Answer: 2,000 yeahhhhhhhhhhhhhhhhh
Answer:
Step-by-step explanation:
The last one
Answer:
The base is 0.1
The base is less than 1 so the function is decreasing
The x intercept is (3,0)
Step-by-step explanation:
The base of a logarithm refers to the number that must be raised to the power of the number on the right hand side of the logarithmic equation in order to yield the number on the left hand side of the logarithmic equation. It is always written as a subscript below the log symbol. In this case, the base is 0.1.
When the base of a logarithm is less than 1, it means that the function is decreasing as is the case in this question.
Looking at the graph, the x axis is cut at the point (3,0). This is the x-intercept of the graph.
Answer:
The final answers are x = 1 OR x = -3.
Step-by-step explanation:
Given the equation is x^2 -3 = -2x
Rewriting it in quadratic form as:- x^2 +2x -3 = 0.
a = 1, b = 2, c = -3.
Using Quadratic formula as follows:- x = ( -b ± √(b² -4ac) ) / (2a)
x = ( -2 ± √(4 -4*1*-3) ) / (2*1)
x = ( -2 ± √(4 +12) ) / (2)
x = ( -2 ± √(16) ) / (2)
x = ( -2 ± 4 ) / (2)
x = (-2+4) / (2) OR x = (-2-4) / (2)
x = 2/2 OR x = -6/2
x = 1 OR x = -3
Hence, final answers are x = 1 OR x = -3.
Answer:
![V = \left[\begin{array}{ccc}5&-1\end{array}\right]](https://tex.z-dn.net/?f=V%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We want to reflect this 2x1 vector on the line y = x.
To make this reflection we must use the following matrix:
![R=\left[\begin{array}{cc}0&1\\1&0\\\end{array}\right]](https://tex.z-dn.net/?f=R%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%261%5C%5C1%260%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Where R is known as the reflection matrix on the line x = y
Now perform the product of the vector <-1,5> x R.
![\left[\begin{array}{ccc}-1\\5\end{array}\right]x\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]\\\\\\\left[\begin{array}{ccc}-1(0) +5(1)&-1(1)+5(0)\end{array}\right]\\\\\\\left[\begin{array}{ccc}5&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%5C%5C5%5Cend%7Barray%7D%5Cright%5Dx%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%280%29%20%2B5%281%29%26-1%281%29%2B5%280%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%5Cend%7Barray%7D%5Cright%5D)
The vector matrix that represents the reflection of the vector <-1,5> across the line x = y is:
