Common Core: High School - Algebra : Graph Two Variable Linear Equations and System of Linear Equations as a Half Plane: CCSS.Math.Content.HSA-REI.D.12

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

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Example Questions

Example Question #631 : High School: Algebra

Is the point \displaystyle \left( 22 , 720 \right) included in the inequality \displaystyle y \geq 10 x^{9}?

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle 720 \geq 10 \cdot 22 ^{9}

\displaystyle 720 \geq 10 \cdot 1207269217792

\displaystyle 720 \geq 12072692177920

Since \displaystyle 720 is not greater than or equal to \displaystyle 12072692177920 the point is not included in the inequality.

 

Example Question #632 : High School: Algebra

Is the point \displaystyle \left( 1 , -965 \right) included in the inequality \displaystyle y \geq - 33 x^{6}?

 

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle -965 \geq -33 \cdot 1 ^{6}

\displaystyle -965 \geq -33 \cdot 1

\displaystyle -965 \geq -33

Since \displaystyle -965 is not greater than or equal to \displaystyle -33 the point is not included in the inequality.

 

Example Question #3 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \displaystyle \left( 42 , -318 \right) included in the inequality \displaystyle y \geq 30 x^{4}?

 

Possible Answers:

No

Yes

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle -318 \geq 30 \cdot 42 ^{ 4 }

\displaystyle -318 \geq 30 \cdot 3111696

\displaystyle -318 \geq 93350880

Since \displaystyle -318 is not greater than or equal to \displaystyle 93350880 the point is not included in the inequality.

 

Example Question #4 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \displaystyle \left( 9 , -705 \right) included in the inequality \displaystyle y \geq 17 x^{11}?

Possible Answers:

No

Yes

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle -705 \geq 17 \cdot 9 ^{ 11 }

\displaystyle -705 \geq 17 \cdot 31381059609

\displaystyle -705 \geq 533478013353

Since \displaystyle -705 is not greater than or equal to \displaystyle 533478013353 the point is not included in the inequality.

Example Question #5 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \displaystyle \left( 37 , -448 \right) included in the inequality \displaystyle y \geq 3 x^{7}?

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle -448 \geq 3 \cdot 37 ^{ 7 }

\displaystyle -448 \geq 3 \cdot 94931877133

\displaystyle -448 \geq 284795631399

Since \displaystyle -448 is not greater than or equal to \displaystyle 284795631399 the point is not included in the inequality.

 

Example Question #631 : High School: Algebra

Is the point \displaystyle \left( 10 , 297 \right) included in the inequality \displaystyle y \geq 7 x^{11}?

Possible Answers:

No

Yes

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the  and  value.

\displaystyle 297 \geq 7 \cdot 10 ^{ 11 }

\displaystyle 297 \geq 7 \cdot 100000000000

\displaystyle 297 \geq 700000000000

Since \displaystyle 297 is not greater than or equal to \displaystyle 700000000000 the point is not included in the inequality.

 

Example Question #632 : High School: Algebra

Is the point \displaystyle \left( 3 , 731 \right) included in the inequality \displaystyle y \geq 12 x^{6}?

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle 731 \geq 12 \cdot 3 ^{ 6 }

\displaystyle 731 \geq 12 \cdot 729

\displaystyle 731 \geq 8748

Since 731 is not greater than \displaystyle 8748 the point is not included in the inequality.

Example Question #633 : High School: Algebra

Is the point \displaystyle \left( 9 , 405 \right) included in the inequality \displaystyle y \geq - 33 x^{11}?

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle 405 \geq -33 \cdot 9 ^{ 11 }

\displaystyle 405 \geq -33 \cdot 31381059609

\displaystyle 405 \geq -1035574967097

Since \displaystyle 405 is greater than \displaystyle -1035574967097 the point is included in the inequality.

 

Example Question #1 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \displaystyle \left( 37 , -112 \right) included in the inequality \displaystyle y \geq - 3 x^{3}?

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle -112 \geq -3 \cdot 37 ^{ 3 }

\displaystyle -112 \geq -3 \cdot 50653

\displaystyle -112 \geq -151959

Since \displaystyle -112 is greater than \displaystyle -151959 the point is included in the inequality.

 

Example Question #2 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \displaystyle \left( 6 , -393 \right) included in the inequality \displaystyle y \geq 26 x^{11}?

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the  and \displaystyle y values.

\displaystyle -393 \geq 26 \cdot 6 ^{ 11 }

\displaystyle -393 \geq 26 \cdot 362797056

\displaystyle -393 \geq 9432723456

Since \displaystyle -393 is not greater than or equal to \displaystyle 9432723456 the point is not included in the inequality.

All Common Core: High School - Algebra Resources

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