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3 years ago

3x^2 -5x -2=0

Mathematics

2 answers:

Kipish [7]3 years ago

6 0

Answer:

Step-by-step explanation:

1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)

Two numbers that work are -6 and +1

-6 x +1 = -6

-6 + -1 = -5

2. Split the middle term into the two numbers that you found.

3x^2 -6x +x -2 = 0

I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.

3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'

3x (x-2) +1 (x-2) = 0

4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.

(3x + 1) (x-2) = 0

5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.

3x + 1 = 0 x-2 = 0

3x = -1 x = 2

x = -1/3

6. The solutions to this equation are x = 2 and x = -1/3

Ronch [10]3 years ago

3 0

Answer:

Step-by-step explanation:

Start by separating (not factoring) -5x. For example, we might get {-2x, - 3x} (note how these combine to produce -5x). Might have to try several combinations to find the right one.

Then 3x^2 -5x -2=0 could possibly be x(3x - 2) - (3x - 2), or

x(3x - 2) - 1(3x - 2).

Notice how the factor (3x - 2) shows up twice. If we factor out (3x - 2) we are left with (x - 1). We check these results by multiplying (3x - 2) and (x - 1) together, so we can be sure that the result is the original 3x^2 -5x -2=0.

(3x - 2)(x - 1) = 3x^2 - 3x - 2x + 1 results in 3x^2 - 5x + 2. Unfortunately, the sign of that 2 is incorrect; we'd hoped for -2, not +2.

To check this further, I used synthetic division with 1 as divisor; the remainder is -4, which tells us that (x - 1) is not a factor of 3x^2 -5x -2=0.

Please double check to ensure that you have copied this problem down correctly.

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Answer:

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See explanation below.

Step-by-step explanation:

Part 1)

What is crucial to know is what is the time at which each zombie would reach Alice and Bob, and that is given by the quotient between the distance away each zombie is, divided by the zombie's speed:

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Then, it is this quotient for each zombie, that one has to estimate given the input values distance and speed, and it is the output "time" ( $t_i$ ) for each zombie, what we need to analyze so as to prioritize an order regarding which zombie to kill first.

Part 2)

Shooting the closest zombie first is not a good idea, since the speed of that closest zombie may be much slower than another zombie further away, but with much larger speed. Again, the important value to analyze is the time that it would take each zombie to reach Alice and Bob.

Part 3)

Shooting the fastest zombie first is not a good idea either, because that fastest zombie could be located very far away from the visitors, and other zombies closer by may reach them first.

Part 4)

The order that should be used to kill the zombies is given by the value of the time to reach Bob and Alice based on the quotient distance (di) over speed (si) explained in Part 1). The zombie that shows smallest time should be shot first, and then the others in increasing order of time value.

Part 5)

Notice that the individual zombie information is not presented in the question, but the student should be able to calculate the quotients for each zombie, and considering that there could be at most one shot every second, estimate the number of seconds that the time for each zombie in increasing order would allow until the addition of shooting time per second in the appropriate order cannot match the arrival time of the zombies that are left.

One should count number of seconds from the first shot (to the zombie with shortest arrival time), and then increase in one unit (one shot per second), to the following zombie with slightly larger arrival time), and so on, until the addition of seconds (one second per shot and per increasing arrival time of zombie) exceeds the next zombie arrival time.

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Vedmedyk [2.9K]

Answer:

The first option and the third option

Step-by-step explanation:

Since the figure moved 4 places down and 4 places to the right.

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