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3 years ago

Match the system of equations on the left with the number of solutions on the right

Mathematics

1 answer:

erastova [34]3 years ago

6 0

Answer:

top to bottom, the answers are b, c, a

Step-by-step explanation:

One way to find the solution to a system of equations is to substitute values in. For the first one,

y=2x+3

y=2x+5,

we can substitute 2x+3 =y into the second equation to get

y=2x+5

2x+3 = 2x+5

subtract 2x from both sides

3 = 5

As 3 is not equal to 5, this is never equal and therefore has no solution

For the second one,

y= 2x+7

y = (-2/3)x + 10

We can plug y=2x+7 into the second equation to get

2x + 7 = y = (-2/3)x + 10

2x + 7 = (-2/3)x + 10

add (2/3)x to both sides to make all x values on one side

2x + (2/3)x + 7 = 10

subtract 7 from both sides to make only x values on one side and only constants on the other

2x + (2/3)x = 3

(6/3)x + (2/3)x = 3

(8/3)x = 3

multiply both sides by 3 to remove a denominator

8x = 9

divide both sides by 8 to isolate x

x=9/8

There is only one value for when the equations are equal, so this has one solution

For the third one

y = x-5

2y = 2x - 10

Plug x-5 = y into the second equation

2 * y= 2*(x-5)

2 * (x-5) = 2x - 10

2x-10 = 2x-10

add 10 to both sides

2x=2x

As 2x is always equal to 2x, no matter what x is, there are infinitely many solutions for this system

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2,000 water bottles are being labeled and boxed. Each box holds 6 water bottles. How many bottles will be left over?

kap26 [50]

We just have to divide 2,000 by 6
lets do the math:)
2,000 ÷ 6 = 333.333333333
So if we round this it becomes 2
<span>So your answer is B.) 2 </span>

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3 years ago

1.What is the true density of water?

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A common unit of measurement for water's density is gram per milliliter (1 g/ml) or 1 gram per cubic centimeter (1 g/cm3). Actually, the exact density of water is not really 1 g/ml, but rather a bit less (very, very little less), at 0.9998395 g/ml at 4.0° Celsius (39.2° Fahrenheit).
Water density changes with temperature and salinity. Density is measured as mass (g) per unit of volume (cm³). Water is densest at 3.98°C and is least dense at 0°C (freezing point). Water density changes with temperature and salinity.
When water is a liquid, the water molecules are packed relatively close together but can slide past each other and move around freely (as stated earlier, that makes it a liquid). Pure water has a density of 1.000 g/cm3 at 4˚ C. As the temperature increases or decreases from 4˚ C, the density of water decreases.

Step-by-step explanation:

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