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
No change. She gave the salesperson exactly the right amount to buy the racecar.
Answer:the third option is correct
Step-by-step explanation:
The system of equations are
y = 2x^2 - 5x - 7 - - - - - - - - - - -1
y = 2x + 2 - - - - - - - - - - - - - 2
We would equate equation 1 and equation 2. It becomes
2x^2 - 5x - 7 = 2x + 2
2x^2 - 5x - 2x - 7 - 2 = 0
2x^2 - 7x - 9 = 0
We would find two numbers such that their sum or difference is -7x and their product is - 18x^2. The two numbers are 2x and - 9x. Therefore
2x^2 + 2x - 9x - 9 = 0
2x(x + 1) - 9(x + 1) = 0
2x - 9 = 0 or x + 1 = 0
2x = 9 or x = - 1
x = 9/2 = 4.5
Substituting x = 4.5 or x = -1 into equation 2, it becomes
y = 2 × 4.5 + 2 or y = 2 × - 1 + 2
y = 11 or y = 0
Therefore, the solutions are
(4.5, 11) (- 1, 0)
Number of 1 inch cubes:
Volume of the 1 inch cubes = 1*1*1 = 1 cubic inches.
Volume of the 5 inch cubes = 5*5*5 = 125 cubic inches.
Number = Volume of the 5 inch cubes / Volume of the 1 inch cubes
= 125 /1 = 125.
125 of the 1-inch cubes.
