An=a1(r)^(n-1)
a7=a1(r)^(7-1)=a1r^6
a10=a1(r)^(10-1)=a1r^9
a10/a7=(a1r^9)/(a1r^6)=r^3
a10/a7=3/81=r^3
3/81=1/27
1/27=r^3
cube root both sides
1/3=r
subsitute
a7=a1r^6
81=a1(1/3)^6
81=a1(1/729)
times 729 both sides
59049=a1
first term is 59049
common ratio is 1/3
Answer:
11.55
Step-by-step explanation:
SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
The angle at lower left is the complement of 60°, so is 30°. Then the side x satisfies the equation ...
tan(30°) = x/20
Multiplying by 20 gives ...
20·tan(30°) = x ≈ 11.55
-2x > 12 OR -2(x + 1) < -10
Each inequality is solved separately.
The first one, divide both sides by -2, when you divide by a negative, you change the inequality sign.
So x < 6
For the second inequality, distribute the -2, this gives us -2X -2< -10.
Add 2 to both sides.
-2x < -8
Divide both sides by -2.
When dividing by a negative you change the inequality sign
So x > 4
The answer is:
x < 6 OR x > 4
No they are not proportional
8:5:3 this is the simplest ratio
