<h3>
Answer: f(x) = x + 13 </h3>
This is the same as y = x+13
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Explanation:
Let's find the slope
I'll use the first two rows as the (x1,y1) and (x2,y2) points
m = (y2-y1)/(x2-x1)
m = (19-18)/(6-5)
m = 1/1
m = 1
The slope is 1.
Now apply the point slope formula and solve for y
y - y1 = m(x - x1)
y - 18 = 1(x - 5)
y - 18 = x - 5
y = x-5 + 18
y = x + 13
f(x) = x + 13 is the final answer
As a check, note how something like x = 5 leads to...
f(x) = x+13
f(5) = 5+13 ... replace x with 5
f(5) = 18
We see that x = 5 leads to f(x) = 18. That verifies the first row. I'll let you check the remaining three rows.
The equation y = x+13 has slope 1 and y intercept 13.
Answer:
10/3
Step-by-step explanation:
|x+3|=4x-7
So |-(x+3)|=|x+3|
We are going to try out two cases:
-(x+3)=4x-7 and x+3=4x-7
-x-3=4x-7 3=3x-7
-3=5x-7 10=3x
4=5x x=10/3
x=4/5
We are going to test out both because we could something that isn't actually a solution, this is called extraneous.
First thing I'm going to check is 4x-7 for it being positive.
4(4/5)-7=20/5-7=-15/5=-3 so 4/5 will not work because absolute value result can't be negative
4(10/3)-7=40/3-7=19/3 which is positive
checking |x+3| to see if is 19/3 for x=10/3 we see that is so that is the answer
See explanation below.
Explanation:
The 'difference between roots and factors of an equation' is not a straightforward question. Let's define both to establish the link between the two..
Assume we have some function of a single variable
x
;
we'll call this
f
(
x
)
Then we can form an equation:
f
(
x
)
=
0
Then the "roots" of this equation are all the values of
x
that satisfy that equation. Remember that these values may be real and/or imaginary.
Now, up to this point we have not assumed anything about
f
x
)
. To consider factors, we now need to assume that
f
(
x
)
=
g
(
x
)
⋅
h
(
x
)
.
That is that
f
(
x
)
factorises into some functions
g
(
x
)
×
h
(
x
)
If we recall our equation:
f
(
x
)
=
0
Then we can now say that either
g
(
x
)
=
0
or
h
(
x
)
=
0
.. and thus show the link between the roots and factors of an equation.
[NB: A simple example of these general principles would be where
f
(
x
)
is a quadratic function that factorises into two linear factors.
Answer: 190
Step-by-step explanation:
