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Afina-wow [57]
3 years ago
13

Calculate the area of the triangle with the following vertices (3, -7), (6, 4), (-2, -3)

Mathematics
1 answer:
Monica [59]3 years ago
3 0

Answer:

\boxed{\mathsf{A} \triangle = \red{\dfrac{67}{2}u.a}}

Step-by-step explanation:

Let's follow up with the solution. Considering a triangle with the vertices \mathsf{A(x_A, y_A)}, \mathsf{B(x_B, y_B)} and \mathsf{C(x_C, y_C)}, have a look at the representation in the cartesian plan.

From this representation we can say that the area (A) of a triangle through the knowledge of <u>analytical geometry</u> is given by the determinant of the vertices divided by two, mathematically,

\mathsf{A} \triangle =  \dfrac{\left| \begin{array}{ccc}  \mathsf{x_A} & \mathsf{y_A }& 1 \\  \mathsf{x_B} &  \mathsf{ y_B} & 1 \\ \mathsf{ x_C} &  \mathsf{ y_C} & 1 \end{array} \right|}{2}

So, applying this knowledge we're going to have,

\mathsf{A} \triangle =  \dfrac{\left| \begin{array}{ccc}  3 & -7 & 1 \\ 6 &  4 & 1 \\ -2 &  -3 & 1 \end{array} \right|}{2}

\mathsf{A} \triangle =  \dfrac{1}{2}\left[  \left.\begin{array}{ccc}   3 & -7 & 1 \\ 6 &  4 & 1 \\ -2&  -3 & 1 \end{array}  \right| \begin{array}{cc} 3 & -7 \\ 6 & 4 \\ -2 & -3 \end{array} \right]

\mathsf{A} \triangle = \dfrac{12 + 14 - 18 - (-8 - 9 - 42)}{2}

\red{\mathsf{A} \triangle = \dfrac{67}{2} = 33,5u.a}

Hope you enjoy it, see ya!)

\green{\mathsf{FROM}}: Mozambique, Maputo – Matola City – T-3

DavidJunior17

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14 - x = 0
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3 years ago
A man can buy 20 mangoes or 30 oranges. If he wants a each amount of each, how many of each would he get? Write an EQUATION to s
DochEvi [55]

Answer:

12

Step-by-step explanation:

In this question, there are two variables: the number of mangoes(y) bought and the number of oranges bought(x).

Let's say the man have z money, mangoes price is \frac{1}{20}z and the oranges price is \frac{1}{30}z. The equation for money and number of mangoes and oranges will be:

money = mango price * mangoes bought + orange price * orange bought

z= \frac{1}{20}z * x + \frac{1}{30}z *y

1= \frac{1}{20}x +\frac{1}{30}y

-\frac{1}{30}y= \frac{1}{20}x -1

y= -1.5x + 30

y= 30 - 1.5x

If he want equal number of mango and orange, that mean y=x. The calculation will be:

y= 30 - 1.5x

x= 30 - 1.5x

x+ 1.5x = 30

2.5x= 30

x= \frac{30}{2.5}= 12

8 0
3 years ago
Sophia is 6 years older than her brother Eric. The sum of their ages is 28
Step2247 [10]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

To find the cube root, divide all of the exponents by 3. For a cube root, the sign is unchanged.

A) ∛(-27/64a^9b^6) = -∛(3^3/4^3·a^9·b^6) = -3/4a^3b^2

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B) 9.6×10^-8 ÷ (3×10^-7) = (9.6/3)×10^(-8-(-7)) = 3.2×10^-1

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C) ∛(-0.001a^(3n+3)) = -∛(0.1^3·a^(3n+3)) = -0.1a^(n+1)

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