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shepuryov [24]
3 years ago
14

Which is a counterexample to this conjecture?

Mathematics
1 answer:
valkas [14]3 years ago
7 0
I think that the answer should be c but i am not sure <span />
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If A(-5,7), B(-4,-5), C(-1,-6) and D(4,5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
MrMuchimi
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 = \left[\begin{array}{ccc} x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right]

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
8 0
3 years ago
Emily would like to buy some new
bonufazy [111]

Answer:

$14,277.80

Step-by-step explanation:

The standard formula for compound interest is given as;

A = P(1+r/n)^(nt) .....1

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case;

P = $7,400

t = 8 years

n = 4 (quarterly)

r = 9.5% = 0.095

Using equation 1.

A = $7,400(1+0.095/4)^(4×7)

A = $7,400(1.02375)^(28)

A = $7,400(1.929432606035)

A = $14,277.80

final amount/value after 8 years A =$14,277.80

6 0
2 years ago
PLEASE HELP, WILL GIVE MAX POINTS IF CORRECT. Look at the diagram of the tennis court below. The diagram contains examples of li
zvonat [6]

Answer:

playing surface=plane

corner of serving box=vertex

baseline=line segment

net=plane

intersection of baseline and side line=vertex

Step-by-step explanation:

what I remember from my geometry course, super sorry if any are wrong

3 0
2 years ago
What is the volume of a sphere that has a 12m diameter?
lesya [120]
Volume of Sphere = (4/3)*(pi)*(r^3)
 
                            r = (D/2) = 6 m
                        
                              =<span>(4/3)*(pi)*((6^3)

                              = 904.7786.. m^3
I hope this helps.</span>
5 0
3 years ago
Evaluate (x)=3+1=3x+ 1over the domain {1,2,3,4,} . What is the range of<br> (x)
katrin [286]

Answer: Step-by-step explanation:

Step-by-step explanation:

The range of a function is the set of images associated with a given domains. As domain is a discrete set, the range can be determined by evaluating the function at each element in domain:

x = 0

x = 1

x = 2

x = 3

The range of r(x) is .

8 0
2 years ago
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