<h3>Given</h3>
three numbers: a, b, c
a+b+c = 11
2a +5b +6c = 32
3a -b = 22
<h3>Find</h3>
a, b, c
<h3>Solution</h3>
The equations can be represented by the augmented matrix
![\left[\begin{array}{ccc|c}1&1&1&11\\2&5&6&32\\3&-1&0&22\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%261%2611%5C%5C2%265%266%2632%5C%5C3%26-1%260%2622%5Cend%7Barray%7D%5Cright%5D)
A graphing calculator gives the solution
(a, b, c) = (8, 2, 1)
The three numbers are 8, 2, and 1.
_____
If you want to solve this by hand, you could use Cramer's rule, or you could do the row operations by and. For example, subtract twice the first equation from the second to get
... 3b +4c = 10
Subtract 3 times the first equation from the third to get
... -4b -3c = -11
These two equations can be solved by your favorite method to find
... b = (-44 +30)/(-16 +9) = -14/-7 = 2 . . . . . using Cramer's rule
... c = (-40 +33)/-7 = 1
Then the first equation can be used to find <em>a</em>.
... a + 2 + 1 = 11
... a = 8 . . . . . . . . . . . as above
Answer: see image
<u>Step-by-step explanation:</u>
Count how many spaces the vertex is away from the line x = -1. Then place that vertex the same distance on the other side of the line x = -1.
Answer:
AFCE = 30
P+Q = 11
Step-by-step explanation:
From the picture, you can see the figure can be decomposed into two identical large triangles with area 20, and 4 identical longer ones, that have to cover the remaining area 40, thus 10 each.
From that you can count the area.
Second puzzle is just trial and error.
Elliott's bed -> 75 in
Elliott before -> 5 ft 11 in = 71 in
Elliott after -> 71 + 6 = 77 in
77 - 75 = 2 in
Elliott's bed is shorter than him by 2 inches.
The answer to this equation is 1/2