Instructions: Identify the vertices of the feasible region for the given linear programming constraints.

Optimization Equation: z=−3x+5y

Constraints:

x+y≥−2
3x−y≤2
x−y≥−4

Fill in the vertices of the feasible region:

(0, )
(-3, )
(3, )

Answer: c -2

Step-by-step explanation:

y=-2x+3

-2 is the slope because y= mx+b and m is the slope

Answer:

a) D [-2x +3] | b) D [-2]

Step-by-step explanation:

Get it into the form y=mx+b

To do this subtract 2x from 2x+y=3 to get y= -2x+3

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Part B: Find the slope

The slope is the coefficient in front of the x in the slope-intercept form.

In this case, it is -2.

Therefore, -2 is the slope of the line.

Answers: [-2x + 3] and [-2]

The evaluation of the functions in the question are as follows;

1. a) [tex]y = \dfrac{1}{x^2+5} -3[/tex]is not a quadratic function

b) The function is a quadratic function

c) The function is a quadratic function

d) The function is a quadratic function

2. Please find attached the graph of the function, y = -2·(x + 3)² + 4, created (for clarity) with MS Excel

a) The axis of symmetry is; x = -3

b) The maximum value is; (-3, 4)

c) The x-intercepts are; √2 - 3, and -√2 + 3

d) y-intercept is (0, -14)

e) The domain is the set of all real numbers

The range is (-∞, 4]

A function is a rule that maps an input value unto an output, such that each input has exactly one output.

A quadratic function is a function of the form; y = a·x² + b·x + c

a) The function [tex]y = \dfrac{1}{x^2+5} -3[/tex], when simplified, we get;

[tex]y = \dfrac{1 - 3\cdot x^2 - 15}{x^2+5}[/tex], which is a rational polynomial.

Therefore, the function is not a quadratic function.

b) x² = y - 1

y = x² + 1

The above function is in the form; y = a·x² + b·x + c, where;

a = 1, b = 0, c = 1

c) y = 3·x - 7 + 4·x²

The above function is in the form y = a·x² + b·x + c, where;

a = 4, b = 3, and c = -7

d) The function y = 6·x - 3·√x can be expressed as; √x = z

Therefore; z² = x

Therefore; y = 6·x - 3·√x = 6·z² - 3·z

y = 6·z² - 3·z

The above function is a quadratic function, therefore, the function;

y = 6·x - 3·√3 is a quadratic function

2. The function y = -2·(x + 3)² + 4 is in the vertex form of the equation of a quadratic equation; y = a·(x - h)² + k

Where;

a = The leading coefficient

(h, k) = The coordinates of the vertex

Comparing the values, we get;

The vertex, (h, k) = (-3, 4)

a = -2

When x = 0, we get; y = -2·(0 + 3)² + 4 = -2 × 9 + 4 = -14

With a vertex of (-3, 4), we get;

When x = -6, y = -14

The graph can be obtained by drawing a parabola with vertex at (-3, 4), and passing through the points (0, -14), and (-6, -14)

Please find attached the graph of the function y = -2·(x + 3)² + 4, created with the points (0, -14), (-6, -14), and vertex point (-3, 4), created with MS Excel

a) The axis of symmetry is the line about which the graph is symmetrical

The axis of symmetry is the line x = -3

b) The maximum value is the vertex of the graph, which is the point (-3, 4)

c) The x-intercept are the point the graph intersects the x-axis, which are obtained by plugging in y = 0, as follows;

y = 0 = -2·(x + 3)² + 4

(x + 3)² = -4/(-2) = 2

x + 3 = ±√(2)

x = ±√(2) - 3

The x-intercepts are; x = √2 - 3, and -√2 - 3

d) The y-intercepts are the point the graph intersects the y-axis, which is the point where x = 0

Therefore, the y-intercept is the point (0, -14)

e) The domain is the set of possible input values or x-values

The domain of the function, as presented in the graph is the set of all real numbers

The domain is; (-∞, ∞)

The range is the set of the possible y-values

The graph of the function indicates that the maximum y-value is the point y = 4

Therefore, the range of the function is; -∞ < y ≤ 4, which is (-∞, 4]

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Answer: y = -x+7

Step-by-step explanation:

Let's first set up it in slope-intercept form.

y = -x+b

We can find b using point (4,3).

Substitute 4 for x and 3 for y to get:

-3 + b = 4

b = 7

Therefore, the line is y = -x+7

Answer:

We can start solving the problem by using a system of equations. Let x be the number of pieces of fruit on a small tray, and y be the number of pieces of fruit on a large tray.

From the information given, we know that:

Yesterday: x + 4y = 166 (1)

Today: 4x + 4y = 232 (2)

We have two equations and two unknowns, so we can use substitution to solve for one variable in terms of the other, and then substitute that back into the other equation.

From equation (1) we can solve for x:

x = 166 - 4y

Now we can substitute this into equation (2)

4(166 - 4y) + 4y = 232

Simplifying and solving for y:

-672 + 16y = 232

16y = 904

y = 56.5

This means that each large tray has 56.5 pieces of fruit.

