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Answer: choice 4. f(x) and g(x) have a common x-intercept</h3>
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Explanation:
For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.
The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.
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Side notes:
- Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
- Choice 2 is not true. Point B is not on the parabola.
- Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.
So u have to rearrange to find x again
You look at the equation and u can see that if u take away 14 from both sides it will leave u with:
X/-3<-2
Now as x is over - 3, the opposite of divide is multiply, so you multiply both sides by - 3.
This leaves you with your answer:
x<6
So the number line which represents this is C.
Let b>a,
a+b=40 so we can say a=40-b
We are told that b-a=6.5, using a found above in the equation gives us:
b-(40-b)=6.5
b-40+b=6.5
2b-40=6.5
2b=46.5
b=23.25, and since a=40-b
a=40-23.25
a=16.75
So a=16.75 and b=23.25
check...
16.75+23.25=40, 40=40
23.25-16.75=6.5, 6.5=6.5
Answer:
- A) x > 3 and x < 2 has no solutions
Step-by-step explanation:
Given inequalities below and we are looking for a pair with no solution.
Let's verify:
A) x > 3 and x < 2,
- It has no solutions since the two inequalities have no common interval.
B) x > - 3 and x < - 2,
- Its solution is -3 < x < - 2, the interval between two given endpoints.
C) x > - 3 and x < 2,
- Similar to option B, the interval is between two endpoints:
D) x > - 3 and x > - 2,
- Its solution is x > - 2, the two inequalities cover almost same interval.
Answer:
Step-by-step explanation:
