Answer:
$51.70 is the original price
Step-by-step explanation:
Step 1:
Turn 40% into a decimal which makes it 0.40
ex. 50% would be 0.50, 5% would be 0.05 etc.
Step 2:
Put the numbers into this formula: Original Price (x) - Percent Off times Original Price = Sales Price
x - 0.40x = 31.02 this is basically 1x - 0.40x = 31.02 so,
Solving the left side of our equation gives us 1x - 0.40x = 0.60x
so now you have: 0.60x = 31.02
Step 3:
Divide both sides by 0.60 which gets x by itself and gives us the original price which is $51.70
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
The area of the pentagon is 140
Answer:
Step-by-step explanation:
<u>Sum of the angles of triangle equals 180</u>
- x + 12 + 2x - 29 + x + 5 = 180
<u>Simplified</u>
Answer:
It is equal to each other
Step-by-step explanation:
![\sqrt{\frac{1}{x^2}} = \frac{1}{x}\\\sqrt[3]{\frac{1}{x^3}} = \frac{1}{x}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B1%7D%7Bx%5E2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%5C%5C%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7Bx%5E3%7D%7D%20%3D%20%5Cfrac%7B1%7D%7Bx%7D)
