2/3 = 4/6 after we multiply top and bottom by 2 (2*2 = 4, 2*3 = 6)
So we can turn
5/6 + 2/3
into
5/6 + 4/6
Then add the numerators to get 5+4 = 9
So 5/6 + 4/6 = 9/6 which reduces to 3/2 (divide both parts by 3)
The last thing to do is convert 3/2 into a mixed number. If you use long division you'll find that 3 divided by 2 = 1 remainder 1
Or you can think of it like this
3/2 = (2+1)/2 = 2/2 + 1/2 = 1 + 1/2 = 1&1/2
So the final answer, as a mixed number, is 1 & 1/2
Whole part = 1
Fraction part = 1/2
4x=3y+3 and 6y= 8x+ 36 and y=3x-1 and y= 6- x/3
4x=3y+3 and 6y= 8x are parallel and y=3x-1 and y= 6- x/3 are perpendicular.
See the attached plot for answer.
Answer: The length of the shortest piece is 16 inches
The length of the medium piece is
20 inches
The length of the longest piece is 25 inches.
Step-by-step explanation:
Total length of the party sandwich is 61 inches. This length is to be cut into three different pieces.
Let x= the size of the longest piece.
Let y = the size of the medium piece.
Let z = the size of the shortest piece.
The middle piece will be 4 inches longer than the shortest piece. This means that
y = z + 4 - - - - - - 1
The shortest piece will be 9 inches shorter than the longest piece. This means that
x = z +9 - - - - - - -2
Since total length of the party sandwich is 61 inches, it means that
x + y + z = 61 - - - - - - -3
We will substitute equation 1 and equation 2 into equation 3. It becomes
z + 9 + z + 4 + z = 61
13 + 3z = 61
3z = 61 - 13 = 48
z = 48/3 = 16
y = z + 4 = 16 + 4
y = 20
x = z + 9 = 16 + 9
x = 25
2x^2-4x-30 would be your answer
<span><span>(<span><span>2x</span>−10</span>)</span><span>(<span>x+3</span>)
</span></span><span>=<span><span>(<span><span>2x</span>+<span>−10</span></span>)</span><span>(<span>x+3</span>)
</span></span></span><span>=<span><span><span><span><span>(<span>2x</span>)</span><span>(x)</span></span>+<span><span>(<span>2x</span>)</span><span>(3)</span></span></span>+<span><span>(<span>−10</span>)</span><span>(x)</span></span></span>+<span><span>(<span>−10</span>)</span><span>(3)
</span></span></span></span><span>=<span><span><span><span>2<span>x2</span></span>+<span>6x</span></span>−<span>10x</span></span>−30
</span></span><span>=<span><span><span>2<span>x2</span></span>−<span>4x</span></span>−<span>30</span></span></span>
|7-10| = 3 (absolute value), then multiply to the negative sign. answer:-3
