Differentiate both sides with respect to time :
We're given that at the moment , so that
units per second (D).
Answer:
Emilias inequality, x<6 is correct because the number of hours is less than it equal to 6. Emilias number line is correct. The endpoint is correctly filled in and the number line should be shaded to the left of the endpoint.
First denominator -- x
<span>first numerator ---- x-2 </span>
<span>new denominator -- x+3 </span>
<span>new numerator ---- x+1 </span>
<span>(x-2)/x + 3/20 = (x+1)/(x+3) </span>
<span>times 20x(x+3) , the LCD </span>
<span>20(x+3)(x+1) + 3x(x+3) = 20x(x+1) </span>
<span>expanding and simplifying gave me </span>
<span>x^2 + 3x - 40 = 0 </span>
<span>(x-5)(x+8) = 0 </span>
<span>x = 5 or x=-8 </span>
<span>if x=5, the original fraction was 3/5 </span>
<span>if x=-8 the original fraction was -10/-8 or 5/4 </span>
<span>check for 3/5 , new fraction would be 6/8 or 3/4 </span>
<span>3/5 + 3/20 = 12/20 + 3/20 = 15/20 = 3/4 </span>
<span>but for 5/4, new fraction would be 8/7 </span>
<span>5/4 + 3/20 = 28/20 = 7/5 ≠ 8/7 </span>
<span>BUT, if we take the unsimplified fraction -10/-8 , new fraction would be -7/-5 = 7/5 </span>
<span>So the original fraction would be 3/5 for sure, but </span>
<span>also the unsimplified fraction -10/-8</span>
Step-by-step explanation:
b = 11
c = 11✓2 because the properties of 45 45 90 triangle
The equation of a straight line in "standard form" resembles Ax + By + C = 0.
Starting with y − 3 = 1/3(x − 6) (which is the equation of a line in point-slope form), remove the fractional coefficient 1/3 by multiplying both sides of this equation by 3:
3y - 9 = x - 6.
We want all terms except for 0 to appear on one side of this equation. Subtract 3y from both sides, obtaining:
-9 = 1x - 3y - 6
Finally, add 9 to both sides, obtaining:
0 = 1x - 3y + 3
This result has the form Ax + By + C = 0, and is thus in standard form.