If sin θ + cos θ = $\frac{\sqrt3}{2}$, and θ is an acute angle, find the value of sin² θ + cos² θ − 2sin θ cos θ.

If (x+y):(y+z):(z+x)=7:9:13 for positive reals x,y,z, find x:y:z?

A chord AC subtends an angle of 90° at the center O. If the radius of the circle is 8 cm, what is the length of the chord AC?

A parallelogram has adjacent sides of 18 cm and 10 cm, and the angle between them is 60°. Find the exact area of the parallelogram and the height corresponding to the longer side.

A machine produces 120, 150, 130, and 100 units on four consecutive days. How many units should it produce on the 5th day to bring the average output to 130 units?

Which of the following equations represents a line parallel to \(3x - 2y = 6\)?

Riya invests 60,000 and Kabir invests 80,000. At the end of the year, they earn a profit of 70,000. How much profit does Kabir get?

Sum of A and B is 150 percent more than the sum of C and D. C is 25 percent more than D. If A is 100 percent more than B and D = 400, then what is the value of A?

There are 15 numbers. The average of all 15 is 20. The average of the first 9 numbers is 18.

The average of the last 7 numbers is 24. What is the 9^th number?