What are the basic steps to solve a linear equation?To solve a linear equation, follow these steps: 1) Simplify both sides of the equation by combining like terms. 2) Move variable terms to one side and constant terms to the other using addition or subtraction. 3) Isolate the variable by dividing or multiplying both sides by the coefficient of the variable.
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How do you solve for x in the equation 5x + 12 = 37?
How do you solve for x in the equation 5x + 12 = 37?To solve for x in the equation 5x + 12 = 37, first subtract 12 from both sides to get 5x = 25. Then, divide both sides by 5 to find x = 5.
Who painted the Mona Lisa and what is it famous for?
Who painted the Mona Lisa and what is it famous for?The Mona Lisa was painted by Leonardo da Vinci. It is famous for its exquisite detail, the subject’s enigmatic expression, and its pioneering use of sfumato technique. The painting is also renowned for its historical significance and its place in art history as a masterpiece of the Italian Renaissance.
How can you use a chi-square test to determine whether there is a significant association between categorical variables in a contingency table?
How can you use a chi-square test to determine whether there is a significant association between categorical variables in a contingency table?To use a chi-square test to determine if there is a significant association between categorical variables in a contingency table, follow these steps: (1) Formulate the null and alternative hypotheses. (2) Calculate the expected frequencies for each cell. (3) Compute the chi-square statistic using the formula χ² = Σ[(O-E)²/E], where O is the observed frequency and E is the expected frequency. (4) Determine the degrees of freedom (df) as (rows-1)*(columns-1). (5) Compare the chi-square statistic to the critical value from the chi-square distribution table at the desired significance level. If the calculated χ² exceeds the critical value, reject the null hypothesis, indicating a significant association.
Explain how the various components of the autonomic nervous system interact to manage the body’s response to stress.
Explain how the various components of the autonomic nervous system interact to manage the body’s response to stress.The autonomic nervous system (ANS) manages stress through its sympathetic and parasympathetic branches. The sympathetic nervous system (SNS) activates the ‘fight or flight’ response, releasing adrenaline and increasing heart rate. The parasympathetic nervous system (PNS) promotes ‘rest and digest,’ restoring calm by lowering heart rate and enhancing digestion. Together, they maintain homeostasis.
How do you find the domain and range of a function in precalculus?
How do you find the domain and range of a function in precalculus?To find the domain of a function, determine all possible input values (x-values) that do not cause division by zero or other undefined operations. The range is the set of all possible output values (y-values) that result from using the domain values. Analyze the function’s behavior, considering restrictions like square roots, logarithms, and rational expressions.
What is the difference between a traditional economy and a market economy?
What is the difference between a traditional economy and a market economy?A traditional economy relies on customs, rituals, and beliefs to make economic decisions, often centered around agriculture and barter. In contrast, a market economy is driven by supply and demand, with prices set through competition, and decisions made by individuals and businesses seeking profit.
What was the significance of the Declaration of Independence and when was it signed?
What was the significance of the Declaration of Independence and when was it signed?The Declaration of Independence, signed on July 4, 1776, was a pivotal document asserting the Thirteen Colonies’ freedom from British rule. It articulated principles of individual liberty and government by consent, laying the foundation for American democracy and inspiring movements for self-determination worldwide.
How do you prove that the sum of the interior angles of a triangle equals 180 degrees using parallel lines and transversals?
How do you prove that the sum of the interior angles of a triangle equals 180 degrees using parallel lines and transversals?To prove the sum of the interior angles of a triangle equals 180 degrees using parallel lines and transversals, extend one side of the triangle and draw a line parallel to the opposite side through the third vertex. The alternate interior angles formed are congruent to the triangle’s angles, and the linear pair formed with the exterior angle sums to 180 degrees.
How do you solve a quadratic equation using the quadratic formula?
How do you solve a quadratic equation using the quadratic formula?To solve a quadratic equation using the quadratic formula, follow these steps: For a quadratic equation in the form ax^2 + bx + c = 0, the quadratic formula is x = (-b ± √(b² – 4ac)) / (2a). Substitute the values of a, b, and c into the formula, then calculate the discriminant (b² – 4ac). Finally, solve for x by completing the operations indicated in the formula.
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How do I solve the equation 3(x + 2) equals 18 and what properties should I use to simplify the expression?
Answer 1 To solve the equation 3(x + 2) = 18, first use the Distributive Property to expand it to 3x + 6 = 18. Then, apply the Subtraction Property of Equality to isolate the variable: 3x = 12. Finally, use the Division Property of Equality to solve...
What are the main functions of the human skeletal system?
Answer 1 The human skeletal system provides structural support, facilitates movement by serving as points of attachment for muscles, protects vital organs, produces blood cells within bone marrow, stores and releases minerals such as calcium and...
How do you find the vertex of a parabola given its equation in standard form?
Answer 1 To find the vertex of a parabola given its equation in standard form y = ax^2 + bx + c, use the vertex formula: x = -b/(2a). Substitute this x-value back into the equation to find the corresponding y-value. The vertex is at the point (x,...
How does F. Scott Fitzgerald critique the American Dream in ‘The Great Gatsby’ and what examples from the book support this critique?
Answer 1 F. Scott Fitzgerald critiques the American Dream by illustrating its corruption and unattainability through the characters and their actions in 'The Great Gatsby.' Jay Gatsby's relentless pursuit of wealth and status to win Daisy's love...
How do I determine all the possible solutions for the equation sin(2x) = cos(x) within one period in radians?
Answer 1 To find all solutions for sin(2x) = cos(x) within one period [0, 2π), use the identity sin(2x) = 2sin(x)cos(x). This converts the equation to 2sin(x)cos(x) = cos(x). Solving, we get cos(x)(2sin(x) - 1) = 0. The solutions are x = π/2, 3π/2,...
How do human activities like deforestation and fossil fuel combustion contribute to climate change and what are some methods to mitigate their impact?
Answer 1 Human activities such as deforestation and fossil fuel combustion significantly contribute to climate change by increasing atmospheric concentrations of greenhouse gases like CO2. Deforestation reduces carbon sequestration, while fossil fuel...