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
We have been given that length of PQ and QR is 25 cm and 8 cm respectively.
We can find possible side length of PR in order to form a triangle using triangle inequality theorem.
Triangle inequality theorem states that the sum of lengths of two sides of a triangle must be greater than length of third side of triangle.
The length of PR should be either less than sum of PQ and QR or greater than difference of PQ and QR.
![PR](https://tex.z-dn.net/?f=PR%3C25%2B8)
Let us find the other possible length of PR.
![PR>17](https://tex.z-dn.net/?f=PR%3E17)
Therefore, the length of PR should be either less than 33 or greater than 17 so that PQ, QR and PR can form a triangle.
Answer:
the answer would be x=3
Step-by-step explanation:
the lines the have 1 line across it equal the same. same for the ones with 2. for example AB has one line across so it also equals CD because it has one line across (in the little octagonal shape). BC has two lines and so does AH so BC=AH
Answer:
Let's solve your system by substitution.
x+2y=6;x−y=3
Step: Solvex+2y=6for x:
x+2y=6
x+2y+−2y=6+−2y(Add -2y to both sides)
x=−2y+6
Step: Substitute−2y+6forxinx−y=3:
x−y=3
−2y+6−y=3
−3y+6=3(Simplify both sides of the equation)
−3y+6+−6=3+−6(Add -6 to both sides)
−3y=−3
−3y
−3
=
−3
−3
(Divide both sides by -3)
y=1
Step: Substitute1foryinx=−2y+6:
x=−2y+6
x=(−2)(1)+6
x=4(Simplify both sides of the equation)
Answer:
x=4 and y=1
Step-by-step explanation:
Answer:
x=4 and y=1
Answer:
>
Step-by-step explanation:
1 - 3 ?? -4
-2 ?? -4
The appropriate symbol for this ?? relation is >.
1 -3 > -4