Question

Which of the following correctly demonstrates the Associative Property of Addition?(1 point) Responses y−(x+1)=(y−x)+1 y minus left parenthesis x plus 1 right parenthesis equals left parenthesis y minus x right parenthesis plus 1 x⋅(y+z)=(x⋅y)+z x times left parenthesis y plus z right parenthesis equals left parenthesis x times y right parenthesis plus z m⋅(x⋅y)=(m⋅x)⋅y m times left parenthesis x times y right parenthesis equals left parenthesis m times x right parenthesis times y (x+y)+z+r=x+(y+z)+r

Answer 1

The Associative Property of Addition states that the way in which numbers are grouped in addition does not change their sum. In mathematical terms, this property can be expressed as:

\[ (a + b) + c = a + (b + c) \]

From the options provided, the correct demonstration of the Associative Property of Addition is:

\[ (x + y) + z = x + (y + z) \]

However, since that option is not explicitly listed, we can analyze the closest expression in your options that relates to addition.

The option that correctly demonstrates the associative property using the context of addition is:

\[ (x + y) + z = x + (y + z) \]

However, I do not see that specific expression in the list you provided. Please let me know if you would like further assistance!

Answer 2

Which of the following demonstrates the Associative Property of Multiplication?(1 point) Responses (3⋅5)⋅2=(3⋅5)⋅2 left parenthesis 3 times 5 right parenthesis times 2 equals left parenthesis 3 times 5 right parenthesis times 2 (3⋅5)⋅2=3⋅(5⋅2) left parenthesis 3 times 5 right parenthesis times 2 equals 3 times left parenthesis 5 times 2 right parenthesis (3⋅5)+2=(3+5)⋅2 left parenthesis 3 times 5 right parenthesis plus 2 equals left parenthesis 3 plus 5 right parenthesis times 2 (3+5)⋅2=3+(5⋅2)

Answer 3

The Associative Property of Multiplication states that the way in which numbers are grouped in multiplication does not change their product. In mathematical terms, this property can be expressed as:

\[ (a \cdot b) \cdot c = a \cdot (b \cdot c) \]

From the options you provided, the correct demonstration of the Associative Property of Multiplication is:

\[ (3 \cdot 5) \cdot 2 = 3 \cdot (5 \cdot 2) \]

This shows the property in action, as it emphasizes that regrouping the multiplication does not change the result. Thus, this response is the correct answer.

Answer 4

Use the Associative Property to determine which expressions are equivalent.(1 point) Responses −3⋅(4x⋅−2)⋅−6y=−7xy negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals negative 7 x y −3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y) negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals left parenthesis negative 3 times 4 x right parenthesis left parenthesis negative 2 times negative 6 y right parenthesis −3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals left parenthesis negative 3 times 4 x right parenthesis times negative 2 minus 6 y −3⋅(4x⋅−2)⋅−6y=18−8x negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals 18 minus 8 x

Answer 5

To apply the Associative Property to determine which expressions are equivalent, let's analyze them separately.

The Associative Property states that when multiplying, the grouping of terms can change without affecting the product. This is expressed mathematically as:

\[ a \cdot (b \cdot c) = (a \cdot b) \cdot c \]

Now let’s evaluate the responses step by step.

1. Option 1: \(-3 \cdot (4x \cdot -2) \cdot -6y = -7xy\)

   • This is unlikely to be true. One side is a product and the right side is a linear expression.

2. Option 2: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\)

   • This uses the associative property to rearrange the multiplication. It is valid.

3. Option 3: \(-3 \cdot (4x \cdot -2) \cdot -6y = ( -3 \cdot 4x)( -2 \cdot -6y)\)

   • This is also valid and correctly applies the property.

4. Option 4: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x) \cdot -2 - 6y\)

   • This expression is not equivalent due to incorrectly applying the operation where the \(-6y\) should still be multiplied.

5. Option 5: \(-3 \cdot (4x \cdot -2) \cdot -6y = 18 - 8x\)

   • This does not hold because the left expression is a product, and the right side is an explicit value and sum.

From the analysis, Options 2 and 3 are valid expressions demonstrating the Associative Property correctly. The expression would factor nicely, and they can be viewed as equivalent because they are essentially the same restructured appointees of the original expression using the associative property.

The correct answer is therefore: \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\) or \(-3 \cdot (4x \cdot -2) \cdot -6y = (-3 \cdot 4x)(-2 \cdot -6y)\).

Answer 6

"Are Commercial Honeybees Making Wild Bees Sick?" by Berly McCoy Everyone wants to save the bees. But as populations decline every year, we may be saving them to death. Human efforts to breed more of these insects in artificial beehives and plant more flowers may seem the obvious way to stave off heavy losses. New research shows the answer is not that clear cut, because viruses may be spilling over from commercial honeybee colonies into wild bee populations, according to a study from the University of Vermont published Wednesday in PLOS One. 1 of 3 Question Use the article excerpt below to answer the question. What evidence from the text best supports the analysis that human actions are related to bumblebee decline? (1 point) Responses the fact that people have tried to breed more bees the fact that people have tried to breed more bees the study that shows viruses may be spilling over from commercial hives to wild bees the study that shows viruses may be spilling over from commercial hives to wild bees the claim that people may be saving the bees to death the claim that people may be saving the bees to death the question about how wild bees pick up viruses if they do not enter managed honeybee colonies