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Common Core: 6th Grade Math : Grade 6

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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All Common Core: 6th Grade Math Resources

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Example Questions

Example Question #112 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 18 m + 13 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 67\\ \hline 14 & 265\\ \hline 15 & 294\\ \hline 18& 347\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 67\\ \hline 8 & 314\\ \hline 14 & 530\\ \hline 19& 710\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 68\\ \hline 8 & 159\\ \hline 14 & 268\\ \hline 19& 359\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 67\\ \hline 8 & 157\\ \hline 14 & 265\\ \hline 19& 355\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 67\\ \hline 8 & 157\\ \hline 14 & 265\\ \hline 19& 355\\ \hline \end{tabular}}$

Explanation:

In the equation 18 m + 13 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Because we are given tables in our answer choices, we can plug in the given value for {m} from the table and use our equation from the question to see if that equals the value given for {n} in the table.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 68\\ \hline 8 & 159\\ \hline 14 & 268\\ \hline 19& 359\\ \hline \end{tabular}}$

{18(3)+13=68}

{54+13=68}

${67\neq 68}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {18 m + 13 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 85\\ \hline 12 & 458\\ \hline 17 & 638\\ \hline 19& 710\\ \hline \end{tabular}}$

{18(4)+13=85}

{72+13=85}

{85=85}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{18(12)+13=458}

{216+13=458}

${229\neq 458}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 67\\ \hline 14 & 265\\ \hline 15 & 294\\ \hline 18& 337\\ \hline \end{tabular}}$

{18(3)+13=67}

{54+13=67}

{67=67}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{18(14)+13=265}

{252+13=265}

{265=265}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{18(15)+13=294}

{270+13=294}

${283\neq 294}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 67\\ \hline 7 & 139\\ \hline 14 & 265\\ \hline 18& 337\\ \hline \end{tabular}}$

{18(3)+13=67}

{54+13=67}

{67=67}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{18(7)+13=139}

{126+13=139}

{139=139}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{18(14)+13=265}

{252+13=265}

{265=265}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{18(18)+13=337}

{324+13=337}

{337=337}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #113 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 5 m = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -4\\ \hline 3 & -13\\ \hline 8 & -37\\ \hline 13& -61\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -5\\ \hline 3 & -30\\ \hline 8 & -80\\ \hline 13& -130\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -5\\ \hline 3 & -15\\ \hline 8 & -40\\ \hline 13& -65\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -25\\ \hline 6 & -30\\ \hline 9 & -34\\ \hline 13& -55\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -5\\ \hline 3 & -15\\ \hline 8 & -40\\ \hline 13& -65\\ \hline \end{tabular}}$

Explanation:

In the equation - 5 m = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -4\\ \hline 3 & -13\\ \hline 8 & -37\\ \hline 13& -61\\ \hline \end{tabular}}$

{-5(1)+0=-4}

{-5+0=-4}

${-5\neq -4}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 5 m = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -10\\ \hline 12 & -120\\ \hline 13 & -130\\ \hline 16& -160\\ \hline \end{tabular}}$

{-5(2)+0=-10}

{-10+0=-10}

{-10=-10}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-5(12)+0=-120}

{-60+0=-120}

${-60\neq -120}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -25\\ \hline 6 & -30\\ \hline 9 & -34\\ \hline 13& -65\\ \hline \end{tabular}}$

{-5(5)+0=-25}

{-25+0=-25}

{-25=-25}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-5(6)+0=-30}

{-30+0=-30}

{-30=-30}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-5(9)+0=-34}

{-45+0=-34}

${-45\neq -34}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -30\\ \hline 7 & -35\\ \hline 9 & -45\\ \hline 18& -90\\ \hline \end{tabular}}$

{-5(6)+0=-30}

{-30+0=-30}

{-30=-30}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-5(7)+0=-35}

{-35+0=-35}

{-35=-35}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-5(9)+0=-45}

{-45+0=-45}

{-45=-45}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-5(18)+0=-90}

{-90+0=-90}

{-90=-90}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #114 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 2 m - 13 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -5\\ \hline 7 & 2\\ \hline 8 & 6\\ \hline 12& 22\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -5\\ \hline 7 & 1\\ \hline 8 & 3\\ \hline 12& 11\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -11\\ \hline 3 & -7\\ \hline 5 & 8\\ \hline 12& 21\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -4\\ \hline 7 & 3\\ \hline 8 & 6\\ \hline 12& 15\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -5\\ \hline 7 & 1\\ \hline 8 & 3\\ \hline 12& 11\\ \hline \end{tabular}}$

