Answer:
y-3
Problem:
What is the remainder when the dividend is xy-3, the divisor is y, and the quotient is x-1. ?
Step-by-step explanation:
Dividend=quotient×divisor+remainder
So we have
xy-3=(x-1)×(y)+remainder
xy-3=(xy-y)+remainder *distributive property
Now we just need to figure out what polynomial goes in for the remainder so this will be a true identity.
We need to get rid of minus y so we need plus y in the remainder.
We also need minus 3 in the remainder.
So the remainder is y-3.
Let's try it out:
xy-3=(xy-y)+remainder
xy-3=(xy-y)+(y-3)
xy-3=xy-3 is what we wanted so we are done here.
The first one is 84 ounces and the second one is 20 ounces
Answer: (x + 3, y - 4)
Explanation: The shape in the middle goes to the right three and down four to match the shape at the bottom
To tessellate a surface using a regular polygon, the interior angle must be a sub-multiple (i.e. factor) of 360 degrees to cover completely the surface.
For a regular three-sided polygon, the interior angle is (180-360/3)=60 °
Since 6*60=360, so a regular three-sided polygon (equilateral triangle) tessellates.
For a regular four-sided polygon, the interior angle is (180-360/4)=90 °
Since 4*90=360, so a regular four-sided polygon (square) tessellates.
For a regular five-sided polygon, the interior angle is (180-360/5)=108 °
Since 360/108=3.33... (not an integer), so a regular five-sided polygon (pentagon) does NOT tessellate.
For a regular six-sided polygon, the interior angle is (180-360/6)=120 °
Since 3*120=360, so a regular six-sided polygon (hexagon) tessellates.
