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 #266 : Reasoning With Equations & Inequalities

Is the point \(\displaystyle \left(23,-42\right)\) included in the inequality\(\displaystyle y\geq- 25 x^{5}\) ?

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle -42\geq-25\cdot23^{5}\)\(\displaystyle -42\geq-25\cdot6436343\)\(\displaystyle -42\geq-160908575\)

Since \(\displaystyle -42\)is greater than\(\displaystyle -160908575\)the point is included in the inequality.

Example Question #267 : Reasoning With Equations & Inequalities

Is the point \(\displaystyle \left(11,-4\right)\) included in the inequality\(\displaystyle y\geq- 40 x^{6}\) ?

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle -4\geq-40\cdot11^{6}\)\(\displaystyle -4\geq-40\cdot1771561\)\(\displaystyle -4\geq-70862440\)

Since \(\displaystyle -4\)is greater than\(\displaystyle -70862440\)the point is included in the inequality.

Example Question #268 : Reasoning With Equations & Inequalities

Is the point \(\displaystyle \left(4,25\right)\) included in the inequality\(\displaystyle y\geq- 28 x^{4}\) ?

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle 25\geq-28\cdot4^{4}\)\(\displaystyle 25\geq-28\cdot256\)\(\displaystyle 25\geq-7168\)

Since \(\displaystyle 25\)is greater than\(\displaystyle -7168\)the point is included in the inequality.

Example Question #269 : Reasoning With Equations & Inequalities

Is the point \(\displaystyle \left(26,29\right)\) included in the inequality\(\displaystyle y\geq4 x^{2}\) ?

Possible Answers:

No

Yes

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle 29\geq4\cdot26^{2}\)\(\displaystyle 29\geq4\cdot676\)\(\displaystyle 29\geq2704\)

Since \(\displaystyle 29\) is not greater than or equal to \(\displaystyle 2704\) the point is not included in the inequality.

Example Question #270 : Reasoning With Equations & Inequalities

Is the point \(\displaystyle \left(29,3\right)\) included in the inequality\(\displaystyle y\geq- 25 x^{3}\) ?

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle 3\geq-25\cdot29^{3}\)\(\displaystyle 3\geq-25\cdot24389\)\(\displaystyle 3\geq-609725\)

Since \(\displaystyle 3\)is greater than\(\displaystyle -609725\)the point is included in the inequality.

Example Question #91 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \(\displaystyle \left(28,-47\right)\) included in the inequality\(\displaystyle y\geq- 33 x^{6}\) ?

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle -47\geq-33\cdot28^{6}\)\(\displaystyle -47\geq-33\cdot481890304\)\(\displaystyle -47\geq-15902380032\)

Since \(\displaystyle -47\)is greater than\(\displaystyle -15902380032\)the point is included in the inequality.

Example Question #92 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \(\displaystyle \left(15,-43\right)\) included in the inequality\(\displaystyle y\geq- 19 x^{2}\) ?

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle -43\geq-19\cdot15^{2}\)\(\displaystyle -43\geq-19\cdot225\)\(\displaystyle -43\geq-4275\)

Since \(\displaystyle -43\)is greater than\(\displaystyle -4275\)the point is included in the inequality.

Example Question #93 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \(\displaystyle \left(29,29\right)\) included in the inequality\(\displaystyle y\geq- 24 x^{5}\) ?

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle 29\geq-24\cdot29^{5}\)\(\displaystyle 29\geq-24\cdot20511149\)\(\displaystyle 29\geq-492267576\)

Since \(\displaystyle 29\)is greater than\(\displaystyle -492267576\)the point is included in the inequality.

Example Question #94 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \(\displaystyle \left(1,-44\right)\) included in the inequality\(\displaystyle y\geq11 x^{3}\) ?

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle -44\geq11\cdot1^{3}\)\(\displaystyle -44\geq11\cdot1\)\(\displaystyle -44\geq11\)

Since \(\displaystyle -44\) is not greater than or equal to \(\displaystyle 11\) the point is not included in the inequality.

Example Question #95 : Graph Two Variable Linear Equations And System Of Linear Equations As A Half Plane: Ccss.Math.Content.Hsa Rei.D.12

Is the point \(\displaystyle \left(7,-7\right)\) included in the inequality\(\displaystyle y\geq5 x^{3}\) ?

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle -7\geq5\cdot7^{3}\)\(\displaystyle -7\geq5\cdot343\)\(\displaystyle -7\geq1715\)

Since \(\displaystyle -7\) is not greater than or equal to \(\displaystyle 1715\) the point is not included in the inequality.

All Common Core: High School - Algebra Resources

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