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uysha [10]
3 years ago
10

Which of the following equations is an example of the Associative Property of Addition?

Mathematics
2 answers:
Sholpan [36]3 years ago
8 0

Answer: I think the answer to your question is option B.

blagie [28]3 years ago
3 0

Answer: Choice B

(3+4) + 2 = 3 + (4+2)

=========================================

Explanation:

The general rule for the associative property of addition is

(a+b)+c = a+(b+c)

the a,b,c stay in the same order from left to right. The only thing that changes is the way we group the pair of terms. On the left side, we have a & b together with c left out. Then on the right side, we have b & c together with 'a' excluded.

Addition of any group of numbers can be done in any order, which is why this property is valid (though perhaps there's a more rigorous proof out there). For this specific problem, a = 3, b = 4, and c = 2.

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1. Which of the following systems is consistent and dependent?
Kamila [148]

Answer:

Choice d.

Step-by-step explanation:

Consistent means the linear functions will have at least one solution.

Independent means the it will just that one solution.

Dependent means the system will have infinitely many solutions.

So we are looking for a pair of equations that consist of the same line.

y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.

If m and b are the same amongst the pair, then that pair is the same line and the system is consistent and dependent.

If m is the same and b is different amongst the pair, then they are parallel and the system will be inconsistent (have no solution).

If m is different, then the pair will have one solution and will be consistent and independent.

---------------------------

Choice A:

First line has m=1 and b=4.

Second line has m=1 and b=-4.

These lines are parallel.

This system is inconsistent.

Choice B:

First line is x+y=4 and it isn't in y=mx+b form.

Second line is 2x+2y=6 and it isn't in y=mx+b form.

These lines do have the same form though. This is actually standard form.

If you divide second equation by 2 on both sides you get:  x+y=3

The lines are not the same.

We are looking for the same line.

Now we could go ahead and determine to call this system.

If x+y has value 4 then how could x+y have value 3.  It is not possible. There is no solution. These lines are parallel.

Need more convincing. Let's put them into slope-intercept form.

x+y=4

Subtract x on both sides:

y=-x+4

m=-1 and b=4

x+y=3

Subtract x on both sides:

y=-x+3

m=-1 and b=3.

The system is inconsistent because they are parallel.

Choice c:

I'm going to go ahead in put them both in slope-intercept form:

3x+y=3

Subtract 3x on both sides:

y=-3x+3

So m=-3 and b=3

2y=6x+6

Divide both sides by 2:

y=3x+3

So m=3 and b=3

The m's are different so this system will by consistent and independent.

Choice d:

The goal is the same. Put them in slope-intercept form.

4x-2y=6

Divide both sides by -2:

-2x+y=-3

Add 2x on both sides:

y=2x-3

m=2 and b=-3

6x-3y=9

Divide both sides by -3:

-2x+y=-3

Add 2x on btoh sides:

y=2x-3

m=2 and b=-3

These are the same line because they have the same m and the same b.

This system is consistent and dependent.

8 0
3 years ago
What is the result when the number 12 is increased by 25%?
irina [24]
12 divided by 4 is 25% so add the 12 and four together
3 0
3 years ago
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One type of insect is 0.0052 meters long. what is this length in scientific notation?
pochemuha
Your answer would be:
5.2*10^(-3)

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4 0
3 years ago
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50 ÷ (-5) =<br><br><br> Please simplify
mafiozo [28]

Answer:

-10

Step-by-step explanation:

50 ÷ (-5)

First ignore the brackets and the negative sign.

Then divide 50 by 5 to get 10

Then return the negative sign so the answer is; -10

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3 years ago
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3 years ago
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