answer:From 3^x = 2, we get x = log_{3}2. Also, given log_{3} frac{9}{4} = y, Therefore, 2x+y = 2log_{3}2 + log_{3} frac{9}{4} = log_{3}4 + log_{3} frac{9}{4} = log_{3}9 = 2. Hence, the answer is boxed{2}. This solution involves converting an exponential equation into a logarithmic equation and then simplifying it using the properties of logarithms. This question tests the understanding of the properties of logarithms and the conversion between exponential and logarithmic forms, making it a foundational problem.

answer:To find the sum of the even integers from 602 to 700 inclusive, we first need to determine how many even numbers there are in this range and what the first and last even numbers are. The first even number in this range is 602, and the last even number is 700. To find the number of even numbers in this range, we can use the formula for the number of terms in an arithmetic sequence: Number of terms = (Last term - First term) / Common difference + 1 Since we are dealing with even numbers, the common difference is 2 (because even numbers are 2 units apart). So, we have: Number of terms = (700 - 602) / 2 + 1 Number of terms = 98 / 2 + 1 Number of terms = 49 + 1 Number of terms = 50 So, there are 50 even numbers between 602 and 700 inclusive. Now, to find the sum of these even numbers, we can use the formula for the sum of an arithmetic series: Sum = (Number of terms / 2) * (First term + Last term) Plugging in the values we have: Sum = (50 / 2) * (602 + 700) Sum = 25 * (1302) Sum = 32550 Therefore, the sum of the even integers from 602 to 700 inclusive is boxed{32,550} .

answer:1. **Convert Hours to Minutes**: There are 60 minutes in one hour. Thus, for 3.5 hours: [ 3.5 text{ hours} times 60 text{ minutes/hour} = 210 text{ minutes} ] 2. **Convert Minutes to Seconds**: There are 60 seconds in one minute. Thus, for 210 minutes: [ 210 text{ minutes} times 60 text{ seconds/minute} = 12600 text{ seconds} ] 3. **Final Answer**: [ boxed{12600 text{ seconds}} ]

answer:1. Given a point (M(x_1, y_1)) through which the line passes, and the point lies on the line described by the equation: [ Ax + By + C = 0 ] Thus, the coordinates of (M) must satisfy this equation: [ A x_{1} + B y_{1} + C = 0 ] 2. To find the general equation of the line passing through point (M), we substitute (M(x, y)) in the general form and consider: [ A(x - x_{1}) + B(y - y_{1}) = 0 ] 3. Next, if another point (N(x_2, y_2)) also lies on this line, then its coordinates must satisfy the same general linear equation: [ A(x_2 - x_1) + B(y_2 - y_{1}) = 0 ] 4. We have derived the two relations: [ begin{aligned} A(x - x_1) &= -B(y - y_{1}) A(x_{2} - x_{1}) &= -B(y_{2} - y_{1}) end{aligned} ] 5. By dividing these two relations term by term, we get: [ frac{x - x_{1}}{x_{2} - x_{1}} = frac{y - y_{1}}{y_{2} - y_{1}} ] This can also be written as: [ frac{x - x_{1}}{x_{2} - x_{1}} - frac{y - y_{1}}{y_{2} - y_{1}} = 0 ] 6. Therefore, the equation of the line passing through the points (M) and (N) is: [ boxed{frac{x - x_{1}}{x_{2} - x_{1}} = frac{y - y_{1}}{y_{2} - y_{1}}} ]