A particular baseball diamond is actually a square with 7575-foot sides. What is the distance from home plate to second base? Express the answer in simplified radical form. Then find a decimal approximation.

 feet.

Step-by-step explanation:

Please find the attachment.

We have been that a particular baseball diamond is actually a square with 75-foot sides.

We can see that distance from home plate to second base would be equal to hypotenuse with each leg of 75-ft.

We will use Pythagoras theorem to find the distance x as:

Now, we will take positive square root of both sides as:

Therefore, the exact distance from home plate to second base is feet or approximately 106.07 feet.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions