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4 years ago

(4x – 12) + (–x + 7)

Mathematics

2 answers:

Evgesh-ka [11]4 years ago

8 0

Answer:

3x-5

Step-by-step explanation:

(4x – 12) + (–x + 7)

Open the parenthesis

=4x-12-x+7

Solve the like terms:

=3x-5

The answer is 3x-5

Andre45 [30]4 years ago

5 0

Answer:

3x -5

Step-by-step explanation:

(4x – 12) + (–x + 7)

= 4x – 12 –x + 7

= 3x -5 (answer)

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A finance magazine did a survey and found that the average American family spends $1,600 on a summer vacation. If the distributi

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3 years ago

How much grain can this container hold?

ludmilkaskok [199]

Answer:

953.78 in^3 of grain.

Step-by-step explanation:

The volume of a cylinder = π r^2 h.

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8 0

3 years ago

Read 2 more answers

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

triangle AMY ~ MEG , AM = 5 MY=7 AY =3. MEG IS A DILATION of AMY by a scale facyor of 1/3. fimd the perimeter of MEG.

Mademuasel [1]

Answer:

Explanation:

From the question, we're told that triangles AMY and MEG are similar. If triangle AMY has sides AM = 5, MY = 7, and AY = 3 then we can find the side lengths of triangle MEG since we're told from the question that it is a dilation of AMY by a scale factor of 1/3.

So all we need to is multiply the corresponding sides of AMY by 1/3, so we'll have;

$\begin{gathered} ME=5\ast\frac{1}{3}=\frac{5}{3} \\ EG=7\ast\frac{1}{3}=\frac{7}{3} \\ MG=3\ast\frac{1}{3}=3 \end{gathered}$

We can then go ahead and find the perimeter of MEG. Note that to find the perimeter of a triangle, we add all the length of its sides;

$\begin{gathered} \text{Perimeter of MEG}=\frac{5}{3}+\frac{7}{3}+3 \\ =\frac{5+7+9}{3} \\ =\frac{21}{3} \\ =7 \end{gathered}$

The perimeter of MEG is 7.

6 0

1 year ago