Answer:
j
Step-by-step explanation:
Answer:
n = 60.22
Step-by-step explanation:
Hello
To find Sn, we need to draw out equations for each a₇ and a₁₉
In an arithmetic progression,
Sn = a + (n-1)d
Where Sn = sum of the A.P
a = first term
d = common difference
a₇ = 32
32 = a + (7-1)d
32 = a + 6d ........equation (i)
a₁₉ = 140
140 = a + (19-1)d
140 = a + 18d .........equation (ii)
Solve equation (i) and (ii) simultaneously
From equation (i)
32 = a + 6d
Make a the subject of formula
a = 32 - 6d .....equation (iii)
Put equation (iii) into equation (ii)
140 = (32 - 6d) + 18d
140 = 32 - 6d + 18d
Collect like terms
140 - 32 = 12d
12d = 108
d = 108 / 12
d = 9
Put d = 9 in equation (i)
32 = a + 6(9)
32 = a + 54
a = 32 - 54
a = -22
When Sn = 511
Sn = a + (n - 1)d
Substitute and solve for n
511 = -22 + (n-1) × 9
511 = -22 + 9n - 9
511 = -31 + 9n
511 + 31 = 9n
542 = 9n
n = 542 / 9
n = 60.22
Answer:
x = 2
Step-by-step explanation:
-4(3 - 2x) + 2x = 2 x 4
-12 + 8x + 2x = 2 x 4
-12 + 8x + 2x = 8
-12 + 10x = 8
-12 + 12 + 10x = 8 + 12
10x = 20
x = 2
Step-by-step explanation:
We are given with the two sides of a right angled triangle having lengths of 5 and 13. It is required to find the length of the third side of a right triangle. We know that hypotenuse of right angled triangle is the longest side.
For right angle triangle, we use Pythagoras theorem as :
H²=P²+B²
P is perpendicular distance
B is base
Putting H = 13 and P = 5, then
B² = H²-P²
B² = (13)²-(5)²
B²=144
B=12
So, the length if the third side of a right triangle is 12. It is the only solution.
50 liters i’m sure. you didn’t give an exact pattern
