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2 years ago

What is the most precise name for quadrilateral ABCD with vertices A(-2, -2), B(-2, 0), C(1, 0), and D(1, -2)

Mathematics

2 answers:

True [87]2 years ago

8 0

D.Trapezoid is the answer

Ad libitum [116K]2 years ago

7 0

Answer: The correct option is (D) Trapezoid.

Step-by-step explanation: Given that the co-ordinates of the vertices of quadrilateral ABCD are A(-2, -2), B(-2, 0), C(1, 0), and D(1, -2).

We are to select the most precise name of the quadrilateral ABCD from the given options.

The lengths of the sides of the quadrilateral ABCD are calculated using distance formula as follows:

$AB=\sqrt{(-2+2)^2+(-2-0)^2}=\sqrt{0+4}=2~\textup{units},\\\\BC=\sqrt{(-2-1)^2+(0-0)^2}=\sqrt{9+0}=3~\textup{units},\\\\CD=\sqrt{(1-1)^2+(0+2)^2}=\sqrt{0+4}=2~\textup{units},\\\\DA=\sqrt{(1+2)^2+(-2+2)^2}=\sqrt{9+0}=3~\textup{units}.$

The slopes of the sides are calculated as follows:

$\textup{slope of AB, }m=\dfrac{0+2}{-2+2}=\textup{cannot be determined},\\\\\textup{slope of BC, }n=\dfrac{0-0}{1+2}=0,\\\\\textup{slope of CD, }o=\dfrac{-2-0}{1-1}=\textup{cannot be determined},\\\\\textup{slope of DA, }p=\dfrac{-2+2}{-2-1}=0.$

Since, AB = CD, AD = BC and slope of BC (n) = slope of DA (p), so we have

the opposite sides are congruent and one pair of opposite sides are parallel.

Therefore, the most precise name for the quadrilateral ABCD is a TRAPEZOID.

Thus, (D) is the correct option.

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3 years ago

Read 2 more answers

Which choice is equivalent to the quotient below?

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None of the choices are equivalent
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a is 4
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2 years ago

A report on consumer financial literacy summarized data from a representative sample of 1,664 adult Americans. Based on data fro

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Answer:

a. The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.

b. Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Sample of 1,664 adult Americans, 939 people in the sample would have given themselves a grade of A or B in personal finance.

This means that $n = 1664, \pi = \frac{939}{1664} = 0.5643$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 - 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.54$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 + 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.588$

The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.

(b) Is the confidence interval from part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of A or B?

Yes, because the confidence interval is entirely above 0.5.

Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

8 0

2 years ago

Solve F(x) for the given domain. F(x) = x² + 3x - 2 F(3)=____ a. 13 b. 16 C. 40

Llana [10]

Answer:

B. 16

Step-by-step explanation:

F(3) means we must plug the number "3" into the equation for each x.

(3)^2 + 3(3) -2

9 + 9 - 2

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2 years ago