Two ways:
1) guess factors(trial and error)
2) use quadratic formula.
If you use this method then a = -3, b = -6 and c = -1
x = -b +/- [sqrt(b^2 -4ac)/2a]
substituting a, b, and c into our equation we get:
x = - (-6)+/- [sqrt ((-6)^2) - 4(-3)(-1))/2 (-3)]
x = + 6 +/- [sqrt (36 -4 (3)/-6)] if I didnt make a mistake in my signs
x = + 6 +/- [sqrt (36 -12)/-6)]
x = 6 +/- [sqrt (24)/-6] but sqrt 6 x sqrt of 4 = sqrt 24 hence
x = 6 +/- [ sqrt 6 x sqrt 4 /-6] that is:
x = 6 +/- [sqrt 6 x 2 /-6 ]
so x = 6 + [sqrt 6 x 2/-6] and x = 6 - [sqrt 6 x 2/-6]
Answer: Represents when the equation is at 5 gallons of water 1.5 pounds of salt is needed to have the correct salinity
Step-by-step explanation:
800 + 16x = 720 + 21x. Cancel out the 720 to get 80 + 16x = 21x. Subtract 16x from both sides to get 80 = 5x. Divide by 5 to get 16 = x, or x = 16. 16 hours. The charge is 800 + 16(16), = 720 + 21(16) which = 800 + 256 = 720 + 336 which = 1,056 = 1,056. Hope this helped!
USING PYTHAGORAS THEORAM,
x²+3²= 5²
x²+9= 25
x²= 25-9 = 16
x= √16
x= 4
OPTION D
Answer:
-10
-5
5
Step-by-step explanation:
From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250
The Remainder Theorem is going to take a bit to solve.
You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.
The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.
However just to get the roots, the graph shows that
x = -10
x = - 5
x = 5
The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give
f((10) = 10^3 + 10*10^2 - 25*10 - 250
f(10) = 1000 + 1000 - 250 - 250
f(10) = 2000 - 500
f(10) = 1500 which is not 0.
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f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250
f(1) = 1 + 10 - 25 - 250
f(1) = -264 which again is not zero