Answer:
Step-by-step explanation:
Given that , the sum of the first nine terms of an arithmetic series is 162 and the sum of the first 12 terms is 288.
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• The sum of n terms of an AP is
![\boxed{\orange{\sf S_n = \dfrac{n}{2}[2a+(n-1)d] }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Corange%7B%5Csf%20S_n%20%3D%20%5Cdfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D%20%7D%7D)
• nth term of an AP is given by ,
to write 98 as a product of its prime factors we have to first find the prime factors of 98
prime factors are prime numbers by which the given number can be divided by.
98 we have to keep dividing it by prime numbers
98 is an even number so we can first divide by 2
98 / 2 = 49
49 is a multiple of 7 which too is a prime number so we can divide 49 by 7
49/7 = 7
7 can be divided again by 1
7/7 = 1
98 is divisible by 2 and 7
so 98 written as a product of prime factors is
98 = 2 x 7 x 7
Answer:
HJ = 8 JE = 4
Step-by-step explanation:
it is given that H is the midpoint of GE and J is the midpoint of FE. According to the midpoint theorem the line segment connecting the midpoint of two sides is parallel to the three side and its length is half of the third side. since JH is connecting the midpoints.
HJ= 1/2 (GF)
x + 3 = 1/2 (4x - 4)
x + 3 = 2x - 2
x = 5
^ Thus meaning the value of x is 5.
Now you just fill into your equations:
HJ = x + 3 = (5) + 3 = 8
JE = x - 1 = (5) - 1 = 4
Therefore, HJ = 8; JE = 4.
40×4×4=640
b=20 h=4
using formula:
1/2×base×height
1/2×20×4=40
its says scale by factor 4:
b=80 h=16
using formula:
1/2×base×height
1/2×80×16=640
answer------>>>>640cm^2
Answer:
( √15 + 8)/7
Step-by-step explanation:
TanA = -√15
.we are to find tan(A-π/4).
In trigonometry
Tan(A-B) = TanA - TanB/1+ tanAtanB
Hence:
tan(A-π/4) = TanA - Tanπ/4/1+ tanAtanπ/4
Substitute tan A value into the formula
tan(A-π/4) = -√15-tanπ/4 / 1+(-√15)(tanπ/4
tan(A-π/4) = -√15-1/1-√15
Rationalize
-√15-1/1-√15 × 1+√15/1+√15
= -√15-√225-1-√15/(1-√225)
= -2√15-15-1/1-15
= -2√15 -16/(-14)
= -2(√15+8)/-14
= √15 + 8/7
Hence the required value is ( √15 + 8)/7
