Answer:
18c - 30d + 36
Step-by-step explanation:
6(3c - 5d + 6)
6 × 3c = 18c
6 × -5d = -30d
6 × 6 = 36
Answer:
∠1 ≅ ∠2
Step-by-step explanation:
As shown in the figure:
We need to prove e ∥ f using the congruent angle.
So, check the options:
A) ∠2 ≅ ∠4 ⇒ (Wrong)
B) ∠1 ≅ ∠2 ⇒ (True) because a ∥ b (Given)
C) ∠2 ≅ ∠3 ⇒ It is required to prove that to prove e ∥ f , it can't be used.
D) ∠1 ≅ ∠4 ⇒ (Wrong)
The complete sentence will be:
We see that <u>∠1 ≅ ∠2</u> by the alternate exterior angles theorem.
Therefore, angle 2 is congruent to angle 3 by the transitive property.
So we are given the system:
Written in matrix form we get:
![\left[\begin{array}{cc}2&4\\6&3\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}8\\-3\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%264%5C%5C6%263%5Cend%7Barray%7D%5Cright%5D%20%0A%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%20)
We compute the solution like this:
![ \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{cc}2&4\\6&3\end{array}\right] ^{-1} \left[\begin{array}{c}8\\-3\end{array}\right] \\= \left[\begin{array}{cc}-3&4\\6&-2\end{array}\right] \left[\begin{array}{c}8\\-3\end{array}\right] \dfrac{1}{18}\\= \left[\begin{array}{c}2\\-3\end{array}\right]](https://tex.z-dn.net/?f=%20%0A%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%0A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%264%5C%5C6%263%5Cend%7Barray%7D%5Cright%5D%20%5E%7B-1%7D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%3D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-3%264%5C%5C6%26-2%5Cend%7Barray%7D%5Cright%5D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%20%5Cdfrac%7B1%7D%7B18%7D%5C%5C%3D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
The solution is :
![\left[\begin{array}{c}2\\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
For number 4 you do x + 19 = 90
90 - 19 = 71 so x = 71
