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

Is the point $\left(7,16\right)$ included in the inequality $y\geq- 31 x^{4}$ ?

Yes

Explanation

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ value. $16\geq-31\cdot7^{4}$ $16\geq-31\cdot2401$ $16\geq-74431$ Since is greater thanthe point is included in the inequality.

Is the point $\left(7,42\right)$ included in the inequality $y\geq- 29 x^{2}$ ?

Yes

Explanation

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ value. $42\geq-29\cdot7^{2}$ $42\geq-29\cdot49$ $42\geq-1421$

Since is greater than the point is included in the inequality.

Is the point $\left(48,2\right)$ included in the inequality $y\geq29 x^{2}$ ?

Yes

Explanation

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ value. $2\geq29\cdot48^{2}$ $2\geq29\cdot2304$ $2\geq66816$

Since is not greater than or equal to the point is not included in the inequality.

Is the point $\left(8,10\right)$ included in the inequality $y\geq11 x^{3}$ ?

Yes

Explanation

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ value. $10\geq11\cdot8^{3}$ $10\geq11\cdot512$ $10\geq5632$

Since is not greater than or equal to the point is not included in the inequality.

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

Yes

Explanation

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

Since is greater thanthe point is included in the inequality.

Is the point $\left(2,-11\right)$ included in the inequality $y\geq- 15 x^{4}$ ?

Yes

Explanation

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ value. $-11\geq-15\cdot2^{4}$ $-11\geq-15\cdot16$ $-11\geq-240$

Since is greater thanthe point is included in the inequality.

Is the point $\left(28,43\right)$ included in the inequality $y\geq- 21 x^{6}$ ?

Yes

Explanation

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ value. $43\geq-21\cdot28^{6}$ $43\geq-21\cdot481890304$ $43\geq-10119696384$

Since is greater than the point is included in the inequality.

Is the point $\left(47,35\right)$ included in the inequality $y\geq36 x^{3}$ ?

Yes

Explanation

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ value. $35\geq36\cdot47^{3}$ $35\geq36\cdot103823$ $35\geq3737628$

Since is not greater than or equal to the point is not included in the inequality.

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

Yes

Explanation

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