Answer:
<h3>X=-3</h3>
Step-by-step explanation:
Isolate x on one side of the equation.
<u><em>DISTRIBUTIVE PROPERTY</em></u>
A(B+C)=AB+AC
A(B-C)=AB-AC
3(4x+4) (First, expand.)
3*4x=12x
3*4=12
12x+12
2(5x+9)-12
2*5x=10x
2*9=18
10x+18
18-12=6
12x+12=10x+6
12x+12-12=10x+6-12 (Subtract 12 from both sides.)
6-12 (Solve.)
12-6=6
12x=10x-6
12x-10x=10x-6-10x (Subtract 10x from both sides.)
12x-10x (Solve.)
12x-10x=2x
2x=-6
2x/2=-6/2 (Then, divide by 2 from both sides.)
-6/2 (Solve.)
-6/2=-3
x=-3
As a result, the final answer is x=-3.
Working step by step I first see all my different groups then add them all together
so
12 - cats
15 - dogs
6 - both
9 - neither
12 students + 15 students + 6 students + 9 students = 42 students
therefore 42 students are in the class
16 + 10 + 3 + 12 = 41
I’m sorry if i got it wrong!
Answer:
b
Step-by-step explanation:
integer because is a negative number
Answer:
x=4, y=4, λ=-16
Step-by-step explanation:
We have this 3x3 system of linear equations:
λ
λ
So, let's rewrite the system in its augmented matrix form
![\left[\begin{array}{cccc}4&0&1&0\\0&4&1&0\\1&1&0&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D4%260%261%260%5C%5C0%264%261%260%5C%5C1%261%260%268%5Cend%7Barray%7D%5Cright%5D)
Let´s apply row reduction process to its associated augmented matrix:
Swap R1 and R3
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\4&0&1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C4%260%261%260%5Cend%7Barray%7D%5Cright%5D)
R3-4R1
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\0&-4&1&-32\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C0%26-4%261%26-32%5Cend%7Barray%7D%5Cright%5D)
R3+R2
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\0&0&2&-32\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C0%260%262%26-32%5Cend%7Barray%7D%5Cright%5D)
Now we have a simplified system:
x+y+0=0
0+4y+λ=0
0+0+2λ=-32
Solving for λ, x, and y
λ=-16
x=4
y=4
