Write an equation that you can use to solve for x

Mathematics

2 answers:

sasho [114]3 years ago

6 0

Both of the angles that have x and 47 degrees are supplementary. They are on the same line. Supplementary= 180

So,

x+47= 180

Subtract 47 on both sides.

x= 133

I hope this helps!
~kaikers

Zigmanuir [339]3 years ago

5 0

We can use the rule of adjacent angles on a straight line. This means that if the angles which are next to each other are on the same straight line, their sum would be equal to 180°.

So, to solve for x, we can write this equation:
x° = 180° - 47° (abbreviation: adj. ∠s on st. line)

in additional, the answer of x should be 133, note that you don't need to add a degree sign in it because the equation is written as x° instead of x.

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Answer: third option 268.8

Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s
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