m∠FDE = 52°
Solution:
Given data:
DE ≅ DF, CD || BE, BC || FD and m∠ABF = 116°
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠ABF + m∠CBF = 180°
116° + m∠CBF = 180°
m∠CBF = 64°
If CD || BE, then CD || BF.
Hence CD || BE and BE || FD.
Therefore BFCD is a parallelogam.
<em>In parallelogram, Adjacent angles form a linear pair.</em>
m∠CBF + m∠BFD = 180°
64° + m∠BFD = 180°
m∠BFD = 116°
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠BFD + m∠DFE = 180°
116° + m∠DFE = 180°
m∠DFE = 64°
we know that DE ≅ DF.
<em>In triangle, angles opposite to equal sides are equal.</em>
m∠DFE = m∠DEF
m∠DEF = 64°
<em>sum of all the angles of a triangle = 180°</em>
m∠DFE + m∠DEF + m∠FDE = 180°
64° + 64° + m∠FDE = 180°
m∠FDE = 52°
So the fencing perimiter is 70 by 114
perimiter=2 times width +2 times legnth
width=70
legnth=144
perimiter=70 times 2+114 times 2=140+228=368
needs to buy 368 feet
Answer:
b11 = -14
b12 = 9
b13 = 8
Step-by-step explanation:
* Lets revise some notes to solve the problem
- Any matrix has a dimension m × n, where m is the number of rows
and n the number of columns
- We can add matrices with same dimensions
* Now lets solve the problem
∵ ![B+\left[\begin{array}{ccc}15&-7&4\\0&1&2\end{array}\right]=\left[\begin{array}{ccc}1&2&12\\4&0&2\end{array}\right]](https://tex.z-dn.net/?f=B%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D15%26-7%264%5C%5C0%261%262%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%2612%5C%5C4%260%262%5Cend%7Barray%7D%5Cright%5D)
- Let ![B=\left[\begin{array}{ccc}b11&b12&b13\\b21&b22&b23\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Db11%26b12%26b13%5C%5Cb21%26b22%26b23%5Cend%7Barray%7D%5Cright%5D)
∴ ![\left[\begin{array}{ccc}b11&b12&b13\\b21&b22&b23\end{array}\right]+\left[\begin{array}{ccc}15&-7&4\\0&1&2\end{array}\right]=\left[\begin{array}{ccc}1&2&12\\4&0&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Db11%26b12%26b13%5C%5Cb21%26b22%26b23%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D15%26-7%264%5C%5C0%261%262%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%2612%5C%5C4%260%262%5Cend%7Barray%7D%5Cright%5D)
- Lets add and find the missing
* Lets start with the first rows
∵ b11 + 15 = 1 ⇒ subtract 15 from both sides
∴ b11 = -14
∵ b12 + -7 = 2 ⇒ add 7 to both sides
∴ b12 = 9
∵ b13 + 4 = 12 ⇒ subtract 4 from both sides
∴ b13 = 8
* Now lets start with the second rows
∵ b21 + 0 = 4
∴ b21 = 4 ⇒ given
∵ b22 + 1 = 0 ⇒ subtract 1 from both sides
∴ b22 = -1 ⇒ given
∵ b23 + 2 = 2 ⇒ subtract 2 from both sides
∴ b23 = 0 ⇒ given
Answer:
a= 1183/456
Step-by-step explanation:
In pic
(Hope this helps can I pls have brainlist (crown) ☺️)