Now we can substitute this value back into the first equation:

x + 4(56.5) = 166

x = 166 - 226

x = -60

This solution doesn't make sense, because the number of pieces of fruit can't be negative. This means that there is no solution to the system of equations, and it is impossible to determine the number of pieces of fruit on each size tray based on the information given.

Step-by-step explanation:

Answer:

0 votes

Step-by-step explanation:

Answer:fx

Step-by-step explanation:

The value of the x is 11.

What are vertically opposite angles?

Opposite angles are the angles directly opposite each other where two lines cross. The intersection point is called the vertex, which is where the lines connect to form the angle. Opposite angles are also called vertical angles. In this instance, the word vertical refers to the vertex as opposed to direction.

We have given,

Two opposite angles:

(6x + 1)°, and 67°

So, We need to determine the value of x.

We know that the property of opposites angles, which the opposite angles are equal to each other.

So, (6x + 1)° = 67°

By calculating further:

6x + 1 = 67

6x = 67 - 1

6x = 66

x = 66/6

x = 11

Hence, the value of the x is 11.

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Therefore , the solution to the given problem of function comes out to be ss a result, Rolle's Theorem remains true.

Mathematics deals with numbers and their variants, formulae and associated structures, geometries and their areas, and locations where they might be found. The term "function" describes the connection between a group of input, of which each has a corresponding output. A function is an association among inputs and outputs where each input results in a single, unique output. A realm as well as a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On activities, one-to-one activities, many-to-one functions, within operations, and on functions are the four main categories of functions that are available.

Here,

Consider

f(-1)=1-[tex](-1 )^{\frac {2}{3}}[/tex]=0

and f(1)=1-[tex](-1 )^{\frac {2}{3}}[/tex]=0

So, f(-1)= f(1) (1)

As a result of differentiating f(x) with regard to x, we now have

f'(x)= -2 / 3

Consequently, f'(0) is false.

So, at 0inleft (-1,1 ), f cannot be deduced.

Therefore, the given function in the range (-1,1) does not satisfy Rolle's theorem.

As a result, no c exists in (-1,1) for which f'(c )=0 even though f(-1)=f(1 ).

As a result, Rolle's Theorem remains true.

Therefore , the solution to the given problem of function comes out to be ss a result, Rolle's Theorem remains true.

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The probability that the hospital has 7 fatalities this week is approximately 0.0199

The probability that the hospital has 7 fatalities in a week, given an average of 7 fatalities per week, can be calculated using the Poisson distribution. The Poisson distribution is a discrete probability distribution that models the number of events (in this case, fatalities) that occur in a fixed interval of time (in this case, a week) with a certain average rate (in this case, 7 fatalities per week). The probability of k events happening in a given interval of time is given by the following formula:

P(k;λ) = (e^(-λ))*(λ^k)/k!

Where λ is the average number of events per interval of time and k is the number of events we are interested in.

In this case, we are looking for the probability that there are 7 fatalities this week, given that the average number of fatalities per week is 7. So we can plug in the values into the equation:

P(7;7) = (e^(-7))(7^7)/7! =0.149

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The value of x in the following parallelogram is 15

You should recall that a parallelogram is a quadrilateral whose opposite sides are equal and parallel

The given sides are

This means that

X + 10 = 2x -5

Collecting like terms we have

x-2x = -5-10

-x = -15

Dividing by -

We have x= 15

Therefore x is 15 in the parallelogram.

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The solution to the expression -11/14 x (-1/17) is 11/238

From the question, we have the following parameters that can be used in our computation:

-11/14x(-1/17)

Express properly

So, we have the following representation

-11/14 x (-1/17)

Remove the brackets

This gives

-11/14 x (-1/17) = 11/14 * 1/17

So, we have

-11/14 x (-1/17) = 11/238

Hence, the solution is 11/238

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Cos 120 is in the second quadrant and therefore is a negative signed value

A plane is divided into four sections, or quadrants, by an x-axis and a y-axis in a rectangular coordinate system. The letter O stands for the origin, which is the place where the two axes converge.

In the first quadrant, there are angles between 0 and 90.

In the second quadrant, there are angles between 90 and 180.

In the third quadrant, there are angles between 180 and 270.

In the fourth quadrant, there are angles between 270 and 360.

Cos is only positive in the first quadrant and in the 4th quadrant and always negative in the second and third quadrant

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The slope of the given line that passes through (4, 2) and (6, 3) is m = 1/2.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given are the statements regarding the slope of the line as given.

The line passes through the points -

(4, 2) and (6, 3)

The slope of the line will be -

m = (3 - 2)/(6 - 4)

m = 1/2

Therefore, the slope of the given line that passes through (4, 2) and (6, 3) is m = 1/2.

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When A point is (3, 1) and B point is (-1 , -1), the midpoint of AB is ( 2, 1) . The line segment's exact midway is where the midpoint is located.

