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
Answer:
Step-by-step explanation:
5 + x - 12 = x- 7 (Add the 5 and -12 to simplify)
x - 7 = x - 7 (notice its the same on both sides of equal sign. Add 7 to both sides)
x = x
solution is all real numbers
Part B
5 - 4 - 12 = -4 - 7
-11 = -11
5 + 0 - 12 = 0 - 7
-7 = -7
5 + 5 - 12 = 5 - 7
-2 = -2
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Answer:
The common ratio is 1.2.
After 12 weeks the plant will be 4.46 meters long.
After one year the plant will be 6,552.32 meters long.
Step-by-step explanation:
Given that a marrow plants 0.5 m long and every week it grows by 20%, to find the value of the common ratio, calculate how long the plant is after 12 weeks and comment on the predicted length of the marrow after one year must be performed the following calculations:
0.50 x 1.2 ^ X = Y
Therefore, the common ratio is 1.2.
0.50 x 1.2 ^ 12 = Y
0.50 x 8.916 = Y
4.4580 = Y
Therefore, after 12 weeks the plant will be 4.46 meters long.
0.50 x 1.2 ^ 52 = Y
0.50 x 13,104.63 = Y
6,552.32 = Y
Therefore, after one year the plant will be 6,552.32 meters long.
Answer:
Step-by-step explanation:
Let x represent the number of phone call that she routes.
Laylah has already spent 3 minutes on the phone and she expects to spend 1 more minute with every phone call she routes. This means that if she routes x phone calls, the total number of time that Layla would have spent on the phone is
3 + x
If she routes 23 phone calls, the total time that Layla would have spent on the phone in total is
3 + 23 = 26 minutes