Answer/Step-by-step explanation:
Given:
m<A = 115,
m<B = 78,
m<C = 35,
✔️m<1 = 180 - m<A (angles on a straight line/supplementary angles)
m<1 = 180 - 115 (substitution)
m<1 = 65°
✔️m<2 + m<1 + m<B = 180° (sum of interior angles of a triangle)
m<2 + 65 + 78 = 180
m<2 + 143 = 180
m<2 = 180 - 143 (substitution property of equality)
m<2 = 37°
✔️m<3 = 180° - m<B (supplementary angles)
m<3 = 180 - 78
m<3 = 102°
QUESTION 11
Given :
We take antilogarithm of both sides to get:
Group similar terms to get:
Simplify both sides to get:
Divide both sides by 2 to obtain:
12. Given;
We take antilogarithm to obtain:
Group similar terms to get:
We divide both sides by 5 to get:
13.
We take antilogarithm to get:
Group similar terms
Divide both sides by 4
14. Given ;
We take antilogarithm to get:
Simplify:
Divide both sides by 5
Or
15. Given:
We rewrite in the exponential form to get:
Divide both sides by 10
16. Given:
We take antilogarithm to obtain:
Simplify
Divide both sides by 2
17. Given .
We rewrite in exponential form:
Divide both sides by 3
18. Given
We take antilogarithm to get:
Group similar terms:
We divide both sides by 7
19. Given:
Apply the product rule to simplify the left hand side
We take antilogarithm to obtain:
x=-1 or x=4
But x>0, therefore x=4
20. Given
Apply product rule to the LHS
Rewrite in the exponential form to get:
This implies that:
or
Answer:
10
Step-by-step explanation:
its 5+5
Answer:
2/6561
Step-by-step explanation:
Geometric sequence formula :
where an = nth term, a1 = first term , r = common ratio and n = term position
given ratio : 1/3 , first term : 2 , given this we want to find the 9th term
to do so we simply plug in what we are given into the formula
recall formula :
define variables : a1 = 2 , r = 1/3 , n = 9
plug in values
a9 = 2(1/3)^(9-1)
subtract exponents
a9 = 2(1/3)^8
evaluate exponent
a9 = 2 (1/6561)
multiply 2 and 1/6561
a9 = 2/6561
Part A: a percent decrease
part B: 12.5 percent decrease