Explanation:

In the equation 2 m - 13 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -4\\ \hline 7 & 3\\ \hline 8 & 6\\ \hline 12& 15\\ \hline \end{tabular}}$

{2(4)+-13=-4}

{8+-13=-4}

${-5\neq -4}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {2 m - 13 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -13\\ \hline 6 & -2\\ \hline 9 & 10\\ \hline 13& 26\\ \hline \end{tabular}}$

{2(0)-13=-13}

{0-13=-13}

{-13=-13}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{2(6)-13=-2}

{12-13=-2}

${-1\neq -2}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -11\\ \hline 3 & -7\\ \hline 5 & 8\\ \hline 12& 21\\ \hline \end{tabular}}$

{2(1)-13=-11}

{2-13=-11}

{-11=-11}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{2(3)-13=-7}

{6-13=-7}

{-7=-7}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{2(5)-13=8}

{10-13=8}

${-3\neq 8}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -9\\ \hline 9 & 5\\ \hline 15 & 17\\ \hline 19& 25\\ \hline \end{tabular}}$

{2(2)-13=-9}

{4-13=-9}

{-9=-9}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{2(9)-13=5}

{18-13=5}

{5=5}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{2(15)-13=17}

{30-13=17}

{17=17}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{2(19)-13=25}

{38+-13=25}

{25=25}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #115 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 12 m - 1 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -1\\ \hline 3 & -37\\ \hline 7 & -74\\ \hline 15& -171\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 5 & -61\\ \hline 8 & -97\\ \hline 15& -181\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -12\\ \hline 5 & -59\\ \hline 8 & -94\\ \hline 15& -177\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 5 & -122\\ \hline 8 & -194\\ \hline 15& -362\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 5 & -61\\ \hline 8 & -97\\ \hline 15& -181\\ \hline \end{tabular}}$

Explanation:

In the equation - 12 m - 1 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -12\\ \hline 5 & -59\\ \hline 8 & -94\\ \hline 15& -177\\ \hline \end{tabular}}$

{-12(1)+-1=-12}

{-12+-1=-12}

${-13\neq -12}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 12 m - 1 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 4 & -98\\ \hline 6 & -146\\ \hline 10& -242\\ \hline \end{tabular}}$

{-12(1)-1=-13}

{-12-1=-13}

{-13=-13}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-12(4)-1=-98}

{-48-1=-98}

${-49\neq -98}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -1\\ \hline 3 & -37\\ \hline 7 & -74\\ \hline 15& -171\\ \hline \end{tabular}}$

{-12(0)-1=-1}

{0-1=-1}

{-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-12(3)-1=-37}

{-36-1=-37}

{-37=-37}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-12(7)-1=-74}

{-84-1=-74}

${-85\neq -74}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & -85\\ \hline 15 & -181\\ \hline 17 & -205\\ \hline 19& -229\\ \hline \end{tabular}}$

{-12(7)-1=-85}

{-84-1=-85}

{-85=-85}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-12(15)-1=-181}

{-180-1=-181}

{-181=-181}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-12(17)-1=-205}

{-204-1=-205}

{-205=-205}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-12(19)-1=-229}

{-228+-1=-229}

{-229=-229}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #116 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 18 m - 15 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -15\\ \hline 7 & -282\\ \hline 12 & -462\\ \hline 14& -534\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -15\\ \hline 7 & -141\\ \hline 12 & -231\\ \hline 14& -267\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -14\\ \hline 7 & -139\\ \hline 12 & -228\\ \hline 14& -263\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -15\\ \hline 6 & -123\\ \hline 8 & -148\\ \hline 12& -221\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -15\\ \hline 7 & -141\\ \hline 12 & -231\\ \hline 14& -267\\ \hline \end{tabular}}$

Explanation:

In the equation - 18 m - 15 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -14\\ \hline 7 & -139\\ \hline 12 & -228\\ \hline 14& -263\\ \hline \end{tabular}}$

{-18(0)+-15=-14}

{0+-15=-14}

${-15\neq -14}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {- 18 m - 15 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -15\\ \hline 4 & -174\\ \hline 17 & -642\\ \hline 18& -678\\ \hline \end{tabular}}$

