What is the answer to the equation x^2-6x-16
1 answer:
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Problem 1
Since point P is the tangent point, this means angle OPT is a right angle
angle OPT = 90 degrees
Let's use the Pythagorean theorem to find the missing side 'a'
a^2 + b^2 = c^2
a^2 + 7^2 = 12^2
a^2 + 49 = 144
a^2 = 144 - 49
a^2 = 95
a = sqrt(95)
a = 9.7467943
a = 9.7
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Let's use the sine and arcsine rule to find angle y
sin(angle) = opposite/hypotenuse
sin(y) = 7/12
y = arcsin( 7/12 )
y = 35.6853347
y = 35.7
The value of y is approximate. Make sure your calculator is in degree mode. Arcsine is the same as inverse sine or
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Problem 2
Focus on triangle OHP. This may or may not be a right triangle. The goal is to test if it is or not.
We use the converse of the Pythagorean theorem to check.
Recall that the converse of the Pythagorean theorem says: If a^2+b^2 = c^2 is a true equation, then the triangle is a right triangle. The value of c is always the longest side. The order of a and b doesn't matter.
In this case we have
- a = 7
- b = 13
- c = 16
Which leads to
a^2 + b^2 = c^2
7^2 + 13^2 = 16^2
49 + 169 = 256
218 = 256
We get a false equation at the end, since both sides aren't the same number, which means the original equation is false.
We don't get a^2 + b^2 = c^2 to be true, therefore this triangle is not a right triangle.
Consequently, this means angle OPH cannot possible be 90 degrees (if it was then we'd have a right triangle). Therefore, point P is not a tangent point.
You follow the same basic idea for triangle OQH and show that point Q is not a tangent point either. Or you could use a symmetry argument to note that triangle OPH is a mirror reflection of triangle OQH over the line segment OH. This implies that whatever properties triangle OPH has, then triangle OQH has them as well for the corresponding pieces.
Answer:
a) The minimum sample size is 601.
b) The minimum sample size is 2401.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
For this problem, we have that:
We dont know the true proportion, so we use , which is when we are are going to need the largest sample size.
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)
This is n for which M = 0.04. So
Rounding up
The minimum sample size is 601.
b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.
Now we want n for which M = 0.02. So
The minimum sample size is 2401.
Answer:
7
Step-by-step explanation:
We want to evaluate the fraction below for x = 3. We will put the value of x to be 3:
The answer is 7.