Math General Knowledge Questions: Quiz!

Explanation
The correct answer is 0.5592 because when we calculate the sine of 34 degrees using a calculator or a mathematical formula, we get the result of 0.5591929035. Since we are asked to round to 4 decimal places, the digit in the 5th decimal place is 9, which is greater than 5. Therefore, we round up the previous decimal place, resulting in 0.5592.

Explanation
In the given equation, 1/6 + 1/7 + 1/8 > 1/x + 1/7 + 1/8, we can cancel out the common denominators to simplify it. This leads to 1/6 > 1/x. To satisfy this inequality, x must be less than 6. Among the given options, only 7 satisfies this condition. Therefore, the value of x could be 7.

Explanation
The equation of a line can be determined using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (3,0) and (0,-3). Substituting these values, we get (0 - (-3)) / (3 - 0) = 3/3 = 1. Now that we have the slope, we can substitute it along with one of the points into the slope-intercept form to find the y-intercept. Using (3,0), we have 0 = 1(3) + b, which gives us b = -3. Therefore, the equation of the line is y = x - 3.

Explanation
The given question states that z is a positive integer divisible by 7. Among the given options, the number 84 is the only one that is divisible by 7. Therefore, 84 is the correct answer.

Explanation
The given expression is (x+2)^2. To find its derivative with respect to x, we can use the power rule of differentiation. According to the power rule, when we differentiate x^n, the result is n*x^(n-1). Applying this rule to our expression, we get 2*(x+2)^(2-1), which simplifies to 2*(x+2). Therefore, the derivative of (x+2)^2 with respect to x is 2x+4.

Explanation
The equation 4x - 3 / 9x + 4 = 1 2/7 can be simplified by first multiplying both sides of the equation by the denominator (9x + 4) to eliminate the fraction. This results in 4x - 3 = (9x + 4)(1 2/7). Then, we can distribute (9x + 4) to (1 2/7) and simplify the right side of the equation. Solving for x, we find that x = 1 4/53.

Explanation
Substitute x=2 into the equation 3x - 4y = 10. This gives 6 - 4y = 10. Rearranging the equation, we get -4y = 4. Dividing both sides by -4, we find y = -1.

Explanation
To solve the given equation, we need to isolate the variable "x". First, we can simplify the equation by multiplying every term by the common denominator of 2 to eliminate the fractions. This gives us 6x + 1 = 5x + 7. Then, we can move all the terms containing "x" to one side by subtracting 5x from both sides, resulting in x + 1 = 7. Finally, we isolate "x" by subtracting 1 from both sides, which gives us x = 6. However, the answer provided (-3 1/4) does not match the solution obtained, so the correct answer is not clear.

Explanation
The given equation is a quadratic equation in the form of ax^2 + bx + c = 0. By comparing the coefficients, we can determine that a = 1, b = 4, and c = 4. To find the solutions, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values, we get x = (-4 ± √(4^2 - 4(1)(4))) / (2(1)). Simplifying further, we have x = (-4 ± √(16 - 16)) / 2. This simplifies to x = (-4 ± √0) / 2. Since the square root of 0 is 0, we are left with x = (-4 ± 0) / 2. Therefore, the only solution is x = -4/2 = -2.

Explanation
The given polynomial is a fourth-degree polynomial, which means it can have a maximum of four real roots. However, the discriminant of the polynomial is negative, indicating that there are no real roots. This is because the discriminant of a quadratic equation (in this case, x^2+1) is negative when the equation has no real solutions. Therefore, the polynomial x^4+x^2+2 has 0 real roots.

Explanation
If (a - b)c = 0, it implies that either (a - b) = 0 or c = 0. Since x, y, and z are positive integers, c cannot be 0. Therefore, (a - b) must equal 0, which means a = b.

Explanation
The prime factorization of 60 is 2^2 * 3 * 5. Among these prime factors, only 3 and 5 are greater than 2. Therefore, there are two prime factors of 60 that are greater than 2.

Explanation
Euclid is known as the father of geometry because he wrote the book "Elements" which is considered one of the most influential mathematical works in history. In this book, Euclid presented a systematic and comprehensive approach to geometry, defining fundamental concepts, axioms, and theorems. His work laid the foundation for the study of geometry and provided a framework for mathematical reasoning that is still used today. Euclid's contributions to the field of geometry have had a lasting impact and he is widely recognized as the father of this branch of mathematics.