Answer: 
Step-by-step explanation:
Given : The height of the rectangle = 
The width of the rectangle = 
Formula : Area = height x width
Therefore , the area of triangle in terms of polynomial will be :
![6k^3\times( 2k^2+4k+5)\\\\= 6k^3(2k^2)+6k^3(4k)+6k^3(5)\ \ [\text{Using Distributive property}]\\\\=12k^{3+2}+24k^{3+1}+30k^3\ \ [\text{Using exponents rule}:\ a^n\times a^m=a^{n+m}]\\\\=12k^5+24k^4+30k^3](https://tex.z-dn.net/?f=6k%5E3%5Ctimes%28%202k%5E2%2B4k%2B5%29%5C%5C%5C%5C%3D%206k%5E3%282k%5E2%29%2B6k%5E3%284k%29%2B6k%5E3%285%29%5C%20%5C%20%5B%5Ctext%7BUsing%20Distributive%20property%7D%5D%5C%5C%5C%5C%3D12k%5E%7B3%2B2%7D%2B24k%5E%7B3%2B1%7D%2B30k%5E3%5C%20%5C%20%5B%5Ctext%7BUsing%20exponents%20rule%7D%3A%5C%20a%5En%5Ctimes%20a%5Em%3Da%5E%7Bn%2Bm%7D%5D%5C%5C%5C%5C%3D12k%5E5%2B24k%5E4%2B30k%5E3)
Hence, the area of the entire rectangle =
Answer:
Answers are below in bold
Step-by-step explanation:
1) A = 1/2bh Use this equation to find the area of each triangular base
A = 1/2(8)(6) Multiply
A = 1/2(48) Multiply
A = 12cm² Area of each triangular base
2) A = L x W Use this equation to find the area of the bottom rectangular face
A = 20 x 8 Multiply
A = 160 cm² Area of the bottom rectangular face
3) A = L x W Use this equation to find the area of the back rectangular face
A = 20 x 6 Multiply
A = 120 cm² Area of the back rectangular face
4) A = L x W Use this equation to find the area of the sloped rectangular face
A = 20 x 10 Multiply
A = 200 cm² Area of the sloped rectangular face
5) To find the total surface area of the triangular prism, add together all of the numbers.
A = 12 + 12 + 160 + 120 + 200 Add
A = 504 cm² Total area of the triangular prism
An= mth term.
an=a₁+(n-1)*d
a₁₂=41
a₁₅=140
a₁₂=41
41=a₁+(12-1)*d
41=a₁+11d
a₁+11d=41 (1)
a₁₅=140
140=a₁+(15-1)*d
140=a₁+14d
a₁+14d=140 (2)
With the equiations (1) and (2) build a system of equations
a₁+11d=41
a₁+14d=140
we solve it.
-(a₁+11d=41)
a₁+14d=140
--------------------
3d=99 ⇒d=99/3=33
a₁+11d=41
a₁+(11*33)=41
a₁+363=41
a₁=41-363=-322
an=a₁+(n-1)*d
an=-322+(n-1)*33
an=-322+33n-33
an=-355+33n
an=-355+33n
To check:
a₁₂=-355+33*12=-355+396=41
a₁₅=-355+33*15=-355+495=140.
Answer:
60km
Step-by-step explanation:
In 95 mins,he can run is 20km
In 1 min,he can run is 20/95
= 4/19in lowest
Now,
In 285 mins,he can run is=4/19*285
=4*15 in lowest
=60 km
Answer: c.+dhf+2-4= 6)
Step-by-step explanation: Hope this helps!
