The answer is r=-3. You use the distributive property which is basically multiplying -8 with all the numbers inside the parenthesis. So -8 x r and -8 x -2. This results to -8r+16=40 (Two negative numbers multiplied together will form a positive number). We use inverse operations to subtract 16 from both sides. 16-16 is 0 and 40-16 is 24. So we are left with -8r=24. We want to be left with only r, so we once again use inverse operations to divide -8 from both sides. -8/-8 is 1, and 24/-8 is -3. So we end up with r=-3. Hope this helped :]
Answer:
The other side was decreased to approximately .89 times its original size, meaning it was reduced by approximately 11%
Step-by-step explanation:
We can start with the basic equation for the area of a rectangle:
l × w = a
And now express the changes described above as an equation, using "p" as the amount that the width is changed:
(l × 1.1) × (w × p) = a × .98
Now let's rearrange both of those equations to solve for a / l. Starting with the first and easiest:
w = a/l
now the second one:
1.1l × wp = 0.98a
wp = 0.98a / 1.1l
1.1 wp / 0.98 = a/l
Now with both of those equalling a/l, we can equate them:
1.1 wp / 0.98 = w
We can then divide both sides by w, eliminating it
1.1wp / 0.98w = w/w
1.1p / 0.98 = 1
And solve for p
1.1p = 0.98
p = 0.98 / 1.1
p ≈ 0.89
So the width is scaled by approximately 89%
We can double check that too. Let's multiply that by the scaled length and see if we get the two percent decrease:
.89 × 1.1 = 0.979
That should be 0.98, and we're close enough. That difference of 1/1000 is due to rounding the 0.98 / 1.1 to .89. The actual result of that fraction is 0.89090909... if we multiply that by 1.1, we get exactly .98.
Answer:
Step-by-step explanation:
we would like to figure out the derivative of the following:
to do so, let,
By simplifying we acquire:
use law of exponent which yields:
take derivative in both sides:
use sum derivation rule which yields:
By constant derivation we acquire:
use exponent rule of derivation which yields:
simplify exponent:
two negatives make positive so,
<h3>further simplification if needed:</h3>
by law of exponent we acquire:
simplify addition:
and we are done!
Answer:
no
Step-by-step explanation:
you would get this: 149054.555556
