Point Q is on line segment PR. Given QR= 2x + 4, PQ = x, and PR= 4x – 10, determine the numerical length of PR.

Step-by-step explanation:

Point P is on line segment

O

Q

‾

OQ

. Given

O

P

=

6

,

OP=6,

O

Q

=

4

x

−

3

,

OQ=4x−3, and

P

Q

=

3

x

,

PQ=3x, determine the numerical length of

O

Q

‾

.

OQ

.

Label known information:

Label known information:

O

P

Q

6

3x

OQ = 4x – 3

O

P

+

P

Q

=

OP+PQ=

O

Q

OQ

6

+

3

x

=

6+3x=

4

x

−

3

4x−3

−

4

x

−4x=

−

4

x

−4x

−

x

+

6

=

−x+6=

−

3

−3

−

6

−6=

−

6

−6

−

x

=

−x=

−

9

−9

−

x

−

1

=

−1

−x

=

−

9

−

1

−1

−9

x

=

x=

9

9

Plug in value of

x

to find

O

Q

:

Plug in value of x to find OQ:

O

Q

=

4

x

−

3

=

4

(

9

)

−

3

=

33

OQ=4x−3=4(9)−3=33

You can plug

x

into each expression:

You can plug x into each expression:

O

P

Q

6

3(9)

OQ = 4(9) – 3

Simplify:

Simplify:

O

P

Q

6

27

OQ = 33

Final

Final

O

Q

=

33

OQ=33

d

step-by-step explanation:

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d