13. If 6 times the 6th term of an A.P. is equal to
1 answer:
Answer:
see explanation
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides
6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )
- 7a₁ + 30d = 156d ( subtract 30d from both sides )
- 7a₁ = 126d ( divide both sides by - 7 )
a₁ = - 18d
Now
a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required
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Perimeter = 16.4 units
Using the heron's formula, Area ≈ 10.4 units².
<h3>What is the Heron's Formula?</h3>The heron's formula is used to find the area of a triangle with known side lengths of all its three sides, a, b, and c. The heron's formula is given as: Area = √[s(s - a)(s - b)(s - c)], where s = half the perimeter of the triangle
s = (a + b + c)/2.
Given the following:
K (-4,-1) ,
L(-2, 2),
M (3,-1)
Use the distance formula, d = , to find KL, LM, and KM.
KL = √[(−2−(−4))² + (2−(−1))²]
KL = √13 ≈ 3.6 units
LM = √[(−2−3)² + (2−(−1))²]
LM = √34 = 5.8 units
KM = √[(−4−3)² + (−1−(−1))²]
KM = √49 = 7 units
Perimeter = 3.6 + 5.8 + 7 = 16.4 units
Semi-perimeter (s) = 1/2(16.4) = 8.2 units
KL = a ≈ 3.6 units
LM = b = 5.8 units
KM = c = 7 units
s = 8.2
Plug in the values into √[s(s - a)(s - b)(s - c)]
Area = √[8.2(8.2 - 3.6)(8.2 - 5.8)(8.2 - 7)]
Area = √[8.2(4.6)(2.4)(1.2)]
Area = √108.6336
Area ≈ 10.4 units²
Learn more about heron's formula on:
#SPJ1
Answer:
12
Step-by-step explanation:
using pythagoras theorem
here 15 is hypotenuse since it is opposite 0f 90 degree
9 and x are the other smaller sides of a triangle
according to pythagoras thorem the sum of square of two smaller sides of a triangle is equal to the square of hypotenuse. So,
9^2 + x^2 = 15^2
81 + x^2 = 225
x^2 = 225 - 81
x^2 = 144
x =
x = 12