Answer:
740
Step-by-step explanation:
The n th term of an arithmetic series is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 7 and a₇ = (3 × 7) + 2 = 21 + 2 = 23 , then
a₁ + 2d = 7 → (1)
a₁ + 6d = 23 → (2)
Subtract (1) from (2) term by term
4d = 16 ( divide both sides by 4 )
d = 4
Substitute d = 4 into (1)
a₁ + 2(4) = 7
a₁ + 8 = 7 ( subtract 8 from both sides )
a₁ = - 1
The sum to n terms of an arithmetic series is
= 
[ 2a₁ + (n - 1)d ] , thus
= 
[ (2 × - 1) + (19 × 4) ]
= 10(- 2 + 76) = 10 × 74 = 740
Answer:
x= 3.25
Step-by-step explanation:
4x-5=8
1. Take the -5 to the other side as a plus so now your question is
4x=13
2. to get the x by its self divide both sides by 4.
13 divided by 4 is 3.25
therefore x=3.25
Answer:
The ramp should be 32.9 feet longer.
Step-by-step explanation:
When the ramp is at 
to the ground, its length can be determined by applying the appropriate trigonometric function. Let the length be represented by l, so that;
Sin θ = 
Sin = 
l = 
= 
= 33.0048
l = 33.0 feet
When the angle is reduced to 
, the length of the ramp would be;
Sin θ =
Sin =
l = 
= 
= 65.9152
l = 65.9 feet
Change in length of ramp = 65.9 - 33.0
= 32.9
The ramp should be 32.9 feet longer.
