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Shtirlitz [24]
3 years ago
10

Ariana has a dimes and y nickels. She has at most 12 coins worth a minimum of

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
7 0

Answer:

Solution graph is attached in the answer area.

And one possible solution is (9, 2).

9 number of dimes and 2 number of nickels.

Step-by-step explanation:

Given that:

Number of dimes = a

Number of nickels = y

Total number of coins are at most 12 OR total number of coins are lesser than or equal to 12.

i.e. the inequality can be written as:

a+y \leq 12 ...... (1)

One dime is worth 10 cents or $0.10.

a number of dimes are worth $0.10a.

One nickel is worth 5 cents or $0.05.

y number of nickels are worth $0.05y.

Second inequality can be written as:

0.10a + 0.05 \ge 0.85

OR

2a+y\ge17 ...... (2)

a \ge 0, y \ge 0 ...... (3)

When we graphically represent the inequalities, the graph attached in the answer area represents the answer.

One solution is <em>(9, 2)</em>.

9 number of dimes and 2 number of nickels.

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<h2>Answer and Explanation to questions 13,14,15</h2>

13) \mathbf{\overline{XY}\cong\overline{CD}}        as given in the question.

14) \mathbf{\overline{XY}\cong\overline{YZ}}          Since Y is the midpoint of XZ. So, Y will divide XZ in equal halves into XY and YZ.

15) \mathbf{\overline{CD}\cong\overline{YZ}}

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<h2>Answer and Explanation to questions 16,17,18</h2>

∠3 is supplementary to ∠1 means: ∠3 + ∠1 = 180°

And, according to figure ∠1 + ∠2 = 180° as ∠1 and ∠2 form a straight line.

∠3 + ∠1 = 180°    .............(i)

∠1 + ∠2 = 180°    .............(ii)

subtracting equation (i) and (ii) will give ∠3 = ∠2   ..........(iii)

15) ∠3 is supplementary to ∠1                        as given in the question

16) ∠2 is supplementary to ∠1                        as shown be equation (ii)

18) ∠3 ≅ ∠2                                                      as shown by equation (iii)

<h2>Answer and Explanation to questions 19</h2>

∠3 and ∠4 form a straight line. Therefore, ∠3 + ∠4 = 180°   .......(i)

∠4 and ∠5 form a straight line. Therefore, ∠4 + ∠5 = 180°   .......(ii)

subtracting equation (i) and (ii)

∠3 + ∠4 - (∠4 + ∠5) = 180°-(180°)

∠3 + ∠4 - ∠4 - ∠5 = 180°-180°

∠3 - ∠5 = 0

∴ ∠3 = ∠5     (Hence Proved)

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