1. Points Q,R,S, and T lie on a circle with center P. If the radius of the circle is 1, what is the value of PQ+PR+PS+PT?

2. If 10^ab= 10,000, where a and b are positive integers, what is one possible value of a?

3. In the plane, the line 2x-3y=c passes through the point (5, -1). What is the value of c?

I really have no clue as to what to do on these problems. Please help (explain). Thanks

1. They are all the length of the radius. 1+1+1+1 = 4

2. Since 10^4 = 10,000, a = 0

3. 2(5)-3(-1) = c

1. To find the value of PQ + PR + PS + PT, we need to apply the properties of a circle.

Since the points Q, R, S, and T lie on a circle with center P, the distance from P to any of these points is equal to the radius of the circle. In this case, the radius of the circle is given as 1.

Hence, we can say that PQ = PR = PS = PT = 1.

Now, to find the total value of PQ + PR + PS + PT, we just add up these individual values:

PQ + PR + PS + PT = 1 + 1 + 1 + 1 = 4.

Therefore, the value of PQ + PR + PS + PT is 4.

2. To find a possible value of a in the equation 10^ab = 10,000, we can start by expressing 10,000 as a power of 10.

10,000 can be written as 10^4.

Now, let's equate the two expressions: 10^ab = 10^4.

Since the bases are the same, the exponents must also be equal: ab = 4.

Since a and b are positive integers, we need to find two numbers that multiply together to give 4.

Possible combinations are:
- a = 4, b = 1
- a = 2, b = 2

Therefore, one possible value of a is 4.

3. To find the value of c in the equation 2x - 3y = c when the line passes through the point (5, -1), we substitute the given values into the equation.

We have the equation 2(5) - 3(-1) = c.

Simplifying this expression, we get: 10 + 3 = c.

Thus, c = 13.

Therefore, the value of c is 13.

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