A square with area 4 is inscribed in a square with area 5, with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length a and the other of length b. What is the value of ab?

ab = 1/2.

Step-by-step explanation:

The sides of the large square have length √5 while the sides of the small one have sides of length 2.

Each corner has a right triangle with legs of length a and b and hypotenuse 2.

So we have the system

a + b = √5

a^2 + b^2 = 2^2 = 4

Using the identity   a^2 + b^2 =  (a + b)^2 - 2ab:

4 = (√5)^2 - 2ab

4 = 5 - 2ab

2ab = 5 - 4 = 1

ab = 1/2.

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer

the first one, all those points on the line just make a strait line.