Question 1

Find the indicated system of inequalities.
-Write a system of inequalities that represents the points inside the triangle with vertices (2, 1), (-3, 3), and (-4, -2).

Accepted Answer

The inequalities represent the lines forming the triangle, with the correct direction of inequalities to include the region inside the triangle.

Question 2

Find the indicated system of inequalities.
-Write a system of inequalities that represents the points in the first quadrant less than 7 units from the origin.

Accepted Answer

The equation $x^2 + y^2 < 49$ represents the interior of a circle with radius 7 centered at the origin. The conditions $x>0$ and $y>0$ ensure that only points in the first quadrant are considered.

Question 3

Solve the problem.
-A college theater reserves x tickets for students and y tickets for general admission. Total number of seats available is at most 500. The college reserves a least 2 times as many student tickets as general Admission tickets. The number of student tickets cannot be negative. The number of general
Admission tickets cannot be negative. Write a system of inequalities to represent the described Scenario and graph the solution set.

Accepted Answer

The answer of Solve the problem.
-A college theater reserves x...

Question 4

For parts (a) and (b), write an inequality to represent the given statement.
-Let x represent the number of hours that Emily spends studying algebra, and let y represent the number of hours she spends studying history.
a. Emily will spend no more than 2 hr studying history.
b. The number of hours spent studying algebra cannot be negative.

Accepted Answer

For part (a), "no more than 2 hr studying history" translates to $y \leq 2$. For part (b), "cannot be negative" for algebra study hours means $x \geq 0$.

Question 5

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
y < e ^ { x } \
y > 4 \
x < 2
\end{array}$$

Accepted Answer

The answer of Graph the solution set. If there is...

Question 6

For parts (a) and (b), write an inequality to represent the given statement.
-Let x represent the number of hours that Trenton spends studying algebra, and let y represent the number of hours he spends studying history.
a. Trenton has a total of at most 12 hr to study for both algebra and history combined.
b. Trenton will spend at least 5 hr studying algebra.

Accepted Answer

For part (a), "at most 12 hr" means the total time spent on both subjects cannot exceed 12 hours, hence $x + y \leq 12$. For part (b), "at least 5 hr studying algebra" means the time spent on algebra should be 5 hours or more, hence $x \geq 5$.

Question 7

Graph the solution set.
-$$\begin{array} { l } 
x + 3 y \geq 6 \
x - y \leq - 6
\end{array}$$

Accepted Answer

The answer of Graph the solution set.
-\[\begin{array} { l }...

Question 8

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } > 16 \
x ^ { 2 } + y ^ { 2 } \leq 64
\end{array}$$

Accepted Answer

The answer of Graph the solution set. If there is...

Question 9

Graph the solution set.
-$$\begin{array} { l } 
4 x - y > 4 \
x + y < 6
\end{array}$$

Accepted Answer

The answer of Graph the solution set.
-\[\begin{array} { l }...

Question 10

Solve the problem.
-A weak earthquake occurred roughly 4 km south and 5 km west of the center of Shelbyville. The quake could be felt 7 km away. Suppose the origin of the map is placed at the center of Shelbyville With the positive x-axis pointing east and the positive y-axis pointing north. Write an inequality that Describes the points on the map for which the earthquake could be felt, and determine whether the Quake could be felt at the center of Shelbyville.

Accepted Answer

The correct inequality to describe the points on the map where the earthquake could be felt is a circle equation $(x + 4)^2 + (y + 5)^2 \leq 49$, because the earthquake's radius of effect is 7 km (hence, radius squared is $7^2 = 49$). The earthquake's epicenter is 4 km south and 5 km west of Shelbyville, so its coordinates relative to Shelbyville are (-4, -5). Using the distance formula, the distance from the center of Shelbyville to the earthquake's epicenter is $\sqrt{(-4)^2 + (-5)^2} = \sqrt{16 + 25} = \sqrt{41}$, which is approximately 6.4 km, indicating the quake could indeed be felt at the center of Shelbyville.

Question 11

Graph the solution set.
-$$\begin{aligned}
\frac { 3 } { 4 } x - y & \leq 4 \
x & \geq - 1 \
y & \leq - 2
\end{aligned}$$

Accepted Answer

The answer of Graph the solution set.
-\[\begin{aligned}
\frac { 3 }...

Question 12

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The function to be optimized in a linear programming application is called the________function.

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The region in the plane that represents the solution set to a system of constraints is called the________region.

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
| x | < 3 \
| y | < 4
\end{array}$$

Accepted Answer

The answer of Graph the solution set. If there is...

Question 15

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
y \leq - x ^ { 2 } + 3 \
y \leq - x + 2 \
y > - 4
\end{array}$$

Accepted Answer

The answer of Graph the solution set. If there is...

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The process that maximizes or minimizes a function subject to linear constraints is called________programming.

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \leq 16 \
x ^ { 2 } + y ^ { 2 } \geq 49
\end{array}$$

Accepted Answer

The answer of Graph the solution set. If there is...

Question 18

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \leq 64 \
y \geq x \
y \geq 1
\end{array}$$

Accepted Answer

The answer of Graph the solution set. If there is...

Question 19

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$y \leq \frac { 8 } { x }$ $y > 0$ $y < x$

Accepted Answer

The answer of Graph the solution set. If there is...

Question 20

Graph the solution set.
-$$\begin{aligned}
x + y & < 4 \
0 \leq y & \leq 5 \
x & \geq - 2
\end{aligned}$$

Accepted Answer

The answer of Graph the solution set.
-\[\begin{aligned}
x + y &...

