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Elodia [21]
2 years ago
13

Lamar is solving the equation x2−12x=−6 by completing the square. Which shows Lamar's next step and the solution to the equation

?
Step 1: x^2 - 12x = -6

Step 2: x^2 - 12x + 36= -6 + 36
Mathematics
1 answer:
Levart [38]2 years ago
4 0
Completing the square is a process to find the solutions, or the x-values, to a quadratic equation. This method can only work if it is in the format: x^2 + bx = c
In this equation, the b value is -12 and the c value is -6. The process for completing the square goes like this:

x^2 + bx + (b/2)^2 = c + (b/2)^2

Now let’s solve the equation above using this method.

Step 1: x^2 - 12x + (-12/2)^2 = -6 + (-12/2)^2

Step 2: x^2 - 12x + (-6)^2 = -6 + (-6)^2

Step 3: x^2 - 12x + 36 = -6 + 36

Step 4: x^2 - 12x + 36 = 30

Now, to factor it. After doing the process until now, the left side of the equation can ALWAYS be in the format: (x + a)^2

Step 5: x^2 - 12x + 36 can be factored in this format as (x - 6)^2

Step 6: (x - 6)^2 = 30

Step 7: x - 6 = √30

Step 8: x = 6 ±√30

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Answer:

The probability that no more than more than 11 of them need correction for their eyesight is 0.00512

No, 11 is not a significantly low low number of adults requiring eyesight​ correction .

Step-by-step explanation:

A survey showed that 77​% of adults need correction for their eyesight.

If 22 adults are randomly​ selected, find the probability that no more than more than 11 of them need correction for their eyesight.

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p = 0.77

q = 1-p = 1- 0.77=0.23

We are supposed to find P(x\leq 11)

P(x\leq 11)=P(x=1)+P(x=2)+P(x=3)+.....+P(x=11)

Formula : P(x=r)=^nC_r p^r q^{n-r}

P(x\leq 11)=^{22}C_1 (0.77)^1 (0.23)^{22-1}+^{22}C_2 (0.77)^2 (0.23)^{22-2}+^{22}C_3 (0.77)^1 (0.23)^{22-3}+.....+^{22}C_{11} (0.77)^1 (0.23)^{22-11}

Using calculator

P(x\leq 11)=0.00512

So, The probability that no more than more than 11 of them need correction for their eyesight is 0.00512

No, 11 is not a significantly low low number of adults requiring eyesight​ correction .

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