Answer:
a great tool for these is symbolab
Step-by-step explanation:
Answer: S₁₉ = 855
Step-by-step explanation:
T₄ = a + ( n - 1 )d = 5 , from the statement above , but n = 4
a + 3d = 5 -------------------------1
S₆ = ⁿ/₂[(2a + ( n - 1 )d] = 10, where n = 6
= ⁶/₂( 2a + 5d ) = 10
= 3( 2a + 5d ) = 10
= 6a + 15d = 10 -----------------2
Now solve the two equation together simultaneously to get the values of a and d
a + 3d = 5
6a + 15d = 10
from 1,
a = 5 - 3d -------------------------------3
Now put (3) in equation 2 and open the brackets
6( 5 - 3d ) + 15d = 10
30 - 18d + 15d = 10
30 - 3d = 10
3d = 30 - 10
3d = 20
d = ²⁰/₃.
Now substitute for d to get a in equation 3
a = 5 - 3( ²⁰/₃)
a = 5 - 3 ₓ ²⁰/₃
= 5 - 20
a = -15.
Now to find the sum of the first 19 terms,
we use the formula
S₁₉ = ⁿ/₂( 2a + ( n - 1 )d )
= ¹⁹/₂( 2 x -15 + 18 x ²⁰/₃ )
= ¹⁹/₂( -30 + 6 x 20 )
= ¹⁹/₂( -30 + 120 )
= ¹⁹/₂( 90 )
= ¹⁹/₂ x 90
= 19 x 45
= 855
Therefore,
S₁₉ = 855
<u>Given</u>:
The base of a rectangular prism has an area of 25 square meters. The height of the rectangular prism is 4 meters.
We need to determine the volume of the rectangular prism.
<u>Volume of the rectangular prism:</u>
The volume of the rectangular prism can be determined using the formula,
where B is the base area and h is the height of the prism
Substituting B = 25 and h = 4 in the above formula, we get;
Thus, the volume of the rectangular prism is 100 cubic meters.
Answer:
Answer: $ 18.00
Step-by-step explanation:
You have to change 20 into a decimal which is 0.20
Then multiply 15 and 0.20 which equals 3
Then add 15 and 3 together and you should get 18.
I just took a test and got it right so good luck! :)