Common Core: High School - Algebra : High School: Algebra

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 #731 : High School: Algebra

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

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.\(\displaystyle -44\geq11\cdot1^{3}\)\(\displaystyle -44\geq11\cdot1\)\(\displaystyle -44\geq11\)

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

Example Question #732 : High School: Algebra

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.

Example Question #733 : High School: Algebra

Is the point \(\displaystyle \left(25,20\right)\) included in the inequality\(\displaystyle y\geq- 6 x^{5}\) ?

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.\(\displaystyle 20\geq-6\cdot25^{5}\)\(\displaystyle 20\geq-6\cdot9765625\)\(\displaystyle 20\geq-58593750\)

Since \(\displaystyle 20\)is greater than\(\displaystyle -58593750\)the point is included in the inequality.

Example Question #734 : High School: Algebra

Is the point \(\displaystyle \left(45,38\right)\) included in the inequality\(\displaystyle y\geq9 x^{2}\) ?

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.\(\displaystyle 38\geq9\cdot45^{2}\)\(\displaystyle 38\geq9\cdot2025\)\(\displaystyle 38\geq18225\)

Since \(\displaystyle 38\) is not greater than or equal to \(\displaystyle 18225\) the point is not included in the inequality.

Example Question #735 : High School: Algebra

Is the point \(\displaystyle \left(20,-32\right)\) included in the inequality\(\displaystyle y\geq22 x^{6}\) ?

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.\(\displaystyle -32\geq22\cdot20^{6}\)\(\displaystyle -32\geq22\cdot64000000\)\(\displaystyle -32\geq1408000000\)

Since \(\displaystyle -32\) is not greater than or equal to \(\displaystyle 1408000000\) the point is not included in the inequality.

Example Question #736 : High School: Algebra

Is the point \(\displaystyle \left(27,-21\right)\) included in the inequality\(\displaystyle y\geq- 15 x^{2}\) ?

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.\(\displaystyle -21\geq-15\cdot27^{2}\)\(\displaystyle -21\geq-15\cdot729\)\(\displaystyle -21\geq-10935\)

Since \(\displaystyle -21\)is greater than\(\displaystyle -10935\)the point is included in the inequality.

Example Question #737 : High School: Algebra

Is the point \(\displaystyle \left(31,-43\right)\) included in the inequality\(\displaystyle y\geq- 6 x^{5}\) ?

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.\(\displaystyle -43\geq-6\cdot31^{5}\)\(\displaystyle -43\geq-6\cdot28629151\)\(\displaystyle -43\geq-171774906\)

Since \(\displaystyle -43\)is greater than\(\displaystyle -171774906\)the point is included in the inequality.

Example Question #738 : High School: Algebra

Is the point \(\displaystyle \left(9,0\right)\) included in the inequality\(\displaystyle y\geq- 26 x^{2}\) ?

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.\(\displaystyle 0\geq-26\cdot9^{2}\)\(\displaystyle 0\geq-26\cdot81\)\(\displaystyle 0\geq-2106\)

Since \(\displaystyle 0\)is greater than\(\displaystyle -2106\)the point is included in the inequality.

Example Question #739 : High School: Algebra

Is the point \(\displaystyle \left(6,32\right)\) included in the inequality\(\displaystyle y\geq10 x^{4}\) ?

Possible Answers:

No

Yes

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle 32\geq10\cdot6^{4}\)\(\displaystyle 32\geq10\cdot1296\)\(\displaystyle 32\geq12960\)

Since \(\displaystyle 32\) is not greater than or equal to \(\displaystyle 12960\) the point is not included in the inequality.

Example Question #740 : High School: Algebra

Is the point \(\displaystyle \left(48,-8\right)\) included in the inequality\(\displaystyle y\geq21 x^{6}\) ?

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

To see if the point is included in the inequality, we need to plug in the \(\displaystyle \uptext{x}\) value.\(\displaystyle -8\geq21\cdot48^{6}\)\(\displaystyle -8\geq21\cdot12230590464\)\(\displaystyle -8\geq256842399744\)

Since \(\displaystyle -8\) is not greater than or equal to \(\displaystyle 256842399744\) the point is not included in the inequality.

All Common Core: High School - Algebra Resources

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