5(x-3)-x =
Multiply Everything In The Parentheses By 5
5x-15-x
Given
- f(n) values for n=1,2,3,4
- possible candidates for the function
Solution:
Method: Evaluate some of the values, for each function. A function with ANY value not matching the given f(n) values will be rejected.
N=1, f(n)=4
f(1)=4-3(1-1)=4
f(1)=4+3^(1+1)=4+3^2=4+9=13 ≠ 4 [rejected]
f(1)=4(3^(n-1))=4(3^0)=4
f(1)=3(4^(n-1))=3(4^0)=3*1=3 [rejected]
N=2, f(n)=12
f(1)=4-3(2-1)=4-3(1)=1 ≠ 12 [rejected]
[rejected]
f(1)=4(3^(2-1)=4*3^1=4*3=12
[rejected]
Will need to check one more to be sure
N=3, f(n)=3
[rejected]
[rejected]
f(3)=4(3^(n-1))=4(3^(3-1))=4(3^2)=4*9=36 [Good]
[rejected]
Solution: f(n)=4(3^(n-1))
m x H = ![\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%2637.5%26-12.5%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Step 1; Multiply 5 with this matrix
and we get a matrix ![\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%2610%5C%5C20%2640%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Multiply the fraction
with the matrix
and we get ![\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B2m%7D%7B5%7D%20%26%5Cfrac%7B4m%7D%7B5%7D%20%5C%5C%5Cfrac%7B8m%7D%7B5%7D%20%26%5Cfrac%7B16m%7D%7B5%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step2; Now equate corresponding values of the matrices with each other.
-5 =
and so on. By equating we get the value of m as 
Step 3; Add the matrices to get the value of matrix m.
Adding the three matrices on the RHS we get
.
Step 4; Adding the matrices on the LHS we get the resulting matrix as H +
. Equating the matrices from step 3 and 4 we get the value of H as ![\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%26-1%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
Step 5; Now to find the value of m x H we need to multiply the value of
with the matrix
Step 6; Multiplying we get the matrix m x H = [ -25
]
Answer:

Step-by-step explanation:
The angle marks mean those angles have the same measure. That means the sides opposite them have the same measure, so ...
2x -24 = x -2
x = 22 . . . . . . . . . add 24-x
The length of BC is x, so is 22.
BC = 22
Answer:
18 quarters
Step-by-step explanation: