Algebra

Mitochondria are often referred to as the "powerhouses" of the cell because their primary function is to produce adenosine triphosphate (ATP), the main energy currency of the cell, through a process called oxidative phosphorylation. They also play a crucial role in regulating metabolic processes, including the citric acid cycle and fatty acid oxidation. Additionally, mitochondria are involved in apoptosis (programmed cell death), calcium homeostasis, and the generation of reactive oxygen species. Their ability to adapt to cellular energy demands is essential for maintaining overall cellular health and function.

To find the coordinates of A prime after translating point A (72) by the vector (3, -5), you simply add the vector components to the original coordinates. The x-coordinate will be 7 + 3 = 10, and the y-coordinate will be 2 - 5 = -3. Therefore, the coordinates of A prime are (10, -3).

To address being underweight, it's important to focus on a balanced diet that includes nutrient-dense foods, such as whole grains, lean proteins, healthy fats, fruits, and vegetables. Consider increasing your caloric intake by adding snacks and larger portions at meals. Regular strength training can also help build muscle mass. Additionally, consulting with a healthcare professional or a registered dietitian can provide personalized guidance and support.

To find the slope between the points (39) and (42), we need to interpret these as two points on a line. If we assume these points are (39, y1) and (42, y2) where y1 and y2 are their respective y-values, the slope (m) is calculated using the formula ( m = \frac{y2 - y1}{42 - 39} ). Without specific y-values, the slope cannot be determined numerically. If you provide the y-values, I can help calculate the slope.

I'm sorry, but I can't provide the specific answers to questions from textbooks like "Pre-Algebra with Pizzazz." However, I can help explain concepts or work through similar problems if you provide more details!

To solve the expression ( 6x - 1010 \times 22 ), first calculate ( 1010 \times 22 ), which equals ( 22,220 ). Then, substitute this back into the expression to get ( 6x - 22,220 ). The simplified expression is ( 6x - 22,220 ), and if you need a specific value for ( x ), you can substitute it in to evaluate further.

To replace a variable with a number, simply identify the variable in your equation or expression and substitute it with the desired numerical value. For example, if you have the expression ( x + 5 ) and you want to replace ( x ) with 3, you would write it as ( 3 + 5 ). This substitution allows you to evaluate the expression or solve an equation more easily.

The expression ( 8y - 16 ) can be factored using the distributive property, which yields ( 8(y - 2) ). The expression ( 4(2y - 4) ) can also be simplified to ( 8(y - 2) ) by distributing the 4. Therefore, both expressions are equivalent, demonstrating that ( 8y - 16 ) is equal to ( 4(2y - 4) ).

In inequalities, the direction of the arrow indicates the relationship between values. For example, in the inequality ( x < 5 ), the arrow points to the left, indicating that ( x ) is less than 5. Conversely, for ( x > 2 ), the arrow points to the right, showing that ( x ) is greater than 2. The arrow always points towards the smaller value.

In a graph, the dependent variable is typically placed on the y-axis. This variable is the one that you measure or observe in response to changes in the independent variable, which is plotted on the x-axis. For example, if you're studying the effect of temperature on the growth of plants, the growth (dependent variable) would go on the y-axis, while temperature (independent variable) would go on the x-axis.

Habituation is a psychological process that allows an organism to become less responsive to a repeated, benign stimulus over time. This function helps conserve energy and cognitive resources by filtering out non-threatening stimuli, enabling the organism to focus on more significant changes in its environment that may warrant a response. Essentially, habituation enhances survival by allowing the organism to prioritize attention and react to stimuli that are more relevant or potentially harmful.

The discriminant of a quadratic equation, represented as ( b^2 - 4ac ) in the standard form ( ax^2 + bx + c = 0 ), determines the nature of the roots of the equation. If the discriminant is positive, there are two distinct real roots; if it is zero, there is exactly one real root (a repeated root); and if it is negative, there are no real roots, indicating the roots are complex.

The equation ( y = 6 ) represents a horizontal line on the Cartesian plane. This line runs parallel to the x-axis and intersects the y-axis at the point (0, 6). Since the value of ( y ) is constant at 6 for all values of ( x ), the graph does not change in height.

The degree of a polynomial is defined as the highest power of the variable in the expression. In the term (6x), the variable (x) is raised to the first power (i.e., (x^1)). Therefore, the degree of (6x) is 1.

The common difference refers to the constant amount by which each term in an arithmetic sequence differs from the previous term. In contrast, slope is a measure of the steepness or incline of a line in a coordinate plane, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points. While both concepts involve consistent change, the common difference applies to sequences, whereas slope applies to linear relationships in geometry.

To solve an inequality word problem, first, identify the variables and the relationships described in the problem. Translate the words into a mathematical inequality, using symbols to represent the relationships (e.g., <, >, ≤, ≥). Then, solve the inequality just as you would with an equation, applying algebraic operations while keeping the inequality in mind. Finally, interpret the solution in the context of the original problem to provide a meaningful answer.

The expression ( \frac{x^2 - 25}{x^2 - x - 20} ) can be simplified by factoring both the numerator and the denominator. The numerator, ( x^2 - 25 ), factors to ( (x - 5)(x + 5) ). The denominator, ( x^2 - x - 20 ), factors to ( (x - 5)(x + 4) ). Thus, the expression simplifies to ( \frac{(x - 5)(x + 5)}{(x - 5)(x + 4)} ), and for ( x \neq 5 ), it reduces to ( \frac{x + 5}{x + 4} ).

The number of solutions for a system of two quadratic inequalities can vary widely, depending on the specific inequalities involved. They may have no solutions, a finite number of solutions, or infinitely many solutions. Graphically, the solutions correspond to the regions where the corresponding quadratic curves intersect and how they relate to each inequality. Therefore, analyzing each inequality's graph is crucial to determining the solution set.

Integral : 9x + 8 = 9(x squared)/2 + 8x

Differential : 9x +8 = 9

The sum of the exponents for two variables in a polynomial or algebraic expression is called the degree of the term. For example, in the term (x^m y^n), the degree is (m + n). This concept helps determine the overall degree of the polynomial when combining multiple terms.

To find the square root of 116 using decimals, you can use a calculator or apply the long division method for square roots. If using a calculator, simply input "sqrt(116)" to get approximately 10.770. Alternatively, you can estimate by recognizing that 10.7 squared (10.7 × 10.7) is about 114.49, and 10.8 squared (10.8 × 10.8) is 116.64, indicating the square root lies between these two values. Thus, the square root of 116 is approximately 10.770.

To find 250 squared, you calculate (250 \times 250), which equals 62,500. If by "squared 3" you mean to raise 250 squared to the power of 3, you would then compute (62,500^3), which equals 244,140,625,000,000.

To provide the equation of the line, I need specific details about the line, such as its slope and y-intercept or two points through which it passes. Please provide this information so I can assist you accurately!

2500 multiplied by 03 equals 7500. This is because multiplying by 03 is the same as multiplying by 3. Therefore, 2500 x 3 = 7500.

The steepness of a slope is measured by its gradient, which is the ratio of the vertical rise to the horizontal run. This is often expressed as a percentage or a ratio, such as "rise over run." A steeper slope has a higher gradient, indicating a greater change in elevation over a shorter horizontal distance. In mathematical terms, the slope can also be represented as the tangent of the angle of inclination.