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

9514 1404 393

  3

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.

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Comment on the solution

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

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).