<h3>
Answer: Choice D) 22.5</h3>
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Explanation:
x = length of BC
AC = AB+BC
AC = 6 + x
CE = CD+DE
CE = 22+8
CE = 30
Triangles ACE and BCD are similar triangles (can be proven by the AA similarity theorem due to the fact that AE || BD)
Therefore the corresponding sides are proportional letting us set up the proportion below
AC/BC = CE/CD
(6+x)/x = 30/22 .... substitution
22(6+x) = 30x ... cross multiply
132+22x = 30x
132 = 30x-22x ..... subtract 22x from both sides
132 = 8x
8x = 132
x = 132/8 .... divide both sides by 8
x = 16.5
Now use this to find the length of AC
AC = 6+x
AC = 6+16.5
AC = 22.5
Answer:
∠3 = 81
Step-by-step explanation:
Interior angles in a triangle add up to equal 180°
Hence, 58° + 41° + ∠3 = 180
58 + 41 = 99
99 + ∠3 = 180
* subtract 99 from each side *
99 - 99 cancels out
180 - 99 = 81
we're left with ∠3 = 81°
Step-by-step explanation:
12x - 66 +15 = 3x +12
12x -3x = 66 -15+12
9x = 63
x = 63/9
x = 7
Answer:
Step-by-step explanation:
A parallelogram is a quadrilateral with congruent opposite sides and pair of opposite angles.
Given: parallelogram ABCD
AD≅ BC
AD ║ BC
Thus;
<ABC + DAB = (supplementary angle property)
ΔABD = ΔCBD (each diagonal divides a parallelogram into two congruent triangles)
<ABC = <ADC (both pairs of opposite angles are congruent)
<DAB = <BCD (both pairs of opposite angles are congruent)
AB ≅ CD (opposite sides are congruent)
AB ║ DC (pair of opposite sides are parallel)
Therefore, the quadrilateral ABCD is a parallelogram.
Answer:
discriminant = 0
The real root -2/3
Step-by-step explanation:
The formula for discriminant : b^2 - 4ac
12^2 (-4)×9×4 = 144 - 144 ➡ discriminant = 0 this means the roots is a repeated real number, which means there's only one solution
(3x + 2) × (3x + 2) = 0
3x+ 2 = 0
x = -2/3