Answer:
y
=
4
(
1
2
)
x
Explanation:
An exponential function is in the general form
y
=
a
(
b
)
x
We know the points
(
−
1
,
8
)
and
(
1
,
2
)
, so the following are true:
8
=
a
(
b
−
1
)
=
a
b
2
=
a
(
b
1
)
=
a
b
Multiply both sides of the first equation by
b
to find that
8
b
=
a
Plug this into the second equation and solve for
b
:
2
=
(
8
b
)
b
2
=
8
b
2
b
2
=
1
4
b
=
±
1
2
Two equations seem to be possible here. Plug both values of
b
into the either equation to find
a
. I'll use the second equation for simpler algebra.
If
b
=
1
2
:
2
=
a
(
1
2
)
a
=
4
Giving us the equation:
y
=
4
(
1
2
)
x
If
b
=
−
1
2
:
2
=
a
(
−
1
2
)
a
=
−
4
Giving us the equation:
y
=
−
4
(
−
1
2
)
x
However! In an exponential function,
b
>
0
, otherwise many issues arise when trying to graph the function.
The only valid function is
y
=
4
(
1
2
)
x
Answer:
70 degrees
Opposite angles are equal to each other
A trinomial is a polynomial with three terms. It can be determined if it is a difference of two squares when you factor it.
The resulting factor of a trinomial that is a difference of two squares is: a²<span> – b</span>²<span> = (a + b)(a – b) or (a – b)(a + b)</span>
You will notice that the middle term is missing. This means that the middle term zeroes out as a result of having the same number of different signs (+ and -)
Answer:
Total amount spent for meal = $16.65
Step-by-step explanation:
Given:
Amount spent on dinner = $20
Tip = 20%
Find:
Total amount spent for meal
Computation:
Total amount spent for meal = Amount spent on dinner / (1+tip)
Total amount spent for meal = 20 / 1.2
Total amount spent for meal = 16.666
Total amount spent for meal = $16.65
Answer:
x=-1
Step-by-step explanation:
-7 < 3(x) + 5 ≤ 7
-7 < 3(-1) + 5 ≤ 7
-7 < -3 + 5 ≤ 7
-7 < 2 ≤ 7
