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Over [174]
2 years ago
5

Let [] denote the operation a [] b = a+b -

ac{ab}{2}" alt="\frac{ab}{2}" align="absmiddle" class="latex-formula"> ....

Mathematics
1 answer:
DedPeter [7]2 years ago
8 0

The only statement that holds for the given operation is Statement II

<h3>Operations and numbers</h3>

Given the following operartions

a [] b = a+b - ab/2

We need to<u> check the true statement</u>

For the expression x [] (y+z) =  x [] y +  x [] z

x [] (y+z) = x+y+z - x(y+z)/2

x [] (y+z) = x+y+z - (xy+xz)/2

x [] y +x [] z =  x+y - xy/2 +[x+z - xz/2 ]

x [] y +x [] z = x+y+x+z -xy/2 - xz/2

x [] y +x [] z = 2x+y+z - (xy+xz)/2

This shows that the statement I is incorrect

For the second statement

y [] z =  y+z - yz/2

x [] (y [] z) = x + (y+z - yz/2) - x(y+z-yz/2)/2

x [] (y [] z) = x+y+z-yz/2 -xy/2 - xz/2+xyz/4

For the other expression

x [] y =  x+y - xy/2

(x [] y) [] z = x+y - xy/2 + z - z(x+y - xy/2)/2

(x [] y) [] z = x+y+z- xy/2 -zx/2 - zy/2 + xyz/4

This shows that x [] (y [] z) = (x [] y) [] z is correct (Statement II)

For the third statement

x [] z =  x+z - xz/2

y [] z =  y+z - yz/2

z [] 0 = z+0 - z(0)/2

z [] 0 = z

x[]z + y[]z - z[]0 = x+z - xz/2 + y+z - yz/2 - z

x[]z + y[]z - z[]0 = x+y+z - xz/2 - yz/2

For the expression (x+y)[] z

(x+y)[] z = (x+y)+z - (xyz)/2

Hence the statement III is not valid

Based on the explanations above, the only statement that holds for the given operation is Statement II

Learn more on operations and numbers here: brainly.com/question/2292256

#SPJ1

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lina2011 [118]

Answer:

I think its C but I'm not too sure.

4 0
3 years ago
What is the least number that has 4 odd factors that are all the same?
mixer [17]


1 x 1 x 1 x 1 = 1

Hope this helps. :)

5 0
2 years ago
There are two unknowns you are trying to find, and you cannot express one in terms of the other. Describe how you could use alge
serious [3.7K]

Answer:

When you solve systems with two variables and therefore two equations, the ... of any variable is 1, which means you can easily solve for it in terms of the other ... In the substitution method, you use one equation to solve for one variable and ... Look for a variable with a coefficient of 1 … that's how you'll know where to begin.

Step-by-step explanation:

4 0
3 years ago
M = 1/2 (0, -3)<br> Write the equation of a line using slope intercept form
marshall27 [118]

Answer:

y=\frac{1}{2}x-3

Step-by-step explanation:

slope intercept form is y=mx+b

b is y intercept

so we plug the coordinate into the equation

-3=\frac{1}{2}(0)+b

-3=b

so y intercept is -3

so we then write our equation which is,

y=\frac{1}{2}x-3

5 0
2 years ago
Read 2 more answers
Adrian has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many quar
Mrrafil [7]
I: 635=dimes*10+quarters*25
or shorter
635=d*10+q*25

II: d=q*3+3

Substitute II (d=3q+3) into I to replace d:
635=d*10+q*25
635=(3q+3)*10+q*25
635=30+30q+25q
605=55q
11=q

-> 11 quarters

"What expression represents the number of dimes if q represent quarters"
insert q=11 into II:
II: d=q*3+3
d=11*3+3
d=33+3
d=36
8 0
3 years ago
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