Quiz 5: Systems of Equations and Inequalities

Find the indicated system of inequalities. -Write a system of inequalities that represents the points inside the triangle with vertices (2, 1) , (-3, 3) , and (-4, -2) .

Find the indicated system of inequalities. -Write a system of inequalities that represents the points in the first quadrant less than 7 units from the origin.

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } y < e ^ { x } \\y > 4 \\x < 2\end{array}$

Graph the solution set. - $\begin{array} { l } x + 3 y \geq 6 \\x - y \leq - 6\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } x ^ { 2 } + y ^ { 2 } > 16 \\x ^ { 2 } + y ^ { 2 } \leq 64\end{array}$

Graph the solution set. - $\begin{array} { l } 4 x - y > 4 \\x + y < 6\end{array}$

Graph the solution set. - $\begin{aligned}\frac { 3 } { 4 } x - y & \leq 4 \\x & \geq - 1 \\y & \leq - 2\end{aligned}$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function to be optimized in a linear programming application is called the________function.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The region in the plane that represents the solution set to a system of constraints is called the________region.

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } | x | < 3 \\| y | < 4\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } y \leq - x ^ { 2 } + 3 \\y \leq - x + 2 \\y > - 4\end{array}$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The process that maximizes or minimizes a function subject to linear constraints is called________programming.

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 16 \\x ^ { 2 } + y ^ { 2 } \geq 49\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 64 \\y \geq x \\y \geq 1\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $y \leq \frac { 8 } { x }$ $y > 0$ $y < x$

Graph the solution set. - $\begin{aligned}x + y & < 4 \\0 \leq y & \leq 5 \\x & \geq - 2\end{aligned}$

Quiz 5: Systems of Equations and Inequalities

Find the indicated system of inequalities. -Write a system of inequalities that represents the points inside the triangle with vertices (2, 1) , (-3, 3) , and (-4, -2) .

Find the indicated system of inequalities. -Write a system of inequalities that represents the points in the first quadrant less than 7 units from the origin.

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - y<exy>4x<2\begin{array} { l } y < e ^ { x } \\y > 4 \\x < 2\end{array}y<exy>4x<2​

Graph the solution set. - x+3y≥6x−y≤−6\begin{array} { l } x + 3 y \geq 6 \\x - y \leq - 6\end{array}x+3y≥6x−y≤−6​

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - x2+y2>16x2+y2≤64\begin{array} { l } x ^ { 2 } + y ^ { 2 } > 16 \\x ^ { 2 } + y ^ { 2 } \leq 64\end{array}x2+y2>16x2+y2≤64​

Graph the solution set. - 4x−y>4x+y<6\begin{array} { l } 4 x - y > 4 \\x + y < 6\end{array}4x−y>4x+y<6​

Graph the solution set. - 34x−y≤4x≥−1y≤−2\begin{aligned}\frac { 3 } { 4 } x - y & \leq 4 \\x & \geq - 1 \\y & \leq - 2\end{aligned}43​x−yxy​≤4≥−1≤−2​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function to be optimized in a linear programming application is called the________function.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The region in the plane that represents the solution set to a system of constraints is called the________region.

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - ∣x∣<3∣y∣<4\begin{array} { l } | x | < 3 \\| y | < 4\end{array}∣x∣<3∣y∣<4​

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - y≤−x2+3y≤−x+2y>−4\begin{array} { l } y \leq - x ^ { 2 } + 3 \\y \leq - x + 2 \\y > - 4\end{array}y≤−x2+3y≤−x+2y>−4​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The process that maximizes or minimizes a function subject to linear constraints is called________programming.

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - x2+y2≤16x2+y2≥49\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 16 \\x ^ { 2 } + y ^ { 2 } \geq 49\end{array}x2+y2≤16x2+y2≥49​

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - x2+y2≤64y≥xy≥1\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 64 \\y \geq x \\y \geq 1\end{array}x2+y2≤64y≥xy≥1​

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - y≤8xy \leq \frac { 8 } { x }y≤x8​ y>0y > 0y>0 y<xy < xy<x

Graph the solution set. - x+y<40≤y≤5x≥−2\begin{aligned}x + y & < 4 \\0 \leq y & \leq 5 \\x & \geq - 2\end{aligned}x+y0≤yx​<4≤5≥−2​

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } y < e ^ { x } \\y > 4 \\x < 2\end{array}$

Graph the solution set. - $\begin{array} { l } x + 3 y \geq 6 \\x - y \leq - 6\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } x ^ { 2 } + y ^ { 2 } > 16 \\x ^ { 2 } + y ^ { 2 } \leq 64\end{array}$

Graph the solution set. - $\begin{array} { l } 4 x - y > 4 \\x + y < 6\end{array}$

Graph the solution set. - $\begin{aligned}\frac { 3 } { 4 } x - y & \leq 4 \\x & \geq - 1 \\y & \leq - 2\end{aligned}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } | x | < 3 \\| y | < 4\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } y \leq - x ^ { 2 } + 3 \\y \leq - x + 2 \\y > - 4\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 16 \\x ^ { 2 } + y ^ { 2 } \geq 49\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $\begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 64 \\y \geq x \\y \geq 1\end{array}$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $y \leq \frac { 8 } { x }$ $y > 0$ $y < x$

Graph the solution set. - $\begin{aligned}x + y & < 4 \\0 \leq y & \leq 5 \\x & \geq - 2\end{aligned}$