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hram777 [196]
3 years ago
9

Follow the process of completing the square to solve 2x^2 + 8x - 12 = 0. After adding B^2 to both sides of the equation in step

4, what is the constant on the right side of the equation?
1. -32
2. 112
3. 160
Mathematics
1 answer:
Flauer [41]3 years ago
8 0

For this case we have the following equation 2x ^ 2 + 8x-12 = 0

To complete squares we follow the steps below:

We divide between 2 on both sides of the equation:

x ^ 2 + 4x-6 = 0\\x ^ 2 + 4x = 6

We divide the term by 2 and square it. We add this to both sides of the equation:

x ^ 2 + 4x + (\frac {4} {2}) ^ 2 = 6 + (\frac {4} {2}) ^ 2\\x ^ 2 + 4x + (2) ^ 2 = 6 + 4\\x ^ 2 + 4x + (2) ^ 2 = 10\\(x + 2) ^ 2 = 10

ANswer:

(x + 2) ^ 2 = 10

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4. Assume that the chances of a basketball player hitting a 3-pointer shot is 0.4 and the probability of hitting a free-throw is
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0.0334 = 3.34% probability that the player will make exactly 3 3-pointers and 5-free throws.

Step-by-step explanation:

For each 3-pointer shot, there are only two possible outcomes. Either the player makes it, or the player does not. The same is valid for free throws. This means that both the number of 3-pointers and free throws made are given by binomial distributions.

Since 3-pointers and free throws are independent, first we find the probability of making exactly 3 3-pointers out of 10, then the probability of making exactly 5 free throws out of 10, and then the probability that the player will make exactly 3 3-pointers and 5-free throws is the multiplication of these probabilities.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Probability of making 3 3-pointers out of 10:

The chances of a basketball player hitting a 3-pointer shot is 0.4, which means that p = 0.4. So this is P(X = 3) when n = 10.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.21499

Probability of making 5 free throws out of 10:

The probability of hitting a free-throw is 0.65, which means that p = 0.65. The probability is P(X = 5) when n = 10.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{10,5}.(0.65)^{5}.(0.35)^{5} = 0.15357

Calculate the probability that the player will make exactly 3 3-pointers and 5-free throws.

0.21499*0.15537 = 0.0334

0.0334 = 3.34% probability that the player will make exactly 3 3-pointers and 5-free throws.

5 0
3 years ago
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