Math Trivia For High School

Explanation
The given question asks for the sum of two functions, f(x) and g(x). To find the sum, we simply add the corresponding terms of the two functions. In this case, f(x) = 3x - 2 and g(x) = 2x + 1. Adding the terms, we get (3x + 2x) + (-2 + 1) = 5x - 1. Therefore, the correct answer is 5x - 1.

Explanation
To find f(-1), we substitute -1 into the equation f(x) = -7x + 5. Thus, f(-1) = -7(-1) + 5 = 7 + 5 = 12.

Explanation
The function f(x) is defined as 1/(x-1), which means it is not defined when the denominator (x-1) equals zero. In this case, if we substitute x=1 into the function, we get 1/(1-1), which simplifies to 1/0. Division by zero is undefined in mathematics, so the value of f(1) is undefined.

Explanation
The y-intercept of a linear equation represents the value of y when x is equal to 0. In the given equation, y = 2x - 3, when x is equal to 0, the equation becomes y = 2(0) - 3, which simplifies to y = -3. Therefore, the y-intercept of the equation is -3.

Explanation
When x = -2, substituting this value into the expression x^3 + 2x^2 - 2x gives (-2)^3 + 2(-2)^2 - 2(-2). Simplifying this expression, we get -8 + 8 + 4, which equals 4. Therefore, the correct answer is 4.

Explanation
The y-intercept of a quadratic equation is the point where the graph of the equation intersects the y-axis. To find the y-intercept, we set x = 0 and solve for y. In this equation, when x = 0, y = 0^2 + 2(0) + 1 = 1. Therefore, the y-intercept is (0, 1).

Explanation
The median is the middle value of a set of numbers when they are arranged in order. In this case, the numbers are 1, 2, 3, 4, 5, and 9. The middle two numbers are 3 and 4. To find the median, we take the average of these two numbers, which is 3.5.

Explanation
The inequality -3x + 7 < 2x - 8 can be simplified by adding 3x to both sides and subtracting 7 from both sides. This results in 0 < 5x - 15. By adding 15 to both sides, we get 15 < 5x. Finally, dividing both sides by 5 gives us 3 < x. This can also be written as x > 3.

Explanation
To find the value of x that makes the equation -4x + 7 = -13 true, we need to solve for x. By subtracting 7 from both sides of the equation, we get -4x = -20. Then, by dividing both sides by -4, we find that x = 5. Therefore, the value of x that makes the equation true is 5.

Explanation
To find the value of x that makes the equation "10x - 2 = -4x + 40" true, we need to solve the equation. By simplifying both sides, we get 14x = 42. Dividing both sides by 14, we find that x = 3. Therefore, the value of x that makes the equation true is 3.

Explanation
In this question, a club of 7 needs to choose a President, Vice-President, and Secretary. To find the number of ways this can be done, we can use the concept of permutations. The number of ways to choose the President is 7, as any of the 7 members can be chosen. After the President is chosen, there are 6 remaining members to choose from for the Vice-President. Finally, for the Secretary position, there are 5 members left to choose from. Therefore, the total number of ways to choose a President, Vice-President, and Secretary is 7 * 6 * 5 = 210.

Explanation
The correct answer is 24. The factorial of a number is the product of all positive integers less than or equal to that number. In this case, 4 factorial (4!) is equal to 4 x 3 x 2 x 1, which equals 24.

Explanation
The slope of a line can be found using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (3, 4) and (5, 2). Plugging these values into the formula, we get (2-4)/(5-3) = -2/2 = -1. Therefore, the slope of the line through these points is -1.

Explanation
The question states that 7 less than the product of 5 and a number is equal to 213. To find the number, we need to solve the equation 5x - 7 = 213, where x represents the unknown number. By adding 7 to both sides of the equation, we get 5x = 220. Dividing both sides by 5, we find that x = 44. Therefore, the number is 44.

Explanation
The inequality 4x + 5 > 3 can be solved by subtracting 5 from both sides, which gives 4x > -2. To isolate x, divide both sides by 4, resulting in x > -1/2. This means that any value of x greater than -1/2 will satisfy the inequality.