Answer:
Ratio = 3 : 2 and value of m = 5.
Step-by-step explanation:
We are given the end points ( -3,-1 ) and ( -8,9 ) of a line and a point P = ( -6,m ) divides this line in a particular ratio.
Let us assume that it cuts the line in k : 1 ratio.
Then, the co-ordinates of P =
.
But,
= -6
i.e. -8k-3 = -6k-6
i.e. -2k = -3
i.e. 
So, the ratio is k : 1 i.e
i.e. 3 : 2.
Hence, the ratio in which P divides the line is 3 : 2.
Also,
= m where 
i.e. m = 
i.e. m = 
i.e. m = 
i.e. m = 5.
Hence, the value of m is 5.
Answer:
99°
Step-by-step explanation:
<8 = 99° [Since, corresponding angles of parallel lines]
Answer:
Total paper required = 165 cm²
Step-by-step explanation:
Paper required to cover the entire block = (Surface area of the prism at the base - area of the top of the prism) + Lateral surface area of the pyramid
Surface area of the rectangular prism = 2(lb + bh + hl)
(here l, b, h are the length, width and height respectively)
= 2(5×5 + 5×4 + 4×5)
= 2(25 + 20 + 20)
= 2×65
= 130 cm²
Area of the top of the prism = (side)²
= 5²
= 25 cm²
Lateral area of the square pyramid = 4 × Area of one lateral side
= 4 × ![[\frac{1}{2}(\text{Base})(\text{Height})]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7B2%7D%28%5Ctext%7BBase%7D%29%28%5Ctext%7BHeight%7D%29%5D)
= 4 × ![[\frac{1}{2}(5)(6)]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7B2%7D%285%29%286%29%5D)
= 60 cm²
Total paper required = (130 - 25) + 60
= 105 + 60
= 165 cm²
Answer:
3240 in^3
Step-by-step explanation:
Step one:
given data
The dimension of the form
Length 40 and 1/2 inches long,
Depth 10 inches deep,
The width and 8 inches high
Step two:
The amount of cement is equivalent to the volume of the form

Hence the volume of cement is 3240 in^3
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