C is the circumcenter of triangle PQR. PC=3x+7, RC=5x-15, and QC=51-x
What does QC=

The value of QC is 40.

Given that,

C is the circumcenter of triangle PQR is,

PC = 3x+ 7, RC = 5x -15, and QC = 51 -x.

We have to determine

The value of QC.

According to the question,

The point of intersection of the perpendicular bisectors of the sides of a triangle is called its circumcenter.

The circumcenter is equidistant to all the three vertices of a triangle.

PC = RC = QC

Substitute all the values in the equation and solve for the value of x,

Therefore,

The value of QC is,

Hence, The required value of QC is 40.

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Given:

C is the circumcenter of ΔPQR

PC = 3x + 7

RC = 5x - 15

QC = 51 - x

To find:

QC

Solution:

All vertices or a triangle are equidistant from its circumcenter.

Let us take .

Add 15 on both sides.

Add x on both sides.

Divide by 6 on both sides, we get

x = 11

Substitute x = 11 in QC.

QC = 51 - 11

      = 40

Therefore QC = 40.

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages