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tamaranim1 [39]
3 years ago
8

Sam has $3.30 in quarters and dimes, and the total number of coins is 18. How many quarters and how many dimes?

Mathematics
1 answer:
zhuklara [117]3 years ago
4 0

Answer:

Quarters: 10

Dimes: 8

Step-by-step explanation:

Constraints

value: 0.25q + 0.10d = 3.30

count: q + d = 18

q = 18 - d

0.25(18-d) + 0.10d = 3.30

4.50-0.25d+0.10d = 3.30

4.50-0.15d = 3.30

-0.15d = -1.20

d = 8

q + d = 18

q + 8 = 18

q = 10

Check:

0.25(10) + 0.10(8) = 3.30

2.5+ 0.80 = 3.30

3.30 = 3.30

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Solve for x in IJK Algebra
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Answer:

x = 60

Step-by-step explanation:

The sum of the angles in a triangle is 180

40 + x+20 + x = 180

Combine like terms

2x+60 =180

Subtract 60 from each side

2x+60-60 =180-60

2x =120

Divide by 2

2x/2 =120/2

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5 0
3 years ago
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If a worker can do his job in 5 hours, and a student can do the same job in 8 hours, what part of the work is left to finish aft
Aleks [24]

Answer:

Part of work left to finish after two work hours is 7/20

Step-by-step explanation:

Firstly, we need to calculate their joint work rate

That will be;

1/(1/5 + 1/8) = 1/(13/40) = 40/13

This means that they will complete the task in 40/13 hours

1 whole part takes 40/13

x part will take 2 hours

x * 40/13 = 2

40x = 26

x = 26/40

So the part that will be completed in two hours is 26/40

This means that the part left to complete will be:

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8 0
3 years ago
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20 POINTS HELPPPPP
kiruha [24]

For this case we have the following expression:

\frac {216 ^ {n-2}} {(\frac {1} {36}) ^ {3n}} = 216

We multiply both sides by: (\frac {1} {36}) ^ {3n}

216 ^ {n-2} = 216 * (\frac {1} {36}) ^ {3n}

We divide both sides by 216:

\frac {216 ^ {n-2}} {216} = (\frac {1} {36}) ^ {3n}

To divide powers of the same base, we place the same base and subtract the exponents:

216 ^ {n-2-1} = (\frac {1} {36}) ^ {3n}\\216 ^ {n-3} = (\frac {1} {36}) ^ {3n}

Rewriting:

(6 ^ 3) ^ {n-3} = (\frac {1} {6 ^ 2}) ^ {3n}\\6 ^ {3n-9} = \frac {1} {6 ^ {6n}}\\6^{ 3n-9} * 6^{ 6n} = 1

To multiply powers of the same base, we place the same base and add the exponents:

6^{ 3n-9 + 6n} = 1\\6^{ 9n-9} = 1

We know that any number raised to zero is 1, a ^ 0 = 1.

So, for equality to be true:

9n-9 = 0\\9n = 9\\n = \frac {9} {9}\\n = 1

Answer:

n = 1

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3 years ago
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anyanavicka [17]

Answer:

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