$403.75
Step 1: 415(.15)
Step 2: 475 - 415(.15)
Step 3: 403.75
400,000,000 + 20,000,000 + 8,000,000 + 200,000 + 50,000 + 200 + 30
Let 'x' represent the volume of 6% saline solution
Let 'y' represent the volume of 8% saline solution
Form 2 equations.
Eq. 1: 20+x=y
Meaning 20 cm³ + x cm³=y cm³
Eq 2: 0.06x+0.1(20)=0.08y
Meaning: 6% of x + 10% of 20= 8% of y
Use substitution or elimination to solve this linear system. I used substitution.
Sub. Eq. 1 (20+x=y) into Eq. 2 (0.06x+0.1(20)=0.08y)
0.06x+ 0.1(20)=0.08(20+x)
0.06x+2+1.6=0.08x
-0.02x= -0.4
x=20
Substitute x=20 into equation 1 (you can also use 2 but in this case equation 1 is simpler)
20+x=y
20+20=y
40=y
To check, substitute x=20 and y=40 into equation 2
0.06x + 0.1(20)= 0.08y
0.06(20) +2 = 0.08(40)
1.2+2= 3.2
3.2=3.2
Therefore, Kim would need 20cm³ of 6% saline solution and 40cm³ of 10% saline solution to make 8% solution.
36
+57
------
93
On a number line: Start at 0. Count forward until you reach 36. Once you've reached 36, Mark it. Then you go forward 57, from the mark you made at 36. You should end up on 93 on the number line.
Answer:
![X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\](https://tex.z-dn.net/?f=X%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%261%5C%5C5%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D21%5C%5C20%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Step-by-step explanation:
Given the simultaneous equation
x+y=21
5x+4y=20
To write in matrix form, it must be in the form AX= b
X = A⁻¹b
A⁻¹ is the inverse of matrix A
A is a 2by2 matrix
X is the variables
b is a column matrix
The expression will therefore be written as;
![A=\left[\begin{array}{ccc}1&1\\5&4\\\end{array}\right] \\\\|A| = 1(4)- 5(1)\\|A| = 4-5\\|A| = -1\\A^{-1} = -\left[\begin{array}{ccc}4&-1\\-5&1\\\end{array}\right] \\\\A^{-1} = \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C5%264%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%7CA%7C%20%3D%201%284%29-%205%281%29%5C%5C%7CA%7C%20%3D%204-5%5C%5C%7CA%7C%20%3D%20-1%5C%5CA%5E%7B-1%7D%20%3D%20-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%26-1%5C%5C-5%261%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5CA%5E%7B-1%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%261%5C%5C5%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Hence the required product matrix that represent X is;
