The solution is the point of intersection between the two equations.
Assuming you have a graphing calculator or a program to lets you graph equations (I use desmos) you simply put in the equetions and note down the coordinates of the point of intersection.
In the graph the first equation is in blue and the second in red.
The point of intersection = the solution = (-6 , -1)
If you dont have access to a graphing calculator you could draw the graphs by hand;
1) Draw a table of values for each equation; you do this by setting three or four values for x and calculating its image in y (you can use any values of x)
y = 0.5 x + 2 (Im writing 0.5 instead of 1/2 because I find its easier in this format)
x | y
-1 | 1.5 * y = 0.5 (-1) + 2 = 1.5
0 | 2 * y = 0.5 (0) + 2 = 2
1 | 2.5 * y = 0.5 (1) + 2 = 2.5
2 | 3 * y = 0.5 (2) + 2 = 3
y = x + 5
x | y
-1 | 4 * y = (-1) + 5 = 4
0 | 5 * y = (0) + 5 = 5
1 | 6 * y = (1) + 5 = 6
2 | 7 * y = (2) + 5 = 7
2) Plot these point on the graph
I suggest to use diffrent colored points or diffrent kinds of point markers (an x or a dot) to avoid confusion about which point belongs to which graph
3) Using a ruler draw a line connection all the dots of one graph and do the same for the other
4) The point of intersection is the solution
As per the Intersecting Chords theorem, if two chords cross in a circle, the products of the chord segments' measures are equal. The measure of the line segment is DF is 14 units.
<h3>What is Intersecting Chords theorem?</h3>
If two chords cross in a circle, the products of the chord segments' measures are equal.
As per the Intersecting Chords theorem, the product of DF and FB will be equal to the product of CF and FA, therefore,
DF×FB = CF×FA
(x+8) × 8 = 16 × 7
(x+8) = (16×7)/8
(x+8) = 14
Hence, the measure of the line segment is DF is 14 units.
Learn more about Intersecting Chords theorem:
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Answer:
D
Step-by-step explanation:
In the other tables, their y values have a constant rate of change while as D does not.
Rate of Change for:
A = 5
B = 0.75
C = -5
D = Not Constant (+2 -> +3 -> +4)