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taurus [48]
3 years ago
11

Show that it is not possible for the lengths of the

Mathematics
1 answer:
xeze [42]3 years ago
7 0
1. Check the picture below.

2. By the well known intersecting secants property: AO*OC=BO*OD

3. Since the segments are assumed to be consecutive integers, AO, OC cannot be the smaller, and neither can AO<BO and OC<OD. 
The only possibility is that the multiplication of the smallest to the largest is equal to the multiplication of the middle 2.

4. For example : 4*5=2*10, we must have 4>2 but 5<10

Here the ordering is 2<4<5<10, similarly assume BO<AO<CO<DO

5. since the segments are of consecutive integers length, let them be 

BO=n, AO=n+1, CO=n+2, DO=n+3

6. AO*CO=BO*DO

so n(n+3)=(n+1)(n+2)
     n^{2}+3n=  n^{2}+3n+3
     so 0=3 which makes no sense, so no solution with the assumed conditions.

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Marizza181 [45]
We are interested in selecting 2 people from the 7-person task force.

n = 7
r = 2

nPr = n! / (n-r)!

7!
------
(7-2)!

=
7!
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5!

7×6×5×4×3×2×1
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5×4×3×2×1

= 7×6

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5 0
3 years ago
Q4.
Levart [38]

Probabilities are used to determine the chances of an event

  • The probability of choosing a black counter is 0.6
  • The probability that both counters are white is 0.16

<h3>(a) Probability of selecting two blacks</h3>

The probability is given as:

P(Black\ n\ Black)=0.36

Apply probability formula

P(Black) \times P(Black)=0.36

Express as squares

P(Black)^2=0.36

Take the square root of both sides

P(Black)=0.6

Hence, the probability of choosing a black counter is 0.6

<h3>(b) Probability of selecting two white counters</h3>

In (a), we have:

P(Black)=0.6

Using the complement rule, we have:

P(White) = 1 - P(Black)

So, we have:

P(White) = 1 -0.6

Evaluate

P(White) = 0.4

The probability that both counters are white is then calculated as:

P(White\ and\ White) = P(White) \times P(White)

So, we have:

P(White\ and\ White) =0.4 \times 0.4

P(White\ and\ White) =0.16

Hence, the probability that both counters are white is 0.16

Read more about probabilities at:

brainly.com/question/15858152

6 0
2 years ago
What numbers make this expression undefined x^2+3/x^2-11x-12
marusya05 [52]

\frac{ {x}^{2}  + 3}{ {x}^{2}  - 11x - 12}

Because which numbers will make the expessions undefined. We will focus on the denominator only.

Factor the terms.

(x - 12)(x + 1)

Now which 2 numbers that will make these terms become 0?

12 and - 1 of course.

So these 2 numbers that will make the expressions undefined are 12 and - 1

5 0
2 years ago
Find the midpoint of AB A.(-2,-3) B.(16,4) C.(-2,-11) D.(4,-10)
zheka24 [161]

Answer:

(-2,-1)

Step-by-step explanation:

Using the graph find the coordinates for A and B.

A (-4,2) and B is (0,-4)

Midpoint formula is (x1 + x2)/2 , (y1+y2)/2

x value of the midpoint= (-4+0)/2 = -2

y value of the midpoint= (2 + -4)/2 = -2/2= -1

Midpoint is (-2, -1)

8 0
3 years ago
Create an item with a selling price over $100 a discount of 25% and tax is 9%
Lana71 [14]

First, convert the 25% to a real mathematical number. For percents, this is always done by dividing the 25% by 100%, or 25% / 100% = 0.250.

Second, find out what 25% of $100 is. This is the amount of the sale discount. This is always found by mulitplying 0.250 by the item's cost $100, like this:

0.250 x $100 = $25.00.

So for this sale, you'll save $25.00 on this item.

This means, the cost of the item to you is

$100 - $25.00 = $75.00.

Alternatively, you can think about it this way. The item is 25% off. This means you'll pay 75.000% of the total cost (100% - 25% = 75.000%).

Now what's 75.000% of the total cost?

0.750 x $100 = $75.00.

Just like the result above, the sale price on the item is $75.00.

Hope this helps you on your assignment! :)

5 0
3 years ago
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