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ad-work [718]
3 years ago
15

ABCD is a quadrilateral with A(8,21),B(10,27),C(26,26) and D(18,2). Determine whether ABCD is a trapizoid

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
5 0
<h2>Answer:</h2>

ABCD is a trapezoid

<h2>Step-by-step explanation:</h2>

<em>Given points of the quadrilateral:</em>

A(8,21),B(10,27),C(26,26) and D(18,2)

To show whether ABCD is a trapezoid, we find a pair of parallel sides in ABCD. If two of its sides are parallel to each other then ABCD is a trapezoid.

<em>Step 1:</em> With the given points, sketch a graph. The diagram is attached to this response.

<em>Step 2:</em> As shown in the diagram, the two sides that are likely to be parallel are AB and CD

If these two sides have same gradient/slope, then the quadrilateral is a trapezoid.

Now calculate the slopes of those sides using the slope formula;

m = \frac{y_2 - y_1}{x_2 - x_1}

<em>Calculate the slope of AB </em>(where x₁ = 8, y₁ = 21, x₂ = 10, y₂ = 27)

m(AB) = \frac{27-21}{10-8}

m(AB) = \frac{6}{2}

m(AB) = 3

<em>Calculate the slope of CD </em>(where x₁ = 26, y₁ = 26, x₂ = 18, y₂ = 2)

m(CD) = \frac{2-26}{18-26}

m(CD) = \frac{-24}{-8}

m(CD) = 3

Since the two slopes - m(AB) and m(CD) slopes are equal to 3, the quadrilateral ABCD is a trapezoid.

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To avoid detection at customs, a traveler has placed 6 narcotic tablets in an Urn containing 9 vitamin pills that are similar in
Alexus [3.1K]

Answer:

\frac{4}{91}

Step-by-step explanation:  

We are told that to avoid detection at customs, a traveler has placed 6 narcotic tablets in an Urn containing 9 vitamin pills that are similar in appearance.

To find the probability that the traveler will be arrested for illegal possession of narcotics we will use theoretical probability formula.

\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}

Favorable outcomes will be _{3}^{6}\textrm{C}.

\text{Favorable outcomes}=_{3}^{6}\textrm{C}=\frac{6!}{(6-3)!3!}

\text{Favorable outcomes}=\frac{6!}{3!3!}

\text{Favorable outcomes}=\frac{6\cdot 5\cdot 4\cdot3!}{3\cdot 2\cdot 1\cdot3!}

\text{Favorable outcomes}=\frac{6\cdot 5\cdot 4}{3\cdot 2}

\text{Favorable outcomes}=5\cdot 4=20

Now let us find number of possible outcomes.

\text{Number of possible outcomes}=_{3}^{15}\textrm{C}=\frac{15!}{(15-3)!3!}

\text{Number of possible outcomes}=\frac{15!}{12!3!}

\text{Number of possible outcomes}=\frac{15\cdot 14\cdot 13\cdot 12!}{12!\cdot 3\cdot 2\cdot 1}

\text{Number of possible outcomes}=\frac{15\cdot 14\cdot 13}{ 3\cdot 2\cdot 1}

\text{Number of possible outcomes}=5\cdot 7\cdot 13=455

Upon substituting our values in probability formula we will get,

\text{Probability that the traveler will be arrested for illegal possession of narcotics}=\frac{20}{455}

Upon dividing numerator and denominator by 5 we will get,

\text{Probability that the traveler will be arrested for illegal possession of narcotics}=\frac{4}{91}

Therefore, the probability that the traveler will be arrested for illegal possession of narcotics is \frac{4}{91}.  


6 0
3 years ago
What two numbers adds up 2 and multiplies -80
viva [34]
-8 and 10. 

The 8 has to be negative because otherwise the 2 would end up being negative, not positive.
7 0
3 years ago
a total of 10000 was invested in two business ventures A and B .at the of the first year A and B yielded returns of 6% and 23÷4
wolverine [178]

Answer:

(1)

compound amount = 802.5 $

invest earned = 52.5 $

Step-by-step explanation:

total amount = 10000 $

let amount x invested in ventures A and remaining (1000-x) on ventures B

now,

6x/100 +23/400(1000-x ) = 588.75

{24x+23(1000-x)}/400 =588.75

x=235500-230000

x=5500

Amount invested on A = 5500$

Amount invested on B = 4500$

(2)

principle=750$

time= 1 year

effective invest rate = 7%

a) compound amount = p(1+(r/w)^t

=750{1+(7/100)}^1

=802.5$

b) invest earned = 802.5-700 = 52.5$

3 0
3 years ago
Mr. Zelman wants to give 50% of his comic book collection to his nephew Alex. If Mr. Zelman has 800 comic books, then how many w
BARSIC [14]

Mr. Zelman gave 400 books to his nephew

<em><u>Solution:</u></em>

Given that, Mr. Zelman wants to give 50% of his comic book collection to his nephew Alex

Mr. Zelman has 800 comic books

Number of books with Zelman = 800

Mr. Zelman wants to give 50% of books to Alex

Number of books given to nephew = 50 % of books of Zelman

Therefore, we have to find 50 % of 800

\rightarrow 50 \% \text{ of } 800

\rightarrow 50 \% \times 800\\\\\rightarrow \frac{50}{100} \times 800 = 400

Thus he gave 400 books to his nephew

4 0
3 years ago
D 1. Given the number 47,135,280, what is the place value of the number "1"?
Anit [1.1K]

Answer:

one Hundred Thousand

Step-by-step explanation:

4 0
3 years ago
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