The given points are
P = (-4,11)
Q = (-5,8)
The x-component of vector QP is
-4 - (-5) = 1
The y-component of vector QP is
11 - 8 = 3
The vector QP is
(1,3) or

The magnitude of the vector is
√(1² + 3²) = √(10)
Answer:

The magnitude is √(10).
Answer:
k = -5
Step-by-step explanation:
The variable is k
9k + 1 = -9 + 7k
-7k -1
2k = -10
2k/2 -10/2
k = -5
:)
Answer:
x = 2
Step-by-step explanation:
8(4-x) = 7x + 2
1) Distribute : 32 - 8x = 7x + 2
2) Subtract 32 : -8x = 7x - 30
3) Subtract 7x : -15x = -30
4) Divide 15 : x = 2 :)
Answer:
See Below.
Step-by-step explanation:
We are given that ΔAPB and ΔAQC are equilateral triangles.
And we want to prove that PC = BQ.
Since ΔAPB and ΔAQC are equilateral triangles, this means that:

Likewise:

Since they all measure 60°.
Note that ∠PAC is the addition of the angles ∠PAB and ∠BAC. So:

Likewise:

Since ∠QAC ≅ ∠PAB:

And by substitution:

Thus:

Then by SAS Congruence:

And by CPCTC:

Answer:
a
Step-by-step explanation: