Answer:
R35625
Step-by-step explanation:
(R30,000×.125×18/12)+R30000
=R35625
After plotting the quadrilateral in a Cartesian plane, you can see that it is not a particular quadrilateral. Hence, you need to divide it into two triangles. Let's take ABC and ADC.
The area of a triangle with vertices known is given by the matrix
M =
Area = 1/2· | det(M) |
= 1/2· | x₁·y₂ - x₂·y₁ + x₂·y₃ - x₃·y₂ + x₃·y₁ - x₁·y₃ |
= 1/2· | x₁·(y₂ - y₃) + x₂·(y₃ - y₁) + x₃·(y₁ - y₂) |
Therefore, the area of ABC will be:
A(ABC) = 1/2· | (-5)·(-5 - (-6)) + (-4)·(-6 - 7) + (-1)·(7 - (-5)) |
= 1/2· | -5·(1) - 4·(-13) - 1·(12) |
= 1/2 | 35 |
= 35/2
Similarly, the area of ADC will be:
A(ABC) = 1/2· | (-5)·(5 - (-6)) + (4)·(-6 - 7) + (-1)·(7 - 5) |
= 1/2· | -5·(11) + 4·(-13) - 1·(2) |
= 1/2 | -109 |
<span> = 109/2</span>
The total area of the quadrilateral will be the sum of the areas of the two triangles:
A(ABCD) = A(ABC) + A(ADC)
= 35/2 + 109/2
= 72
Answer:
Step-by-step explanation:
In the first triangle, using Pythagorean's theorem, x^2+3^2=5^2, x = 4
In the second triangle, using Pythagorean's theorem, x^2+7^2=24^2, x = 25
In the third triangle, using Pythagorean's theorem, 8^2+15^2=x^2, x = 17
In the fourth triangle, using Pythagorean's theorem, x^2+8^2=10^2, x = 6
In the fifth triangle, using Pythagorean's theorem, 5^2+12^2=x^2, x = 13
Answer:
8.413 x 10^3
Step-by-step explanation:
Answer:
Rock costs $3.20 per pound.
Step-by-step explanation:
Because sand costs three times as much as rocks per pound, you can determine the cost of rocks per pound by dividing the cost of sand per pound by three: