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2 years ago

Quadrilateral ABCD has vertices A(1, -3) , B(2, 1), C(6, 3), and D(7, -1). Prove or disprove that the Quad ABCD is a rectangle.

1 answer:

7 0

If AC=BD, than Quad ABCD is a rectangle
AC
√(3+3)²+(6-1)²
√6²+5²
√36+25
√61
BD
√(1+1)²+(2-7)²
√2²+(-5)²
√4+25
√29
Quad ABCD is not a rectangle because √61 and √29 are not equal.

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Suppose you are running a racing tournament with 12 horses. All eligible horses run in the race at once, and after the first rac

borishaifa [10]

Answer:

a) 66

b) 45

Step-by-step explanation:

We have 12 horses and after the first race 2 of them have to be eliminated

that condition is equal to consider that 10 horses will be available for the second race.

The number of possiblities we have for the first race is the combination of 12 horses in group of 10

C¹²₁₀ = 12!/ (2!)* (12-2)! = 12*11/2 = 66

For the second race

C¹⁰₈ = 10! / 8! * (10-8)! = 10*9/ 2 = 45

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2 years ago

What is the value of tan(60°)?

Scorpion4ik [409]

Answer:

The exact value of tan(60°) is √(3).

Step-by-step explanation:

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3 years ago

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What is the smallest whole number that can be multiplied by 300 such that the product is a perfect cube?

Neko [114]

300=2×2×5×5×3

We observe that 2 and 5 are grouped in pairs and the 3 is left unpaired.

If we multiply 300 by the factor 3 then

300×3=2×2×5×5×3×3

900=2×2×5×5×3×3 which is a perfect square.

∴ Required number is 3

root of 900 =30

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3 years ago

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FIND 2 EQUIVALENT FORMS FOR EACH FRACTION USING MULTIPLICATION AND DIVISION. 8/12,6/8,9/15,2/16

Alja [10]

8/12: 2/3 and 16/24
6/8: 3/4 and 12/16
9/15: 3/5 and 18/30
2/16: 1/8 and 4/32

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3 years ago

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A toy box contains eight green balls and four purple balls. Suppose you choose a ball at random and then replace it by putting i

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Answer: C. $\dfrac{1}{3}$

Step-by-step explanation:

Given: Box contains 8 green balls and 4 purple balls.

Total balls = 8+4 = 12

event 1 = first picking green ball

event 2 = second picking purple balls.

As first ball was replaced, that means both events are independent.

Probability that you have selected a green ball and then a purple ball = P(purple ball )

Formula for probability = $\dfrac{\text{favorable outcomes}}{\text{total outcomes}}$

Probability of selecting a purple ball (second pick)= $\dfrac{4}{12}$

$=\dfrac{1}{3}$

The required probability $=\dfrac{1}{3}$ , so C is correct option.

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3 years ago