frac{86}{10} = -8.6 ).