We know that
side AB is parallel to side CD
then
∠A=∠D
∠B=∠C
therefore
(2x+6)/10=(x+6)/8-------------> 8*(2x+6)=10*(x+6)------> 16x+48=10x+60
16x-10x=60-48----------> 6x=12---------> x=2
so
AE=2x+6-------> 2*2+6--------> AE=10
the answer is AE=10 units
Answer:
A = π/6 + kπ, or A = 2π/3 + kπ
Step-by-step explanation:
tan A / (1 − tan² A) = √3 / 2
Cross multiply and simplify:
√3 (1 − tan² A) = 2 tan A
√3 − √3 tan² A = 2 tan A
3 − 3 tan² A = 2√3 tan A
0 = 3 tan² A + 2√3 tan A − 3
Solve with quadratic formula:
tan A = [ -2√3 ± √((2√3)² − 4(3)(-3)) ] / 2(3)
tan A = [ -2√3 ± √(12 + 36) ] / 6
tan A = (-2√3 ± √48) / 6
tan A = (-2√3 ± 4√3) / 6
tan A = -√3 or √3/3
Solve for A:
A = 2π/3 + kπ, or A = π/6 + kπ
Hello!
So, this is quite the complex question, and here are the following steps:
What is the quotient of ?
(rationalize the denominator)
(factor 3 from the expression)
(reduce the fraction with 3)
(distributive property)
(simplify 3 · 9²)
(simplify the radical)
(factor 3 from the expression)
(reduce the fraction)
The answer, is simply, choice A, ≈ 0.263758.