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3 years ago

4{[5 (x-3)+2]-3 [2 (x+5)-9]}

2 answers:

8 0

<span>Solve by applying PEMDAS - the order of operations:
P = Parenthesis or brackets
E = Exponents or radicals whichever comes first
M = Multiplication or division whichever comes first
D = Division or multiplication whichever comes first
A = Addition or subtraction whichever comes first
S = Subtraction or addition whichever comes first
.
4{[5(x-3)+2]-3[2(2x+5)-9]

4{[5x-15+2]-3[4x+10-9]}
4{[5x-13]-3[4x+1]}
4{[5x-13]-(12x+3)}
4{[5x-13]-12x+3}
4{5x-13-12x+3}
4{-7x-10}
-28x-40
</span>

Over [174]3 years ago

6 0

Pemdas
parenthasees exponents mult/division additon/subtraction

parethenasees
x-3 and x+5 we can't do anything with so next
5(x-3)=5x-15

2(x+5)=2x+10

5x-15+2=5x-13

(2x+10-9)=2x+1

(5x-13)-3(2x+1)
-3(2x+1)=-6x-3

5x-13-6x-3=-x-16

4(-x-16)=-4x-64

the answer is -4x-64

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The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

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Step-by-step explanation:

The coordinates forming the polygon are

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The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

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Therefore, the length between points AB is

length AB = $\sqrt{(-4 - (-2))^2+(-1-3)^2}$

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Similarly, length BC is given by

Length BC = $\sqrt{(-4)^2+1^2} = \sqrt{17}$ = 4.123 units

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If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

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The perimeter of polygon ABCD'

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= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

$S_{\bigtriangleup}$ = $(\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|$

= $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

$S_{{\bigtriangleup}ABC}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

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Triangle ACD'

A(-4,-1)

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Area of polygon = $S_{{\bigtriangleup}ABCD'}$ = $S_{{\bigtriangleup}ABC}$ + $S_{{\bigtriangleup}ACD'}$ = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

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