The term "midpoint" describes a point along a line that connects two points. The midway is situated between the two reference locations, which are the line's ends. The line connecting these two places is split into two equally sized sections by the middle. A point that splits a line segment into two equal halves is known as the midway. In other words, the line segment's exact midway is where the midpoint is located. It is demonstrably true that the middle of a number line has the same value as the average of any two matching places on the line.

given

midpoint of AB is equal to (x2 - x1) / 2 (3 + 1) / 2 = 2.

the midpoint of AB is 1

the midpoint of AB is (y2 - y1)/2

= (1+1)/2.

= ( 2 ,1 )

When A point is (3, 1) and B point is (-1 , -1), the midpoint of AB is ( 2, 1) .

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Answer:[tex]\frac{15}{8}[/tex] or [tex]2 \frac{7}{8}[/tex]

Step-by-step explanation:

Adding,

[tex]\frac{1}{2}+\frac{3}{4}+\frac{5}{8} =\frac{4+6+5}{8} =\frac{15}{8}[/tex][tex]=2\frac{7}{8}[/tex]

Answer: A. To find out how much concentrated cleaner the worker used, we can set up the equation: x + 15 = 5x/2, where x is the amount of concentrated cleaner used in quarts. Solving for x, we find that the worker used 15 quarts of concentrated cleaner.

B. Since we know that the worker used 15 more quarts of water than concentrated cleaner, we can find out how much water she used by adding 15 quarts to the amount of concentrated cleaner used. In this case, the worker used 15 quarts + 15 quarts = 30 quarts of water.

C. To find out how much solution the worker made, we add the amount of concentrated cleaner used and the amount of water used. In this case, the worker made 15 quarts + 30 quarts = 45 quarts of solution.

Step-by-step explanation:

The number of items is discrete and the total time is a continuous variable recorded by the pet store.

The two things recorded by the pet store;

first is the number of items purchased and another is the time between the given interval of 8 am to 11 am.

we know that

the number of items was counted so it will be discrete and the total time was measured so it will be a continuous variable.

Therefore, the types of variables recorded by the pet store are the number of items as a discrete variable and the total time as a continuous variable.

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Answer:

y = 3x -8

Step-by-step explanation:

8 times less means something will have to be (-8)

3 times the value of x is equal to (3x)

by looking at the answers we can deduct that our answer in fact is y = 3x -8

The correct option is B.

The Equation that represents the line that has a slope of 1/3 and an x-intercept of 5 is y-0 = 1/3(x-5)

The slope of a line is the measure of the steepness of a line and its direction. It can be used to predict whether the lines are parallel, perpendicular, or none.

The slope of any line can be calculated using any two distinct points lying on the line.

y -y1 = m(x-x1)

where y1 = 0

x1 = x-intercept = 5

y-0 = 1/3(x-5)

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Step-by-step explanation:

10x + 17 + 8X - 31 + 6x - 8 = 180

Use this equation and solve this equation and you will find the answer

The simplest forms of the expressions are;

a) 1/4y^10

b) 1/243d^18q

We have to note that the simplest form is the form of the expression that we can not be able to break down further. We mean that when we get to the simplest form, there is no other way that we can be able to express it.

Let us now try to use the laws of the exponents to bring the expressions to the simplest forms.

a) 3(y^-4)^4/12y^-6

1/4y^-16/y^-6

1/4y^-10

1/4y^10

b) (3d^-2)^-4/3d^10q

3^-4 d^-8/3d^10q

1/243d^18q

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Answer: 30

Step-by-step explanation:

n= -3

-3^2 = 9

9(-3) = -27

9-(-27)-6 = 30

Pretest-posttest experimental designs are common is true for the t-test for dependent means rather than t-tests in general.

The correct answer is option B.

The use of pretest-posttest designs extends the posttest alone design with nonequivalent groups, one of the most fundamental methods for assessing the effectiveness of an intervention. One group in this two-group design undergoes therapy, and the final results are produced for the other group.

In conclusion, quasi-experimental design has long been a popular research methodology. An intervention that has been delivered to a group of study participants may be easily evaluated using pre-test and post-test designs, a sort of quasi-experimental research. A pretest is an assessment tool used by study participants before they get any form of therapy. Participants in a study are given a posttest, which is an evaluation tool, following their participation in the study.

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D

ok is the force that I have to go in and out for the June exam and the Zumba

Answer:

Step-by-step explanation:

1)  m∠1 = m∠2

4x - 1 = 2x + 7

2x = 8

x = 8/2 = 4

2)  m∠1 = (m∠YWX) / 2 = 62/2 = 31

3)  AB is 4 squares long.  Start at A, go over 2 squares, then draw a line straight up to point C.

4)  Altitude is the height of a triangle.  Find the midpoint of the bottom line, then draw a line straight up to the vertex (top of the triangle).  Your drawn line should form a right angle with the bottom line.

Answer:

5

Step-by-step explanation:

adde it all upa and get the answer