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Sidana [21]
3 years ago
8

Compounding comparing accounts

Mathematics
1 answer:
Kay [80]3 years ago
8 0

Answer:

hi

Step-by-step explanation:

what's up

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The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo
oee [108]

Answer:

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

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

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

length XY =  \sqrt{x^2+y^2}

Therefore, the length between points AB is

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

= \sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2}  = \sqrt{20}  = 4.472 units

Similarly, length BC is given by

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

Length CD = \sqrt{(-2)^2+5^2} =  \sqrt{29} = 5.385 units

Length DA = \sqrt{(8)^2+(-2)^2} =  \sqrt{68} = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

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)

The length D'A =  \sqrt{(7)^2+(0)^2} =  \sqrt{49} =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 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)|

=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|

= =(\frac{1}{2})|-4-6 -8|= 9 units^2

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

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

=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2} = 10.5 units²

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

Area of polygon ABCD' = 19.5 units².

7 0
3 years ago
F(3) = 25
grandymaker [24]

Answer:

Which statement best explains how enzymes speed up a chemical reaction?

Enzymes add heat to a chemical reaction.

Enzymes lower the activation energy of a chemical reaction.

Enzymes remove heat from a chemical reaction.

Enzymes are not changed as a result of a chemical reaction.

Step-by-step explanation:

6 0
2 years ago
Math! Who’s knows the answer?
kykrilka [37]

Answer:

M=30 degrees

because 102+148=150 and 180-150=30. (remember the sum of a triangle is 180 degrees)

the congruence statement would be SAS (side angle side) because 102 and 48 are the same in both triangles, but the third side is not the same.

8 0
3 years ago
I can earn coins
Airida [17]

Answer:

28 because he loaned ant how loaning gos

6 0
3 years ago
Read 2 more answers
State the x- and y-intercepts of each equation<br><br>y = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D" id="TexFormul
Jet001 [13]

Answer:

yintercept: (0,3) or 3

x intercept: (-4,0) or -4

Step-by-step explanation:

The y intercept is what you get when x=0

.75*0+3

3

The x intercept is what you get when y=0

0=.75x+3

-3=.75x

-4=x

5 0
3 years ago
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