Answer:
Volume = 5625ft³
Step-by-step explanation:
Volume of a triangular prism = 1/2bhl
1/2 x base x height x length
Therefore we have in this case
Base = 15ft
Height = 30ft
Length = 25ft
Volume = 1/2 x 30 x 25 x 15
Volume = 5625ft³
40 cm = 400 mm, so 400 mm / 18 mm = 200:9, or 22.22:1.
A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
(n+5)^2=48
sqrt both sides
n+4=+/-4√3
minus 4 both sides
n=-4+/-4√3
-4+4√3>0 so this cannot be the value of n
n=-4-4√3
the number is -4-4√3
A way to solve this is finding 90% of 428.
428 × 0.90 = 385.2
Rounded, the answer is 385
