If you would like to solve for f(g(x)) when x = 1, you can do this using the following steps:
<span>f(x) = x^2 - 3x + 6
g(x) = x - 3/2
f(g(x)) = f(</span>x - 3/2) = (x - 3/2)^2 - 3 * (x - 3/2) + 6
x = 1
f(g(1)) = f(1 - 3/2) = f(-1/2) = (-1/2)^2 - 3 * (-1/2) + 6 = 1/4 + 3/2 + 6 = 1/4 + 6/4 + 24/4 = 31/4 = 7 3/4
The correct result would be 7 3/4. add me as a friend
-1/5 + 1/2 u = -2/3
-6/30 + 15/30 u = -20/30
+6/30 +6/60
___________________
15/30 u = -14/30
(15/30 u = -14/30) ÷ (15/30)
u = -14/15
u = -.933
Answer:
See below
Step-by-step explanation:
Both horses travel 0 miles in 0 minutes. We can see this on the graph where both lines start at the 0 in the bottom left corner. For the purpose of writing the equations this also shows us that the y-intercept is 0. In a slope-intercept equation, y=mx+b, that number is the b. b is zero in both equations, so we don't need to write anything for that.
For horse A, we can see on the graph that at 4 minutes, horse A has traveled 1 mile. Also, confirming this rate, at 8 minutes, it went 2 miles. This will help us find the rate. The rate will be the number we fill in for the m in the y=mx+b equation. Horse A goes 1mile every 4 minutes. That is a rate of 1/4 miles per minute. So Horse A's equation will be
y = (1/4)x You can make it more *intuitive* possibly by using m for miles and t for time instead, like this:
m = (1/4)t
Horse B is a little bit faster, and you can see this bc the line is a little bit steeper. It goes 2 miles in 5 minutes (confirm you can see it goes 4 miles in 10 minutes)
So Horse B's equation is
y = (2/5)x
or miles = (2/5)time
Mathematically, the equations are the same whether you use x,y or m,t
If Horse A runs for 12 minutes then it will run
miles = (1/4)minutes
miles = (1/4)(12)
miles = 3
If Horse B runs for 12 minutes, then it will run
miles = (2/5)minutes
miles = (2/5)12
miles = 4.8
Your answer would be the second option, (-4,5).
We can find this by substituting in each point into the equation y < |x - 3| and seeing if it is true.
For the first one you get 1 < |2 - 1|. |2 - 1| = |-1| = 1, and 1 cannot be less than itself, so this is false.
For the second one you get 5 < |-4 - 3|. |-4 - 3| = |-7| = 7, and 5 is indeed less than 7, so this is correct.
I hope this helps!
Answer:
Point of intersections are (0, -7) and (5, -2).
Step-by-step explanation:
From the graph attached,
A straight line is intersecting the circle at the two points (0, 7) and (5, -2).
Now solve algebraically,
Equation of the line → y = x - 7 -------(1)
Equation of the circle → (x - 5)² + (y + 7)² = 25 -------(2)
By substituting the value of y from equation (1) to equation (2)
(x - 5)² + (x - 7 + 7)² = 25
(x - 5)² + x² = 25
x² - 10x + 25 + x² = 25
2x² - 10x = 0
x² - 5x = 0
x(x - 5) = 0
x = 0, 5
From equation (1),
y = 0 - 7 = -7
y = 5 - 7 = -2
Therefore, point of intersections are (0, -7) and (5, -2).
