Explain why the x-coordinates of the points where the graphs of the equations y = 2−x and y = 8x+4 intersect are the solutions o
f the equation 2−x = 8x+4. part
b.make tables to find the solution to 2−x = 8x+4. take the integer values of x between −3 and 3. part
c.how can you solve the equation 2−x = 8x+4 graphically?
b.make tables to find the solution to 2−x = 8x+4. take the integer values of x between −3 and 3. part
c.how can you solve the equation 2−x = 8x+4 graphically?
1 answer:
Part 1)
We have two lines: y = 2-x and y = 8x+4
Given two simultaneous equations that are both required to be true.
the solution is the points where the lines cross
Which is where the two equations are equal
Thus the solution that works for both equations is when
2-x = 8x+4
because
where that is true is where the two lines will cross and that is the common point that satisfies both equations.
Part 2) Make tables to find the solution to 2−x = 8x+4. take the integer values of x between −3 and 3
see the attached table
The table shows that none of the integers from [-3,3] work because in no case does
<span>2-x = 8x+4
</span>
To find the solution we need to rearrange the equation to the form x=n
2-x =8x+4
8x+x=2-4
9x=-2
x=-2/9
The only point that satisfies both equations is
where
x = -2/9
Find y:
y = 2-x = 2 - (-2/9) = 2 + 2/9 = 20/9
Verify we get the same in the other equation
y = 8x+4 = 8(-2/9) + 4 = 20/9
Thus the only actual solution, being the point where the lines cross,
is the point (-2/9, 20/9)------> (-0.22,2.22)
Part 3) how can you solve the equation 2−x = 8x+4 graphically?
<span>The point on the graph where the lines cross is the solution to the system of equations
</span>
using a graph tool
see the attached figure
the solution is the point (-0.22,2.22)
We have two lines: y = 2-x and y = 8x+4
Given two simultaneous equations that are both required to be true.
the solution is the points where the lines cross
Which is where the two equations are equal
Thus the solution that works for both equations is when
2-x = 8x+4
because
where that is true is where the two lines will cross and that is the common point that satisfies both equations.
Part 2) Make tables to find the solution to 2−x = 8x+4. take the integer values of x between −3 and 3
see the attached table
The table shows that none of the integers from [-3,3] work because in no case does
<span>2-x = 8x+4
</span>
To find the solution we need to rearrange the equation to the form x=n
2-x =8x+4
8x+x=2-4
9x=-2
x=-2/9
The only point that satisfies both equations is
where
x = -2/9
Find y:
y = 2-x = 2 - (-2/9) = 2 + 2/9 = 20/9
Verify we get the same in the other equation
y = 8x+4 = 8(-2/9) + 4 = 20/9
Thus the only actual solution, being the point where the lines cross,
is the point (-2/9, 20/9)------> (-0.22,2.22)
Part 3) how can you solve the equation 2−x = 8x+4 graphically?
<span>The point on the graph where the lines cross is the solution to the system of equations
</span>
using a graph tool
see the attached figure
the solution is the point (-0.22,2.22)
You might be interested in
9514 1404 393
Answer:
300
Step-by-step explanation:
There are 25 ways to select the first student. After that student is removed from the selection pool for the second student, there are 24 ways to select the second student. This gives 25·24 = 600 ways to select 2 students <em>in a particular order</em>.
Since we don't care about the order, we can divide this number by the number of ways two students can be ordered: AB or BA, 2 ways.
600/2 = 300
There are 300 ways to pick a combination of two students from 25.
__
<em>Additional comments</em>
This sort of selection (2 out of 25) has a formula for it, and an abbreviation for the formula.
"n choose k" can be written nCk or C(n, k)
The function is a ratio of factorials:
nCk = n!/(k!(n-k)!)
If you can typeset this, it is written ...
This is different from the formula for the number of <em>permutations</em> of n things taken k at a time. That would be written nPk or P(n, k) = n!/(n-k)!.