Answer the questions below about Line 1 and Line 2 shown below.
6, plus, 2
6+2
2, plus, 6
2+6
Answer
Attempt 1 out of 3
The expression was rewritten using the .
Line 1 says plus+, which could be represented using dots as ●●●●●●plus+ ●● for a total of dots.
Line 2 says plus+, which could be represented using dots as ●●plus+ ●●●●●● for a total of dots.
Line 1: 6, plus, 2
Line 2: 2, plus, 6
The expression was rewritten using the commutative property of addition.
Line 1 says 6 plus 2, which could be represented using dots as ●●●●●●plus+ ●● for a total of 8 dots.
Line 2 says 2 plus 6, which could be represented using dots as ●●plus+ ●●●●●● for a total of 8 dots.
Answer the questions below about Line 1 and Line 2 shown below.
4, dot, 3
4⋅3
3, dot, 4
3⋅4
Answer
Attempt 1 out of 3
The expression was rewritten using the .
4, dot, 34⋅3 means plus+ plus+ plus+ which equals .
3, dot, 43⋅4 means plus+ plus+ which equals .
Submit Answer
The expression was rewritten using the commutative property of multiplication.
4, dot, 3
4⋅3 means 4 plus 4 plus 4 which equals 12.
3, dot, 4
3⋅4 means 3 plus 3 plus 3 plus 3 which equals 12.
Answer the questions below about Line 1 and Line 2 shown below.
5, dot, left bracket, 1, plus, 9, right bracket
5⋅(1+9)
5, dot, 1, plus, 5, dot, 9
5⋅1+5⋅9
Answer
Attempt 1 out of 3
The expression was rewritten using the .
5, dot, left bracket, 1, plus, 9, right bracket5⋅(1+9) equals 5, dot5⋅ which equals .
5, dot, 1, plus, 5, dot, 95⋅1+5⋅9 equals plus+ which equals .
The expression was rewritten using the distributive property of multiplication over addition.
5, dot, left bracket, 1, plus, 9, right bracket
5⋅(1+9) equals 5⋅1+5⋅9 which equals 5+45 = 50.
5, dot, 1, plus, 5, dot, 9
5⋅1+5⋅9 equals 5+45 = 50.
dentify the property that justifies each step asked about in the answer area below.
Line 1: , left bracket, 4, x, right bracket, left bracket, 7, y, right bracket
Line 1: =
(4x)(7y)
Line 2: , 4, dot, left bracket, x, dot, 7, right bracket, dot, y
Line 2: =
4⋅(x⋅7)⋅y
Line 3: , 4, dot, left bracket, 7, dot, x, right bracket, dot, y
Line 3: =
4⋅(7⋅x)⋅y
Line 4: , left bracket, 4, dot, 7, right bracket, left bracket, x, dot, y, right bracket
Line 4: =
(4⋅7)(x⋅y)
Line 5: , 28, x, y
Line 5: =
28xy
Line 1: The associative property of multiplication justifies the step in Line 1, as the parentheses are rearranged without changing the product.
Line 2: The associative property of multiplication justifies the step in Line 2, as the parentheses are rearranged without changing the product.
Line 3: The commutative property of multiplication justifies the step in Line 3, as the order of multiplication is changed without changing the product.
Line 4: The associative property of multiplication justifies the step in Line 4, as the parentheses are rearranged without changing the product.
Line 5: The expression is simplified further using the multiplication rules, but no specific property is required to justify the step in Line 5.
Identify the property that justifies each step asked about in the answer area below.Line 1: , left bracket, minus, 7, x, plus, 3, right bracket, plus, 2, xLine 1: =(−7x+3)+2xLine 2: , left bracket, 3, plus, left bracket, minus, 7, x, right bracket, right bracket, plus, 2, xLine 2: =(3+(−7x))+2xLine 3: , 3, plus, left bracket, minus, 7, x, plus, 2, x, right bracketLine 3: =3+(−7x+2x)Line 4: , 3, plus, left bracket, minus, 5, x, right bracketLine 4: =3+(−5x)Answer
Line 1: The associative property of addition justifies the step in Line 1, as the parentheses are rearranged without changing the sum.
Line 2: The associative property of addition justifies the step in Line 2, as the parentheses are rearranged without changing the sum.
Line 3: The distributive property of addition over subtraction justifies the step in Line 3, as the negative sign is distributed to both terms inside the parentheses.
Line 4: The combining like terms property justifies the step in Line 4, as the -7x and 2x are combined to simplify the expression.
The table below shows the elevation at which different artifacts were found in an archeological dig.
ArtifactArtifact ElevationElevation
arrow headarrow head 364, feet364 feet
bonebone 0, feet0 feet
necklacenecklace 797, feet797 feet
clay bowlclay bowl minus, 1141, feet−1141 feet
woven blanketwoven blanket minus, 555, feet−555 feet
Which of these artifacts was discovered at sea level?
Answer