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3 years ago

2/3 of the sum of three times a number and six is 10. what is the number?

Mathematics

2 answers:

sammy [17]3 years ago

7 0

Answer:

x=3

Step-by-step explanation:

Write the equation first, 2/3(3x+6)=10

Distribute 2, 2(3x+6)/2

Which equals 6x+12/3=10

Then multiply 3 from both sides 6x+12=30

Subtract 12

6x=18

Divide 6 from both sides

x=3

mestny [16]3 years ago

3 0

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the number. The problem statement tells you ...

2/3(3x +6) = 10

2x +4 = 10 . . . . . . use the distributive property

x +2 = 5 . . . . . . . . divide by 2

x = 3 . . . . . . . . . . .subtract 3

The number is 3.

<em>Comment on the solution</em>

The above shows an "alternative" solution method. The more usual way this might be done is ...

2(3x +6) = 30 . . . . . multiply by 3 to clear fractions

6x +12 = 30 . . . . . . . eliminate parentheses

6x = 18 . . . . . . . . . . . subtract 12

x = 3 . . . . . . . . . . . . divide by 6

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3 years ago

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GREYUIT [131]

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4) reflexive property of congruence

5) SAS theorem

6) property of Congruent triangles

Step-by-step explanation:

Given:

In ΔXYZ, line YW ⊥ XZ

Also XW≅ZW

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4) by reflexive property of congruence that states that any line,object or figure is congruent to itself

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3 years ago

What is the conversion?

Gelneren [198K]

Answer:

see below

Step-by-step explanation:

The conversion factor in the box is the product ...

$\dfrac{1\,\text{kPa}}{1000\,\text{Pa}}\cdot\left(\dfrac{1\,\text{m}}{100\,\text{cm}}\right)^3=10^{-9}\,\dfrac{\text{kPa m}^3}{\text{Pa cm}^3}$

_____

The purpose of a conversion factor is to multiply by 1 in the form of a ratio that changes the units. We know that 1000 Pa = 1 kPa, so the ratio (1 kPa)/(1000 Pa) is the ratio of two equal quantities. It has the value 1 and will change units from Pa to kPa.

Likewise, 100 cm = 1 m, so (1 m)/(100 cm) will change the units from cm to m. However the given expression uses cm³, so we need to multiply by the conversion factor 3 times. That factor is ((1 m)/(100 cm))³ = (1 m³)/(10⁶ cm³).

To choose the appropriate conversion factor, look at the units you have (Pa, cm) and the units you want (kPa, m). Find the relationship these have to each other, and write the ratio so that it will cancel the units you have and leave the units you want.

When SI units are involved the prefixes help you out. k = kilo = 1000; c = centi = 1/100. It is worthwhile to get to know them.

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