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inessss [21]
3 years ago
8

Add 0.5 kg, 50 mg, and 2.5 dg. Reduce the result to grams.

Mathematics
1 answer:
vredina [299]3 years ago
8 0

Answer:

0.25g + 0.05g + 500g = 500.30g

Step-by-step explanation:

The first step is converting everything to grams, by rules of three. Then we add.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

First step: 0.5kg to g

Each kg has 1000g. So

1kg - 1000g

0.5kg - xg

x = 1000*0.5

x = 500g

0.5kg = 500g

Second step: 50mg to g

Each g has 1000mg. So:

1g - 1000mg

xg - 50mg

1000x = 50

x = \frac{50}{1000}

x = 0.05g

50mg = 0.05g

Third step: 2.5dg to g

Each g has 10dg. So:

1g - 10dg

xg - 2.5dg

2.5x = 10

x = \frac{2.5}{10}

x = 0.25g

2.5 dg = 0.25g

Final step: Add

0.25g + 0.05g + 500g = 500.30g

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Let "a" and "s" represent the costs of advance and same-day tickets, respectively. Your problem statement gives you two relations.
.. a + s = 35 . . . . . the combined cost of one of each is 35
.. 15a +40s = 900 . . total paid for this combination of tickets was 900

There are many ways to solve these equations. You've probably been introduced to "substitution" and "elimination" (or "addition"). Using substitution for "a", we have
.. a = 35 -s
.. 15(35 -s) +40s = 900 . . substitute for "a"
.. 25s +525 = 900 . . . . . . . simplify
.. 25s = 375 . . . . . . . . . . . .subtract 525
.. s = 15 . . . . . . . . . . . . . . .divide by 25
Then
.. a = 35 -15 = 20

The price of an advance ticket was 20.
The price of a same-day ticket was 15.
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3 years ago
Use the change of variables s=x+3y, t=y to find the area of the ellipse x2+6xy+10y2≤1.
MArishka [77]

t=y\implies s=x+3t\implies x=s-3t

Then

x^2+6xy+10y^2=(s-3t)^2+6(s-3t)t+10t^2=s^2+t^2\le1

which is a disk of radius 1, hence with area \pi.

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Mark incorrectly evaluated the expression 4x+12-x to the power of 2 where is x-2. Identify and correct mark’s mistake.
nirvana33 [79]

Answer:

The value of 4x+12-x^2 is 16.

Step-by-step explanation:

The given expression is 4x+12-x^2\ at\ x=2.

Put x = 2 in the above expression as follows :

4x+12-x^2=4(2)+12-(2)^2\\\\=8+12-4\\\\=16

Hence, the final answer is 16.

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1) (19,-16).(-7, -15)
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Answer:

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Step-by-step explanation:

4 0
2 years ago
PLZ HELP ill GIVE BRAINIESt!!!!20 Points
shepuryov [24]
She made her mistake at the first step. To simplify a radical, you would find two numbers that multiply by each other to get your original number (under the radical) and have one of the number be a perfect square.

Her reasoning is wrong because 10*10 is not \sqrt{50}. Had she been correct, her answer should have been able to be squared to equal \sqrt{50}

In other words, she should have done \sqrt{25*2}= \sqrt{25} * \sqrt{2}=5 \sqrt{2}
(We used 25 because 25 is a perfect square, 5*5=25).

:)
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