Mathematics, 24.08.2020 21:01 SebiZ3240

jonalyn has five discs, each with a different counting numbers printed on one face. however , she lost three discs and all she can remember is that the sum of the five numbers is 50 and the number in the two remaining discs are 12 and 9. 1. what is the greatest possible value of one of the numbers? 2. what can be the possible values of the three other numbers?

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Answer from: jadawada223

Using a system of equations, it is found that:

The greatest possible value of one of the numbers is 26.The possible values are all values of x,y and z different of 12 and 9 such that:

x + y + z = 29

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There are 5 distinct numbers, with a sum of 50, thus they are:

x + y + z + t + w = 50

Two of them are 12 and 9, thus t = 9, w = 12

, and:

x + y + z + 9 + 12 = 50

x + y + z + 21 = 50

x + y + z = 29

The greatest possible value of one of the numbers is 26, as then one would be 2 and the other 1, having five distinct numbers.The possible values are all values of x,y and z different of 12 and 9 such that:

x + y + z = 29

A similar problem is given at link

Answer from: Tiff7859

(1) 26 (2) 1, 3, 25

Step-by-step explanation:

Let a, b, and c represent the three discs.

a + b + c + 12 + 9 = 50

a + b + c = 29

1) Since a, b, and c are all different numbers then the one possibility is:

a = 1, b = 2, --> c = 26

2) There are many different possibilities for creating a sum of three numbers whose total is 29.

One example is provided above in #1.

Here are few other examples:

1, 3, 25 2, 3, 24 3, 4, 19 4, 5, 20

1, 4, 24 2, 4, 23 3, 5, 18 4, 6, 19

1, 5, 23 2, 5, 22 3, 6, 17 4, 7, 18

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

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step-by-step explanation:

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