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garik1379 [7]
3 years ago
10

A window is twice as long as it is wide. The area of the window is 2x where x

Mathematics
1 answer:
Alchen [17]3 years ago
5 0

Answer:

When we have a rectangle of length L and width W, the area is calculated as:

A = W*L

In this case, W = x, and the area is:

A = 2*x

Then we must have  L = 2.

We know that the area of the window and the frame (together) is:

a = 2*x^2 + 12*x + 16

The area of the frame alone, will be equal to the difference between the area of both objects (a) and the area of the window alone (A)

area of the frame = a - A

                             = (2*x^2 + 12*x + 16) - (2*x) = (2*x^2 + 10*x + 16)

This is the area of the frame

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Answer:

<u>Options 1 and 3</u>

Step-by-step explanation:

We should know that, the system of linear equations can be treated as matrices, i.e: we can modify or make any operations provide that we must apply the same operation for all terms of each equation.

Given:  the solution for the following system is (2,9)

Px + Qy = R  ⇒(1)

Tx + Uy = V  ⇒(2)

We will check which system of equation has the same solution.

<u>System A)</u>  Px + Qy = R

                  (P+T)x + (Q+U)y = R+V  ⇒(3)

So, By summing (1) and (2) we will get the equation (3)

So, system A has the same solution (2,9)

<u>System B)</u> Px + Qy = R

                 (P+2T)x + (Q+2U)y = R-2V  ⇒(4)

By multiplying equation (2) by 2 and add with equation (1), we will get:

 (P+2T)x + (Q+2U)y = R+2V

Which is not the same as equation (4)

So, system B has not the same solution (2,9)

<u>System C)</u> (T-P)x + (U-Q)y = V-R  ⇒(5)

                  Tx + Uy = V  

By multiplying equation (1) by -1 and add with equation (2), we will get the equation (5)

So, system C has the same solution of (2,9)

<u>System D)</u> (T-P)x + (Q+U)y = V-R  ⇒(6)

                  Tx + Uy = V  

We cannot get equation (6) by the same operation over equation (1)

Note the coefficient of x and y⇒ (T-P) and (Q+U)

They must be (T+P) and (Q+U) <u>OR </u>(T-P) and (Q-U)

So, system D has not the same solution of (2,9)

<u>System E)</u> (5T-P)x + (5U-Q)y = V-5R ⇒ (6)

                  Tx + Uy = V  

By subtract equation (1) from 5 times equation (2), we will get:

(5T-P)x + (5U-Q)y = 5V-R

Which is not the same as equation (6)

So, system E has not the same solution (2,9)

As a conclusion, the systems which have the same solution are:

<u>Options 1 and 3</u>

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2 years ago
the beer at the electronic store was $81 before taxes the taxes is 7% what is the total of the price with tax
irga5000 [103]
Beer? at an electronic store? but srsly, 81*.07 is 5.67, total is 86.67
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2) 2(8r + 5) = 24 + 9r
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Answer:

r = 2

Step-by-step explanation:

2(8r + 5) = 24 + 9r

16r + 10 = 24 + 9r

16r - 9r = 24 - 10

7r = 14

r = 2

4 0
3 years ago
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