Answer:
Choice B.
Step-by-step explanation:
In a parallelogram, there are two pairs of parallel, opposite sides.
In a parallelogram, there are two pairs of congruent, opposite sides.
In a parallelogram, there are two pairs of congruent, opposite angles.
The pairs of opposite congruent angles of this parallelogram are:
<ABC and <ADC
<BCD and <BAD
This problem asks about an angle, but the angle is <BDC.
Notice that <BDC is not one of the 4 angles of the parallelogram mentioned above. <BDC is formed by drawing a diagonal. The statement above about pairs of congruent, opposite angles does not apply to <BDC.
Side DC is parallel to side AB.
Diagonal BD is a transversal to lines DC and AB.
<BDC and <ABD are alternate interior angles of the two parallel sides and the transversal.
Answer:
Choice B.
<BDC is congruent to <ABD; Alternate interior angles are congruent.
Answer:
x = -2 and y = -5
Step-by-step explanation:
5x - y = -5
5x + 5 = y
Now , Substituting value of y in 3x-6y = 24
3x - 6(5x + 5) =24
3x - 30x -30 = 24
-27 x - 30 = 24
-30 - 24 = 27x
-54 =27x
x = -54/27
x = -2
Substituting value of x in 5x-y=-5
5 (-2) - y = -5
-10 -y =-5
-10 +5 =y
y = -5
Answer:
11
Step-by-step explanation:
xy = -20
x + y = 1
x + y = 1
x - x + y = -x + 1
y = -x + 1
xy = -20
x(-x + 1) = -20
x(-x) + x(1) = -20
-x² + x = 20
-x² + x + 20 = 0
-1(x²) - 1(-x) - 1(-20) = 0
-1(x² - x - 20) = 0
-1 -1
x² - x - 20 = 0
x = -(-1) ± √((-1)² - 4(1)(-20))
2(1)
x = 1 ± √(1 + 80)
2
x = 1 ± √(81)
2
x = 1 ± 9
2
x = 0.5 ± 4.5
x = 0.5 + 4.5 or x = 0.5 - 4.5
x = 5 or x = -4
x + y = 1
5 + y = 1
- 5 - 5
y = -4
(x, y) = (5, -4)
or
x + y = 1
-4 + y = 1
+ 4 + 4
y = 5
(x, y) = (-4, 5)
The two numbers that add up to 1 and multiply to -20 are -4 and 5.