21. In a parallelogram, opposite angles are equal and adjacent angles are supplementary (add to 180°).
m∠R = m∠P = 180° -m∠Q
m∠Q = 107°
m∠P = 73°
25. If you draw any diagonal, it divides the figure into two congruent triangles (by the SSS postulate). Corresponding angles are congruent, so the diagonal is a transversal between parallel lines. Thus opposite sides are parallel and the figure is a parallelogram.
27. Opposite sides are equal, and the diagonals bisect each other. Your four equations are
2w+4 = 5w-6 . . . . w = 10/3
12 = 3x-3 . . . . . . . x = 5
6y = 4y+6 . . . . . . . y = 3
27 = (5/4)z +2 . . . z = 20
Answer:
-84
Step-by-step explanation:
Let the number be x. Then we have,
(the quotient of a number and -7)
(decreased by 2)
(is 10)
Now we can solve for x,:
So, the original number is -84
The answer you have is good. You don't need to change anything.
That's a 3x3 linear system. Let's do Gaussian elimination
4 3 1 -10 A
1 -3 2 -8 B
11 -2 3 -38 C
0 15 -7 22 D=A-4B
0 31 -19 50 E=C-11B
0 1 -7/15 22/15 F=D/15
1 0 3/5 -18/5 G=B+3F
0 0 -68/15 68/15 H=E-31F -19-31(-7/15), 50-31(22/15)
0 0 1 -1 I=-15/68 H
1 0 0 -3 J=G - 3/5 I
0 1 0 1 K=F+ 7/15 I
We read off from the last three lines the
Answer: x=-3, y=1, z=-1
