(fog)(x) = f[g(x)] ...................
1: one solution
Explanation: We see that the variable x is equal to 9 (and only 9). Therefore there is only one solution
2: infinitely many solutions
Explanation: When an equation has infinitely many solutions, it means that any real number (aka <em>all real numbers</em>) would satisfy that equation. For example 2x = 2x. Any number you plug in for x would result in both sides being equal. So you know an equation has infinitely many solutions if both sides are the same
3: no solution
Explanation: 7 does not equal 4 so you can't solve this equation.
4: no solution
Explanation: 7 is not less than 7, that is impossible, so there is no solution.
5: one solution
Explanation: 8 <em>is</em> greater than or equal to -2, so this inequality is true, meaning it represents one solution
Answer:
Angle between the two vectors is 135°
u•v = -12
Step-by-step explanation:
Given two vectors u = (4,0) and v = (-3,-3).
To find the angle between the two vectors we will use the formula for calculating the angle between two vectors as shown;
u•v = |u||v|cos theta
cos theta = u•v/|u||v|
theta = arccos (u•v/|u||v|)
u•v = (4,0)•(-3,-3)
u•v = 4(-3)+0(-3)
u•v = -12
For |u| and |v|
|u| = √4²+0²
|u| = √16 = 4
|v| = √(-3)²+(-3)²
|v| = √9+9
|v| = √18
|v| = 3√2
|u||v| = 4×3√2 = 12√2
theta = arccos(-12/12√2)
theta = arccos(- 1/√2)
theta = -45°
Since cos is negative in the second quadrant, theta = 180-45°
theta = 135°
To get u•v using the formula u•v = |u||v|cos theta
Given |u||v| = 12√2 and theta = 135°
u•v = 12√2cos 135°
u•v = 12√2× -1/√2
u•v = -12√2/√2
u•v = -12
For the diagram of the vectors, find it in the attachment below.
Answer:
30°
Step-by-step explanation:
To make sure it's complete
Answer:
38
Step-by-step explanation:
For the case of a parallelogram, when the diagonals ( in our case AC & BD) are intersected, they are basically bisected ( divided into two equal halves ). Therefore when the diagonals intersect at point E, we can say that the diagonal AC is divided in two equal halves which in our case are AE and CE. since AE and CE are equal , we can say that,
