If the fractions are equivalent, then yes, they can be re-written in the same simplest form.
The relationship here between the x and y values can be seen in an equation, y=x+3, since every y value is three more than its corresponding x-value. <span />
Lets start with one of the equations.
<span>2x+6y=18
</span>Add -6y to both sides.
<span><span><span><span>2x</span>+<span>6y</span></span>+<span>−<span>6y</span></span></span>=<span>18+<span>−<span>6y
</span></span></span></span><span><span>2x</span>=<span><span>−<span>6y</span></span>+18
</span></span>Divide both sides by 2.
<span><span><span>2x</span>2</span>=<span><span><span>−<span>6y</span></span>+18</span>2
</span></span><span>x = <span><span>−<span>3y </span></span>+ 9 <--
Now lets plug this into the other equation.
</span></span>Simplify both sides of the equation.
<span><span><span>3<span>(<span><span>−<span>3y</span></span>+9</span>)</span></span>+<span>2y</span></span>=13
</span><span>Simplify
</span><span><span><span>−<span>7y</span></span>+27</span>=13
</span>Subtract 27 from both sides.
<span><span><span><span>−<span>7y</span></span>+27</span>−27</span>=<span>13−27
</span></span><span><span>−<span>7y</span></span>=<span>−14
</span></span>Divide both sides by -7.
<span><span><span>−<span>7y/</span></span><span>−7 </span></span>= <span><span>−14/</span><span>−7
</span></span></span><span>y=2
</span>Answer:
<span>y=2</span><span>
Now that we figured out the value for y, lets plug it into either equation.
</span>2x+6(-2)=18<span>
</span>Simplify both sides of the equation.
<span><span><span>2x</span>+<span><span>(6)</span><span>(<span>−2</span>)</span></span></span>=18
</span><span>Simplify
</span><span><span><span>2x</span>−12</span>=18
</span>Add 12 to both sides.
<span><span><span><span>2x</span>−12</span>+12</span>=<span>18+12
</span></span><span><span>2x</span>=30
</span>Divide both sides by 2.
<span><span><span>2x/</span>2 </span>= <span>30/2
</span></span><span>x=<span>15</span></span>
Final answer:
y = 2
x = 15
With percentage in the question, you divide the miles they drove by the total miles in the trip (and of course multiply it by 100).
Joe:
![\frac{20}{65} =.3077](https://tex.z-dn.net/?f=%20%5Cfrac%7B20%7D%7B65%7D%20%3D.3077%20)
.3077 times 100= 31% (just rounded the percentage to the nearest whole number).
Adam:
![\frac{35}{65} =.5385](https://tex.z-dn.net/?f=%20%5Cfrac%7B35%7D%7B65%7D%20%3D.5385)
.5385 times 100= 54%
Laura:
![\frac{10}{65} =.1538](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B65%7D%20%3D.1538)
.1538 times 100= 15%
Tell me if this helps!!
Supplementary means that the two angles, when put together, make a straight line (or 180 degree angle), so let's work this out.
A. The measure of angle 1 = the measure of angle 2: We know this is incorrect, just from looking at the picture, so let's cross that off.
B. The measure of angle 2 = the measure of angle 3: Angle 1 and angle 3 have the same measure, so since angle 2 isn't = to angle 1, angle 2 wouldn't be = to angle 3. Let's cross that off also.
C. Complementary means that the two angle put together make a 90 degree angle, but since angle three is already obtuse (more than 90 degrees), this answer is incorrect.
D. This answer is definitely correct! Angles 1 and 2 are supplementary, and angle 1 is equal to angle 3, therefore, angles two and 3 are also supplementary.
D. Is the correct answer!