9514 1404 393
Answer:
(x, y, z) = (-3, -1, 3)
Step-by-step explanation:
Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.
Use the last equation to write an expression for z.
z = 4 -x +4y
Substitute this into the second equation:
y -4(4 -x +4y) = -13
y -16 +4x -16y = -13
4x -15y -3 = 0
In genera form, the first equation can be written as ...
3x +y +10 = 0
Now, the solution to these two equations can be found to be ...
x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"
y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation
z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z
The solution to the system is (x, y, z) = (-3, -1, 3).
_____
<em>Additional comment</em>
Written as an augmented matrix, the system of equations is ...
![\left[\begin{array}{ccc|c}-3&-1&0&10\\0&1&-4&-13\\1&-4&1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D-3%26-1%260%2610%5C%5C0%261%26-4%26-13%5C%5C1%26-4%261%264%5Cend%7Barray%7D%5Cright%5D)
Answer:
Concept: Caclulating Standard Variables
- We have a five number summary which is more than enough information to calculate our mean.
- The mean is the sum of all the numbers divided by the nth number of numbers.
- Note that we can only find a rough estimation not the EXACT value
- We do (min +max + 2(Q1+median+Q3))/8
- Now let's plug in our values!
- (0+85.3+2(8.4+17.4+30.9))/8
- Which gives us option B
- Hope this helps, give brainlist
Answer:
-9/4, -0.75, -6/10, 5/3, 2.1
Step-by-step explanation:
This is a lot easier to figure out if you simplify the fractions and then change them to decimals
So -9/4 = -2 1/4 or -2.25
-0.75
-6/10 = -0.60
5/3 = 1 2/3 or 1.67
2.1
When you are ordering negatives, the biggest negative is the least. That is why -9/4 (-2.25) is the least number out of the five given.
The next one would be -0.75, because it is the second biggest negative fraction.
The next one is -0.60 because that is the 3rd biggest negative fraction (or the smallest because this is the last negative)
Now, because we're in the positives we start with 1.67, because it is smaller than the other number.
2.1 is our last number, so it is the greatest!
I hope this helped :)
Answer:
x=3
Explanation:
First what you do is move x to one side and the rest of the numbers to another while changing the sign from + to - or - to + like this
6x+4x= 1+-21+50
Then you do the equation on 1 side
6x+4x=30
And then the other but add them like x is not there
10x=30
Your final result should be
X=3
Let C be the number of cats and B be the number of birds.
Each cat has 4 legs while each bird has 2 legs. Thus,
4C + 2B = 22
2B = 22 - 4C
Each cat and each bird has 2 eyes
2C + 2B = 16
Substituting 2B
2C + 22 - 4C = 16
2C = 6
C = 3
2B = 22 - 4(3)
B = 5
2 cats and 5 birds
