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tekilochka [14]
3 years ago
11

A. how many numbers must be selected from the set1, 3, 5, 7, 9, 11, 13, 15 to guarantee that at least one pair of these numbers

add up to 16?
Mathematics
2 answers:
VMariaS [17]3 years ago
8 0

We have been given a data set 1, 3, 5, 7, 9, 11, 13, 15 and we are asked how many numbers must be selected from the set to guarantee that at least one pair of these numbers add up to 16.

Now let us find such numbers from the data set who add up to 16. These numbers are (15,1), (7,9), (13,3) and (11,5).

We can see that 15 and 1 add up to 16, but we can not say that if we choose 2 numbers from our data they will add up to 16. Because if we choose last two numbers or starting two numbers of our given data set it will be false.

If we choose 3 numbers from our data it is not certain that at least one pair add up to 16. So is the case with choosing four numbers.

Now we have to choose such numbers which will certainly add up to 16.

We can see if we choose 5 numbers from our data at least one pair will add up to 16. Either these are initial 5 numbers from our data set or last 5 numbers of our data set.

Therefore, we can guarantee that if we choose 5 numbers from our data set at least one pair will add up to 16.

ki77a [65]3 years ago
4 0
Asked and answered elsewhere.
brainly.com/question/9518737
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A. It is not possible to determine if the triangles are congruent
kirill [66]

Answer:

C. ∆ABD ≅ ∆CBD by the SSS Postulate

Step-by-step explanation:

We can prove that ∆ABD and ∆CBD congruent by the SSS Postulate.

The SSS postulate states that of three sides in one triangle are congruent to three corresponding sides in another, therefore, the two triangles are congruent.

From the diagram shown,

AB ≅ CB,

AD ≅ CD

BD = BD

We have three sides in ∆ABD that are congruent to three corresponding sides in ∆CBD.

Therefore, ∆ABD ≅ ∆CBD by the SSS Postulate

4 0
3 years ago
Use the drop-down menus to complete each equation so the statement about its solution is true.
tino4ka555 [31]

Answer:

No solutions: 7−5+3x−1= 3x + 7

One solution: 7−5+3x−1= 2x + 4

Infinitely Many Solutions  7−5+3x−1= 3x + 1

Step-by-step explanation:

No solutions means it results in no x and a false statement like 3 = 0.

One solution means it results in x = a number.

Infinite solutions means its results in no x and in a true statement like 3=3.

  • So to get No solutions: 7−5+3x−1= 3x + 7

This will eliminate the x and result in 1 = 7 which is false.

  • One solution: 7−5+3x−1= 2x + 4

This will result in x= 3

  • Infinitely Many Solutions  7−5+3x−1= 3x + 1

This will eliminate the x and result in 1 = 1 which is true.

7 0
3 years ago
Find the product 6x500=6x blank hundreds
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500? If you're trying to find x...
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Assume each figure shown has the same orientation. Which figure is the image of square LMNP after a translation of (x, y) → (x +
creativ13 [48]

<u>Answer-</u>

Figure 4 is the image of square LMNP after a translation of (x, y) → (x + 5, y – 3)

<u>Solution-</u>

The co-ordinates of the vertices are,

L = (-3, 1)

M = (-1, 1)

N = (-1, -1)

P = (-3, -1)

A translation of (x, y) → (x + 5, y – 3) means, the point must be shifted 5 units right and then 3 units down.

After the transformation the new co-ordinates will be,

L = (-3+5, 1-3) = (2, -2)

M = (-1+5, 1-3) = (4, -2)

N = (-1+5, -1-3) = (4, -4)

P = (-3+5, -1-3) = (2, -4)

These are the co-ordinates of the figure no. 4

6 0
3 years ago
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