The first step is to assign the decimal number to a variable.
For the repeating fraction 0.111_1, this would look like
.. x = 0.111_1 . . . . . . . . . . where we use an underscore to identify the following digit(s) as repeating
The next step is to multiply that value by 10 to a power equal to the number of repeating digits. If there is one repeating digit (as here), then you want (10^1)x = 10x.
.. 10x = 1.111_1
The third step is to subtract x from this.
.. 10x -x = 1.111_1 -0.111_1 = 1
.. 9x = 1
And the final step is to divide by the coefficient of x.
.. x = 1/9 . . . . . . this is the value of the repeating decimal fraction.
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Here's one that's a little more complicated. It is done the same way.
.. x = 3.254545_45
.. 100x = 325.454545_45
.. 100x -x = 99x = 322.2
.. x = 322.2/99 = 3222/990 = 179/55
Answers:
Lin's finish point is at 205 meters
Elena's velocity is 8.92 meters per second
Diego's finish point is at -259.2 meters or 259 meters behind the start
Andre's velocity is -8.14 meters per second
I hope this helps <3
Take the dot product, if the dot product is zero, they are orthogonal
<span>the dot product here is 15(-5) + 45(12) so the vectors are not orthogonal </span>
<span>to see if they are parallel, take the dot product again, using the definition </span>
<span>u dot v = mag u x mag v cos (theta) where mag is the magnitude of the vector and theta is the angle between them </span>
<span>we know from above that u dot v = 465 </span>
<span>mag u = sqrt[15^2+45^2]=47.43 </span>
<span>mag v = sqrt[5^2+12^2]=13 </span>
<span>so we know: </span>
<span>cos(theta) = 465/(47.43x13) = 0.75 </span>
<span>
so theta = 41 deg</span>
Answer:
33.75 cubic inches of styrofoam can be placed inside the container.
Step-by-step explanation:
Based on given information, the volume of the prism (
), in cubic inches, is determined by using this formula:
(1)
Where:
- Base of the triangular face, in inches.
- Height of the triangular face, in inches.
- Length of the prism, in inches.
If we know that 
, 
and 
, then the volume of the prism is:
33.75 cubic inches of styrofoam can be placed inside the container.
Answer:
x = 23
Step-by-step explanation:
The exterior angle = sum of the 2 opposite interior angles, hence
2x + 3 + 51 = 100
2x + 54 = 100 ( subtract 54 from both sides )
2x = 46 ( divide both sides by 2 )
x = 23
