Divide the miles and time to find the speed.
14.4/3 = 4.8
28.8/6 = 4.8
43.2/9 = 4.8
57.6/12 = 4.8
All the answers are the same, so therefore the speed is 4.8 mph.
Step-by-step explanation:
In order to graph this system of equations, you have to put the equations in terms of y so that you can graph it by hand.
For the first equation:
Subtract x on both sides so that it reads to be
For the second equation:
Subtract 3x on both sides and divide by -1 to make the y positive. Remember that when you divide, the sign always flips:
So the two equations you have to graph now are and .
In order to graph, start from your y-intercept for each of the equations and go vertical/horizontal based on the coefficient of your equation. For instance, for your first equation, you would go down -1 and to the right 1. Repeat until your whole equation is graphed. For the second equation your coefficient is 3, so you would go up 3 from -4 and to the right 1. Repeat.
Once you have your equations graphed, you need to find where the two graphs both have solutions. To do this, pick any point from the graph and plug it into the x and y of one equation. If the equation equals itself, then that area is the solution of the graph for that equation. Make sure to do this for both equations. Once you find the area in which both equations have solutions for each other, that is the area that needs to be shaded.
Here is what your graph should look like:
Answer:
c. 10
Step-by-step explanation:
Eliminate parentheses using the distributive property.
3(b+4) -2(2b+3) = -4 . . . . given
3b +12 -4b -6 = -4 . . . . . parentheses eliminated
-b +6 = -4 . . . . . . . . . . . . collect terms
-b = -10 . . . . . . . . . . . . . . subtract 6
b = 10 . . . . . . . . . . . . . . . . multiply by -1
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The rules of equality require that any operation you perform on one side of the equal sign must also be done on the other side. So when we say "subtract 6", we assume you know that means "subtract 6 from both sides of the equation", for example.
If you graph the three given points, you can see that the vertex (h,k) is (-1,3).
Equation of a quadratic function is: y = a(x - h)² + k
Plug in the vertex and one of the points (I chose (0,1)) and solve for "a".
1 = a(0 + 1)² + 3
-2 = a
Answer: f(x) = -2(x +1)² + 3