Answer:
 19.0681
Step-by-step explanation:
Given in the question that,
angle from ted to the dog = 60° with the ground
height of ted from the ground =  16ft
To find,
distance between dog and the door of ted's building
Considering the scenario make a right angle triangle:
<h3>By using pythagorus theorem:</h3>
Tan 40 = opposite / adjacent
Tan 40 = height / distance between dog and the door
Tan 40 = 16ft / x
x = 16 / tan40
x = 19.068057
x ≈ 19.0681 (nearest to thousand)
So, the dog need to walk 19.0681ft to reach the open door directly below Ted.
 
        
             
        
        
        
3x+5+10x-7=180
13x-2=180
 -2 -2
13x=182
/13 /13
X=14
3(14)+5=47
10(14)-7=133
mm
        
             
        
        
        
Answer:
<h2>
         3.6° and 86.4°</h2>
Step-by-step explanation:
24x   - measure of an angle
x      - the measure of a complementary angle
Complementary angles adds to 90°
x + 24x = 90°
25x = 90°
 x = 90°÷25
x = 3.6°
24x = 24·3.6° = 86.4°
 
        
             
        
        
        
 = 1455
 = 1455
generate a few terms of the sequence using  = 3n + 2
 = 3n + 2
 = ( 3 × 1) + 2 = 5
 = ( 3 × 1) + 2 = 5
 = (3 × 2) + 2 = 8
 = (3 × 2) + 2 = 8
 = (3 × 3 ) + 2 = 11
 = (3 × 3 ) + 2 = 11
 = (3 × 4 ) + 2 = 14
 = (3 × 4 ) + 2 = 14
 = ( 3 × 5 ) + 2 = 17
 = ( 3 × 5 ) + 2 = 17
the terms are 5, 8, 11, 14, 17
these are the terms of an arithmetic sequence
sum to n terms is calculated using  =
 =  [ 2a + (n-1)d]
 [ 2a + (n-1)d]
where a is the first term and d the common difference
d = 8 - 5 = 11 - 8 = 14 - 11 = 3 and  = 5
 = 5
 =
 =  [( 2 × 5) + (29 × 3) ]
 [( 2 × 5) + (29 × 3) ]
= 15( 10 + 87) = 15 × 97 = 1455