{-18(0)-15=-15}

{0-15=-15}

{-15=-15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(4)-15=-174}

{-72-15=-174}

${-87\neq -174}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -15\\ \hline 6 & -123\\ \hline 8 & -148\\ \hline 12& -221\\ \hline \end{tabular}}$

{-18(0)-15=-15}

{0-15=-15}

{-15=-15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(6)-15=-123}

{-108-15=-123}

{-123=-123}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(8)-15=-148}

{-144-15=-148}

${-159\neq -148}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -105\\ \hline 12 & -231\\ \hline 16 & -303\\ \hline 18& -339\\ \hline \end{tabular}}$

{-18(5)-15=-105}

{-90-15=-105}

{-105=-105}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(12)-15=-231}

{-216-15=-231}

{-231=-231}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(16)-15=-303}

{-288-15=-303}

{-303=-303}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{-18(18)-15=-339}

{-324+-15=-339}

{-339=-339}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #117 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 16 m + 15 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 159\\ \hline 13 & 446\\ \hline 14 & 478\\ \hline 16& 542\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 15\\ \hline 2 & 47\\ \hline 3 & 74\\ \hline 11& 201\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 160\\ \hline 13 & 225\\ \hline 14 & 242\\ \hline 16& 275\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 159\\ \hline 13 & 223\\ \hline 14 & 239\\ \hline 16& 271\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 159\\ \hline 13 & 223\\ \hline 14 & 239\\ \hline 16& 271\\ \hline \end{tabular}}$

Explanation:

In the equation 16 m + 15 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 160\\ \hline 13 & 225\\ \hline 14 & 242\\ \hline 16& 275\\ \hline \end{tabular}}$

{16(9)+15=160}

{144+15=160}

${159\neq 160}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {16 m + 15 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 127\\ \hline 9 & 318\\ \hline 11 & 382\\ \hline 18& 606\\ \hline \end{tabular}}$

{16(7)+15=127}

{112+15=127}

{127=127}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{16(9)+15=318}

{144+15=318}

${159\neq 318}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 15\\ \hline 2 & 47\\ \hline 3 & 74\\ \hline 11& 191\\ \hline \end{tabular}}$

{16(0)+15=15}

{0+15=15}

{15=15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{16(2)+15=47}

{32+15=47}

{47=47}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{16(3)+15=74}

{48+15=74}

${63\neq 74}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 15\\ \hline 3 & 63\\ \hline 7 & 127\\ \hline 18& 303\\ \hline \end{tabular}}$

{16(0)+15=15}

{0+15=15}

{15=15}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{16(3)+15=63}

{48+15=63}

{63=63}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{16(7)+15=127}

{112+15=127}

{127=127}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{16(18)+15=303}

{288+15=303}

{303=303}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #118 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if -1 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -1\\ \hline 11 & -1\\ \hline 14 & 10\\ \hline 15& 9\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & 0\\ \hline 16 & 1\\ \hline 17 & 2\\ \hline 19& 3\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & -1\\ \hline 16 & -2\\ \hline 17 & -2\\ \hline 19& -2\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & -1\\ \hline 16 & -1\\ \hline 17 & -1\\ \hline 19& -1\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & -1\\ \hline 16 & -1\\ \hline 17 & -1\\ \hline 19& -1\\ \hline \end{tabular}}$

Explanation:

In the equation -1 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & 0\\ \hline 16 & 1\\ \hline 17 & 2\\ \hline 19& 3\\ \hline \end{tabular}}$

{0(11)+-1=0}

{0+-1=0}

${-1\neq 0}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {-1 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -1\\ \hline 10 & -2\\ \hline 13 & -2\\ \hline 15& -2\\ \hline \end{tabular}}$

{0(8)-1=-1}

{0-1=-1}

{-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{0(10)-1=-2}

{0-1=-2}

${-1\neq -2}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -1\\ \hline 11 & -1\\ \hline 14 & 10\\ \hline 15& 9\\ \hline \end{tabular}}$

{0(1)-1=-1}

{0-1=-1}

{-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{0(11)-1=-1}

{0-1=-1}

{-1=-1}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{0(14)-1=10}

{0-1=10}

${-1\neq 10}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -1\\ \hline 7 & -1\\ \hline 10 & -1\\ \hline 13& -1\\ \hline \end{tabular}}$

{0(0)-1=-1}

{0-1=-1}

{-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{0(7)-1=-1}

{0-1=-1}

{-1=-1}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{0(10)-1=-1}

{0-1=-1}

{-1=-1}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{0(13)-1=-1}

{0+-1=-1}

{-1=-1}

All of these values were correct for our equation; thus, this table is our correct answer.

