Answer:
1. sum of term = 465
2. nth term of the AP = 30n - 10
Step-by-step explanation:
1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore
sum of term = n/2(a + l)
where
a = 1
l = last term = 30
n = number of term
sum of term = 30/2(1 + 30)
sum of term = 15(31)
sum of term = 465
2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......
The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;
a = 20
d = 30
nth term of an AP = a + (n - 1)d
nth term of an AP = 20 + (n - 1)30
nth term of an AP = 20 + 30n - 30
nth term of the AP = 30n - 10
The nth term formula can be used to find the next term progressively. where n = number of term
The sequence will be 20, 50, 80, 110, 140, 170, 200..............
Answer:
The surface area of Triangular base Prism = 3682 cm²
Step-by-step explanation:
Given in question as :
For a Triangular base prism ,
The base of prism (b) = 24 cm
The height of prism (l) = 29 cm
Each side length (s) = 37 cm
The height of base triangle ( h ) = 35 cm
Hence , we know that The surface area of Triangular base prism is
= (b×h) + (2×l×s) + (l×b)
= (24×35) + (2×29×37) + (29×24)
= (840) + (2146) + (696)
= 3682 cm²
Hence The surface area of Triangular base Prism is 3682 cm² Answer
Answer:
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Answer:
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Step-by-step explanation:
Part 1)
we have
------> equation A
------> equation B
Multiply by
the equation A
------> equation C
Multiply by
the equation B

-------> equation D
Adds equation C and equation D

therefore
<u>the answer Part 1) is the option A </u>

Part 2)
we have
------> equation A

Simplify Divide by
both sides

------> equation B
the lines A and B are parallel lines, because the slope m is equal
so
The system has no solution
therefore
<u>the answer Part 2) is the option D</u>
There is no x value as there is no solution to the system.
Part 3)
we have
------> equation A

------> equation B
substitute equation B in equation A
![4x+2[x-3]=6](https://tex.z-dn.net/?f=4x%2B2%5Bx-3%5D%3D6)



therefore
<u>the answer part 3) is the option D</u>

Part 4)
Let
x---------> The number of one-step equations
y---------> The number of two-step equations
we know that

-------> equation A
------> equation B
substitute equation A in equation B
![3[1,120-y]-2y=1,300](https://tex.z-dn.net/?f=3%5B1%2C120-y%5D-2y%3D1%2C300)




therefore
<u>the answer part 4) is the option D</u>
