Answer:
We subtract exponents when diving powers with the same base because they eventually get canceled out when written in expanded form.
Step-by-step explanation:
For example, if we expand the given fractions:
10^3/10^1 = 1000/10 = 100 = 10^2
Now, if we subtract the exponents we get the same result.
10^3-1 = 10^2
So, a^m/a^n = a^m-
n is one of the exponent rules which saves time and makes calculation easier.
Step-by-step explanation:
volume = pi x radius² x height
okay so the cylinders diameter is 8 inches
diameter divided by 2 is radius so 8/2 = 4
so 3 times the radius will be 3x4 = 12
use the formula above and then you will get your answer
Answer:
4.24 km
Step-by-step explanation:
The x-component of the displacement after the turn is ...
d2·cos(θ) = (3.38 km)cos(65.3°) ≈ 1.41239 km
Adding this to the displacement before the turn, we have ...
x-component of displacement = 2.83 km + 1.41 km = 4.24 km
We need to convert this equation to slope-intercept form first.
We can do that by solving for y.
x - 5y = 15
<em><u>Add 5y to both sides.</u></em>
x = 5y + 15
<em><u>Subtract 15 from both sides.</u></em>
x - 15 = 5y
<em><u>Divide both sides by 5.</u></em>
y = 1/5x - 3
We now know the slope is 1/5.
The slope of the line perpendicular to the line with a slope of 1/5 is -5.
The slope of a perpendicular line is the negative reciprocal of the original slope.
Using a graphing calculator, we know the y-intercept of the line that is perpendicular to the original line must have a y-intercept of -6 to run through the points (-2, 5).
The equation of the new line is y = -5x - 6.
Since ABCD is a parallelogram, the opposite sides will be parallel and equal,
Consider that AC acts as a transversal to the parallel lines AB and CD, so we can write,
So by the ASA criteria, the triangle AED is congruent to the triangle CEB,
Then the corresponding parts of the triangles will be equal,
Hence Proved.
