Math Test 1 1029

linear programing

A method for finding the maximum or minimum value of a quantity that is subject to various limitations is called

satisfies both equations in the system.

A solution to a system of linear equations in two variables is an ordered pair that

constraints , corner

A system of linear inequalities is used to represent​ restrictions, or​ _____, on a function that must be maximized or minimized. Using the graph of such a system of​ inequalities, the maximum and minimum values of the function occur at one or more of the​ _____ points.

The​ x-intercept is −2.

According to the example in the video​, which of the following is true about the line that was​ graphed?

The line passes through the point​ (2, 0).

According to the example in the video​, which of the following statements is​ false?

objective

An algebraic expression in two or more variables describing a quantity that must be maximized or minimized is called​ a/an _____ function.

The statement makes sense because linear programming is used to help allocate resources to manufacture products in a way that will maximize profit.

An important application of linear programming for businesses involves maximizing profit.

To solve a system of linear equations by​ graphing, graph both equations in the same rectangular coordinate system. For a system with one​ solution, the coordinates of the point of intersection of the lines is the​ system's solution.

Explain how to solve a system of equations using graphing.

the statement makes sense because the coordinates of the vertices represent the values of the variables in the objective function.

I use the coordinates of each vertex from my graph representing the constraints to find the values that maximize or minimize an objective function.

The statement does not make sense because the graph of the objective function is not required.

In order to solve a linear programming​ problem, I use the graph representing the constraints and the graph of the objective function.

x axis

In the rectangular coordinate​ system, the horizontal number line is called the

origin

In the rectangular coordinate​ system, the point of intersection of the horizontal axis and the vertical axis is called the

y axis

In the rectangular coordinate​ system, the vertical number line is called the

quadrants, 4

The axes of the rectangular coordinate system divide the plane into​ regions, called _____ There are ___ of these regions.

X-Coordanate , y coordinate

The first number in an ordered pair is called the ____ and the second term is called the ___

solution , x ,y, 15>4

The ordered pair ​(9​,6​) is​ a/an _______ of the inequality x+y>4 because when 9 is substituted for​ _______ and 6 is substituted for​ _______ the true statement​ _______ is obtained.

y intercept

The point​ (0,3) lies along a​ line, so 3 is​ a/an ____ of that line.

at right, horizontal, vertical, (0,0)

The rectangular coordinate system is formed using two number lines that intersect ___ angles at their zero points. The ___ line is the​ x-axis and the ___ line is the​ y-axis. Their point of​ intersection, _____ is the origin. Each point in the system corresponds to an ordered pair of real​ numbers, (x,y).

half plane

The set of all points on one side of a line is called a​

graph

The set of all points that satisfy an inequality is called the​ _______ of the inequality.

x- intercept

The​ x-coordinate of the point where a graph crosses the​ x-axis is called the

y=0 , x

To find the​ x-intercept of an​ equation, set ___ and solve the equation for ___

x=0 , y

To find the​ y-intercept of an​ equation, set ___ and solve the equation for ___

A solution with complicated fractions would be difficult to​ "see" as an intersection point on a graph.

What is the disadvantage to solving a system of equations using the graphing​ method?

An ordered pair that satisfies both equations in the system

What is the solution to a system of linear​ equations?

the intersection point.

When solving a system of linear equations by​ graphing, the​ system's solution is determined by locating

The statement is false. The graph of an inequality with the > symbol does not include the​ line, while the s≥ symbol includes the line. Your answer is correct.

the graph of 5x-6y>3 includes the line 5x-6x=3

true linear equation divides

the graph of the linear equation 4x-2y=6 is used to graph the linear inequality 4x-2y>6

solution, satisfies

the ordered pair (4,20) is a/an ___ of the equation y=3x+8 because when 4 is substituted for x and 20 is substituted for y, a true statement is obtained. Also it is said that (4,20) ___ the equation

The statement is false. The test point should be chosen from one of the​ half-planes.

when graphing 3x-5y≥2, to determine which side of the line to shade choose a test point on 3x-5y=2