f (x ) = 2 x + 5
For g (x) we will solve the system:
- 1 =-2 m + b
+
-9 = 2 m + b
----------------------
-10 = 2 b, b = -5
-9 = 2 m - 5
2 m = -4
m = -2
g ( x ) = - 2 x - 5
For h (X):
m = (-1-5 ) / ( 3-0 ) = -6/3 = -2
5 = 0 + b, b = 5
h ( x) = - 2 x + 5.
Now we have 4 linear functions:
1 ) f ( x ) = 2 x + 5
The slope is m = 2, y - intercept: y = 5 , zero: x = -2.5 and the function increases ( m > 0 ).
2 ) g(x) = - 2 x - 5
The slope is m = - 2, y-intercept: y =-5 , zero: x = -2.5 and the function decreases ( m < 0 ).
3 ) h ( x ) = - 2 x + 5
The slope is m = - 2, y - intercept . y = 5, zero: x = 2.5 and the function decreases.
4 ) j (x) = 2 x + 5
The slope is m = 2, y -intercept: y = 5, zero: x = -2.5 and the function decreases.
The functions f( x ) and j ( x ) are parallel and also g( x ) and h ( x ). They have the same slope.
The functions f ( x ) and j (x ) are increasing and h ( x ) and h ( x ) are decreasing.
Answer:
Step-by-step explanation:
W have been given that the vertex of a parabola is at (2, 3) and the point (0, -1) is also on the parabola. We are asked to find the equation of parabola in the form 
.
We know that vertex form of parabola in form 
, where (h,k) in vertex of parabola.
Upon substituting coordinates of vertex, we will get:
To find the value of a, we will substitute coordinates of point (0, -1) as:
Therefore, our required equation would be .
Given:
Christopher scores 2 goals in a soccer game.
His goal total can vary from the average by 1 goal.
To find:
The absolute value equation can be used to calculate Christopher's maximum and minimum goals per game.
Solution:
Let Christopher scores x goals in a soccer game.
Then difference between actual goals and average goals is x-2.
His goal total can vary from the average by 1 goal.
Maximum number of goals = 2+1 = 3
Minimum number of goals = 2-1 = 1
It means, the difference between actual goals and average goals is either -1 and 1.
...(1)
...(2)
Using (1) and (2),we get
Therefore, the correct option is C.
Answer: still air is 150mph. The wind speed is 30mph.
Step-by-step explanation:
X=speed of the plane, Y=speed of the wind.
360/2hours=180
360/3hours=120
2x=180+120
2x=300
X=150
The airplane in still air is 150mph
Add together
X+y=180
150+y=180
Y=180-150
Y=30mph
The wind speed is 30mph
The thousands place is the fourth over to the left
so we are rounding the number 4
To determine weather it rounds up, we look at the number before it (to the right)
The number 2 is less than 5 so the 4 stays a 4
So we write the number until we get to the thousands position, which would be, 174
we then fill in all the numbers after it with zero's so the number, after it is rounded, is 174,000
So your answer is c
