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9a+b-8c-2(a+3b-c) simplified

alekssr [168]

Answer:

The correct simplified answer for 9a + b - 8c - 2 (a + 3b - c) would be 7a - 5b - 6c

Step-by-step explanation:

Hope this helps! Sorry if there is no explanation, I am kinda in a rush.

5 0

3 years ago

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In 4 years, Harry’s age will be the same as Jim’s age is now. In 2 years, Jim will be twice as old as Harry will be. Find their

ololo11 [35]

Jim is 6 / Harry is 2

In 4 years Harry will be 6
In 2 years Jim will be 8 and Harry will be 4 which is twice as much Harry's age.

hope this helps!

5 0

3 years ago

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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

Arrange the following in decreasing order. 3.8 m^2 380 cm? 0.038 km2 3,800 mm Which of the following shows the answers in decrea

Snezhnost [94]

Answer:

C. 0.038 km² > 3.8 m² > 380 cm² > 3800 mm²

Step-by-step explanation:

Convert every measurement to the same unit, say, square metres.

(a) 3.8 m²

No conversion necessary

(b) 380 cm²

$\text{Area} = \text{380 cm}^{2} \times \left (\dfrac{\text{1 m}}{\text{100 cm}} \right )^{2} = \textbf{0.038 m}^{2}$

(c) 0.038 km²

$\text{Area} = \text{0.038 km}^{2} \times \left (\dfrac{\text{1000 m}}{\text{1 km}} \right )^{2} = \textbf{38 000 m}^{2}$

(d) 3800 mm²

$\text{Area} = \text{3800 mm}^{2} \times \left (\dfrac{\text{1 m}}{\text{1000 mm}} \right )^{2} = \textbf{0.0038 m}^{2}$

In decreasing order, 0.038 km² > 3.8 m² > 380 cm² > 3800 mm²

6 0

3 years ago

Find the measure of angle y. Round your answer to the nearest hundredth. (please type the numerical answer only) A right triangl

romanna [79]

Answer:

The angle is 52 degree.

Step-by-step explanation:

length of of side, L = 8

Hypotenuse, H = 13

According to the trigonometry,

$cos y = \frac{L}{H}\\\\cos y = \frac{8}{13}\\\\cos y = 0.62\\\\y = 52^0$

7 0

3 years ago