Please Help!!? Leah is solving the equation using properties of exponents? 2^2x-3=(1/6)^3x+9
1 answer:
HERE IS HOW TO SOLVE:
Simplify {2}^{2}2
2
to 44
4x-3={(\frac{1}{6})}^{3}x+94x−3=(
6
1
)
3
x+9
2 Use Division Distributive Property: {(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}(
y
x
)
a
=
y
a
x
a
4x-3=\frac{1}{{6}^{3}}x+94x−3=
6
3
1
x+9
3 Simplify {6}^{3}6
3
to 216216
4x-3=\frac{1}{216}x+94x−3=
216
1
x+9
4 Simplify \frac{1}{216}x
216
1
x to \frac{x}{216}
216
x
4x-3=\frac{x}{216}+94x−3=
216
x
+9
5 Multiply both sides by 216216
864x-648=x+1944864x−648=x+1944
6 Add 648648 to both sides
864x=x+1944+648864x=x+1944+648
7 Simplify x+1944+648x+1944+648 to x+2592x+2592
864x=x+2592864x=x+2592
8 Subtract xx from both sides
864x-x=2592864x−x=2592
9 Simplify 864x-x864x−x to 863x863x
863x=2592863x=2592
10 Divide both sides by 863863
ANSWER: x= 2592 over 863
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<u>Answer:</u>
○
<u>Step-by-step explanation:</u>
To find the equation of the line, let's first consider the points whose coordinates we have been given:
• (6, 1)
• (2, 0).
The point (2, 0) is what is called the x-intercept, which is the point where the line crosses the x-axis. This means that at this point, the y-coordinate of the line is 0.
Next, let's calculate the slope (gradient) of the line using the formula:
where:
m = gradient,
and
= points on the line.
Using the formula:
⇒
Finally, now that we have two points on the line as well as the line's slope, we can use the following formula to find the equation of the line:
You can use any of the points on the line as and
.
Using (2, 0):
⇒
Therefore the equation of the line is .
Learn more about point-slope form at: