Mathematics, 15.04.2020 19:25 Gabby1128

Given ΔBUG as shown with B(-3,-1), U(-3,3) and G(4,1). Find the area of triangle BUG.

Answers: 2

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Answer from: naysia2006

Using symmetric expression, the area of triangle BUG is: 14 sq. units.

Recall:

The area of a triangle with coordinates of the vertices given can be calculated using the symmetric expression given as: $Area = \frac{1}{2} [x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]$ Let,

$B(-3,-1) = (x_1, y_1)\\\\U(-3,3) = (x_2, y_2)\\\\G(4,1) = (x_3, y_3)$

Plug in the values into $Area = \frac{1}{2} [x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]$

$Area = \frac{1}{2} [-3(3 - 1) + (-3)(1 - (-1)) + 4(-1 - 3)]\\\\Area = \frac{1}{2} [-3(2) + (-3)(2) + 4(-4)]\\\\Area = \frac{1}{2} [-6 + (-6) + (-16)}\\\\Area = \frac{1}{2} [-6 - 6 -16]\\\\Area = \frac{1}{2} [-28]\\\\\mathbf{Area = 14 sq. units}$

Therefore, using symmetric expression, the area of triangle BUG is: 14 sq. units.

Learn more about area of triangle on:

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Answer from: coreybaldwin22

The area of triangle BUG is 14 square units, it is obtained from the points of B(-3,-1), U(-3,3) and G(4,1).

Step-by-step explanation:

The given is,

B(-3,-1), U(-3,3) and G(4,1)

Step:1

Formula for area of triangle with coordinates,

$A=\frac{1}{2} [x_{1} (y_{2} - y_{3} ) + x_{2} ( y_{3} - y_{1} )+x_{3} (y_{1} - y_{2} )]$ ..............(1)

Where, $(x_{1} ,y_{1} )$ , $(x_{2} ,y_{2} )$ and $(x_{3} ,y_{3} )$ are the coordinates of triangle

From the given values,

B ( -3, -1 ) = $(x_{1} ,y_{1} )$

U ( - 3, 3 ) = $(x_{2} ,y_{2} )$

G ( 4 , 1 ) = $(x_{3} ,y_{3} )$

Equation (1) becomes,

$A=\frac{1}{2} [ -3(3-1)+(3)(1-(-1))+4(-1-3)]$

$=\frac{1}{2} [ -3(2)+(3)(1+1)+4(-4)]$

$=\frac{1}{2} [ -6 -6 - 16 ]$

$=\frac{1}{2} [ -28 ]$

= - 14 (Negative sign indicates clockwise traversal)

A = 14 square units

Result:

The area of triangle BUG is 14 square units, it is obtained from the points of B(-3,-1), U(-3,3) and G(4,1).

Given ΔBUG as shown with B(-3,-1), U(-3,3) and G(4,1). Find the area of triangle BUG.

Answer from: Quest

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the (original price) is $420.

0.7x = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

Answer from: Quest

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2 = -20

divide by -2 on each side

-2x^2 /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

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Given ΔBUG as shown with B(-3,-1), U(-3,3) and G(4,1). Find the area of triangle BUG....