Question 2 of 5
1 answer:
The number of solutions in each equation are as follows:
- 1 solution: 4^x = 2^{-x}
- 2 solution: 3/2x + 2 = 2^{x} + 1 and 3x + 1 = 2^{-x}.
- No solution: 4^x + 2 = 3^x - 1 and 2x - 5 = 3^{x} + 2.
In order to determine the number of solutions, we would split the single equation to two different equations and then plot a graph, so as to reveal their solutions.
This ultimately implies that, the number of solutions is equal to the point of intersection between the lines of the equations plotted on a graph.
In conclusion, the number of solutions in each equation are as follows:
- 1 solution: 4^x = 2^{-x}
- 2 solution: 3/2x + 2 = 2^{x} + 1 and 3x + 1 = 2^{-x}.
- No solution: 4^x + 2 = 3^x - 1 and 2x - 5 = 3^{x} + 2.
Read more on number of solutions here: brainly.com/question/12558210
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Hey there!
To start, the point slope form of an equation is as follows:
y-y1=m(x-x1)
y1= the value of the y value in the pair of coordinates
x1= the value of the x values in the pair of coordinates
m= the slope
Because you appear to already have a set of points to plug in for y1 and x1, all you need now is the slope.
As stated in the question, one of the coordinate points in which the equation passes through is the intersection of the lines 3x-y=3 and x+2y=15. **note: the reason you must find the intersection of the two points is because you need two sets of coordinate points in order to calculate the slope of the line that passes through the points.
To find the intersection of these lines, solve the equations for y and graph the equations:
3x-y=3
-y=-3x+3
y=3x-3
x+2y=15
2y=-x+15
y=-1/2x+15/2
(the graph is in the image below)
The point of intersection would be (3,6)
Now that you have two sets of coordinate points, (3,6) and (2,1), you can plug these values into your slope intercept equation to calculate your slope:
(y2-y1)/(x2-x1)
(1-6)/(2-3)
-5/-1
=5
Your slope, or m value would be 5.
Now that you have at least one set of coordinate points and a slope value, you can plug in either set of points and your slope to get either one of the following point slope equations as your answer:
y-1=5(x-2)
or
y-3=5(x-6)
Hope this helps! :)
To start, the point slope form of an equation is as follows:
y-y1=m(x-x1)
y1= the value of the y value in the pair of coordinates
x1= the value of the x values in the pair of coordinates
m= the slope
Because you appear to already have a set of points to plug in for y1 and x1, all you need now is the slope.
As stated in the question, one of the coordinate points in which the equation passes through is the intersection of the lines 3x-y=3 and x+2y=15. **note: the reason you must find the intersection of the two points is because you need two sets of coordinate points in order to calculate the slope of the line that passes through the points.
To find the intersection of these lines, solve the equations for y and graph the equations:
3x-y=3
-y=-3x+3
y=3x-3
x+2y=15
2y=-x+15
y=-1/2x+15/2
(the graph is in the image below)
The point of intersection would be (3,6)
Now that you have two sets of coordinate points, (3,6) and (2,1), you can plug these values into your slope intercept equation to calculate your slope:
(y2-y1)/(x2-x1)
(1-6)/(2-3)
-5/-1
=5
Your slope, or m value would be 5.
Now that you have at least one set of coordinate points and a slope value, you can plug in either set of points and your slope to get either one of the following point slope equations as your answer:
y-1=5(x-2)
or
y-3=5(x-6)
Hope this helps! :)
Answer:
n =
Step-by-step explanation:
7(n - 6) = a(n + 5)
7n - 42 = an + 5a
7n - an = 5a + 42
n( 7 - a ) = 5a + 42
n =