Answer:
(
, 
) and (1, 8 )
Step-by-step explanation:
To find the points of intersection equate f(x) and g(x), that is
3x² + 5 = 4x + 4 ( subtract 4x + 4 from both sides )
3x² - 4x + 1 = 0 ← in standard form
(3x - 1)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
3x - 1 = 0 ⇒ 3x = 1 ⇒ x =
x - 1 = 0 ⇒ x = 1
Substitute these values into either of the 2 functions for corresponding y- coordinates.
Substituting into g(x), then
g(1) = 4(1) + 4 = 4 + 4 = 8 ⇒ (1, 8 )
g( ) = 
+ 4 = ⇒ (, )
Given:
Consider the given graph as a reference of the solution.
To find:
Explanation:
By analyzing the graph, we can define the coordinate of vector u and v:
![\[\begin{align} & \vec{u}=(-8,-9)-(0,0)=(-8,-9) \\ & \vec{v}=(3,7)-(0,0)=(3,7)\end{align}\]](https://tex.z-dn.net/?f=%5C%5B%5Cbegin%7Balign%7D%20%26%20%5Cvec%7Bu%7D%3D%28-8%2C-9%29-%280%2C0%29%3D%28-8%2C-9%29%20%5C%5C%20%20%26%20%5Cvec%7Bv%7D%3D%283%2C7%29-%280%2C0%29%3D%283%2C7%29%5Cend%7Balign%7D%5C%5D)
Now, let perform the dot product of two vectors,
Now, perform the required operation,
Final answer:
Hence, the required solution is:
Answer:
For question 2 the slope is 1. So what you do is get the points you need to put on the graph and move them up one. Like how you did on question 1.
(0.5, 5) (1, 10) (1.5, 15) (2, 20) (2.5, 25)
Question 3 is the same thing but the slope is now 2. Then you would have to pin the points as...
(1, 2) (2, 4) (3, 6) (4, 8) (5, 10)
Hope this helped :)
Answer:
2 rational numbers i believe
Step-by-step explanation:
