13: multiply the amount by the tax rate (to make a percent a decimal move the decimal point 2 places to the left) and add the original amount and the taxed amount together. For 12 do above but then multiply the total by the tip rate and add together (basically the same as the tax again) :) I hope this helps
We are given the equation:
c = 500 + 1100 x – 100 x^2
Solve for x given the value of c = 2300
Rearrange and substitute:
- 100 x^2 + 1100 x + 500 = 2300
Divide everything by -100:
x^2 – 11 x – 5 = - 23
x^2 – 11 x = - 18
Completing the square:
(x – 11/2)^2 = - 18 + (11/2)^2
x – 11/2 = ±3.5
x = 2, 9
<span>So x is 2 or 9</span>
Answer is
Power of a Power Property . The last one
Answer:
hope it helps
Step-by-step explanation:
Let the speed of car starting from A=x km/hr and speed of car starting from B=y km/hr.The relative speed of A with respect to B when moving in the same direction =x−y km/hr.The relative speed of A with respect to B when moving in opposite direction =x+y km/hr.Distance between A and B=80 km.We know, Time=SpeedDistanceFrom the above information, we have,x−y80=8andx+y80=1+6020=34or,x−y80=8⇒10=x−y⇒x−y=10....(i)Also,x+y80=34⇒240=4(x+y)⇒x=60−y....(ii)Substituting (ii) in (i), we get,x−y=10⇒60−y−y=10⇒60−2y=10⇒2y=50⇒y=25Substituting y=25 in equation (ii), we get,x=60−y⇒x=60−25⇒x=35Thus, the speed of car starting from A=x=35 km/hr and speed of car starting from B=y=25 km/hr.
Answer: x = {-1, -3, 2}
<u>Step-by-step explanation:</u>
x³ + 2x² - 5x - 6 = 0
Use the rational root theorem to find the possible roots: ±1, ±2, ±3, ±6
Use Long division, Synthetic division, or plug them into the equation to see which root(s) work <em>(result in a remainder of zero)</em>.
I will use Synthetic division. Let's try x = 1
1 | 1 2 -5 -6
|<u> ↓ 1 3 -2 </u>
1 3 -2 -8 ← remainder ≠ 0 so x = 1 is NOT a root
Let's try x = -1
- 1 | 1 2 -5 -6
|<u> ↓ -1 -1 6 </u>
1 1 -6 0 ← remainder = 0 so x = -1 is a root!
The coefficients of the reduced polynomial are: 1, 1, -6 --> x² + x - 6
Factor: x² + x - 6
(x + 3)(x - 2)
Set those factors equal to zero to solve for x:
x + 3 = 0 --> x = -3
x - 2 = 0 --> x = 2
Using Synthetic Division and Factoring the reduced polynomial, we found
x = -1, -3, and 2