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Example Question #119 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 9 m - 10 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -10\\ \hline 2 & 8\\ \hline 3 & 17\\ \hline 15& 125\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -10\\ \hline 2 & 16\\ \hline 3 & 34\\ \hline 15& 250\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 8\\ \hline 4 & 26\\ \hline 9 & 82\\ \hline 13& 117\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -9\\ \hline 2 & 10\\ \hline 3 & 20\\ \hline 15& 129\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -10\\ \hline 2 & 8\\ \hline 3 & 17\\ \hline 15& 125\\ \hline \end{tabular}}$

Explanation:

In the equation 9 m - 10 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -9\\ \hline 2 & 10\\ \hline 3 & 20\\ \hline 15& 129\\ \hline \end{tabular}}$

{9(0)+-10=-9}

{0+-10=-9}

${-10\neq -9}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {9 m - 10 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 8\\ \hline 9 & 142\\ \hline 12 & 196\\ \hline 18& 304\\ \hline \end{tabular}}$

{9(2)-10=8}

{18-10=8}

{8=8}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(9)-10=142}

{81-10=142}

${71\neq 142}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 8\\ \hline 4 & 26\\ \hline 9 & 82\\ \hline 13& 117\\ \hline \end{tabular}}$

{9(2)-10=8}

{18-10=8}

{8=8}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(4)-10=26}

{36-10=26}

{26=26}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(9)-10=82}

{81-10=82}

${71\neq 82}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -1\\ \hline 4 & 26\\ \hline 5 & 35\\ \hline 15& 125\\ \hline \end{tabular}}$

{9(1)-10=-1}

{9-10=-1}

{-1=-1}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(4)-10=26}

{36-10=26}

{26=26}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(5)-10=35}

{45-10=35}

{35=35}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(15)-10=125}

{135+-10=125}

{125=125}

All of these values were correct for our equation; thus, this table is our correct answer.

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Example Question #120 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 9 m - 12 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 52\\ \hline 13 & 107\\ \hline 14 & 117\\ \hline 19& 163\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -3\\ \hline 5 & 33\\ \hline 12 & 107\\ \hline 15& 133\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 51\\ \hline 13 & 210\\ \hline 14 & 228\\ \hline 19& 318\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 51\\ \hline 13 & 105\\ \hline 14 & 114\\ \hline 19& 159\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 51\\ \hline 13 & 105\\ \hline 14 & 114\\ \hline 19& 159\\ \hline \end{tabular}}$

Explanation:

In the equation 9 m - 12 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

Let's start by testing values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 52\\ \hline 13 & 107\\ \hline 14 & 117\\ \hline 19& 163\\ \hline \end{tabular}}$

{9(7)+-12=52}

{63+-12=52}

${51\neq 52}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} and {n} if {9 m - 12 = n} ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 33\\ \hline 6 & 84\\ \hline 11 & 174\\ \hline 15& 246\\ \hline \end{tabular}}$

{9(5)-12=33}

{45-12=33}

{33=33}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(6)-12=84}

{54-12=84}

${42\neq 84}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -3\\ \hline 5 & 33\\ \hline 12 & 107\\ \hline 15& 133\\ \hline \end{tabular}}$

{9(1)-12=-3}

{9-12=-3}

{-3=-3}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(5)-12=33}

{45-12=33}

{33=33}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(12)-12=107}

{108-12=107}

${96\neq 107}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 42\\ \hline 8 & 60\\ \hline 14 & 114\\ \hline 19& 159\\ \hline \end{tabular}}$

{9(6)-12=42}

{54-12=42}

{42=42}

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(8)-12=60}

{72-12=60}

{60=60}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(14)-12=114}

{126-12=114}

{114=114}

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

{9(19)-12=159}

{171+-12=159}

{159=159}

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #1 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$65.5\textup{ in}^2$

$80\textup{ in}^2$

$58.5\textup{ in}^2$

$117\textup{ in}^2$

$81.5\textup{ in}^2$

Correct answer:

$58.5\textup{ in}^2$

Explanation:

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

1 1

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=13\times 9$

A=117

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$117\div 2= 58.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Common Core: 6th Grade Math : Grade 6

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #112 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #113 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #114 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #115 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #116 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #117 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #118 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #119 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #120 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Example Question #1 : Geometry

All Common Core: 6th Grade Math Resources

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