Identify the vertices of the feasible region and use them to find the maximum and/or minimum value for the given linear programming constraints.

System of Linear Programming:

z=−3x+5y

x+y≥−2

3x−y≤2

x−y≥−4

Maximum value of z:

Minimum value of z

The solution of the inequalities is (0.375, 4.25)

The system of inequalities is given as:

3y > 2x + 12

2x + y ≤ 5

Next, we plot the inequalities on a graph (see attachment)

From the graph, both inequalities intersect at

(x, y) = (0.375, 4.25)

This represents the solution of the inequalities

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Answer:

-1/2

Step-by-step explanation:

-3/8+-1/8=-4/8 which is equal to -1/2

Answer:

1/4

Step-by-step explanation:

(3/8)+(-1/8)

= (3/8) - (1/8)

= 2/8

= 1/4

The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the total amount of money invested, hence:

(0.5* x * 0.11) + (0.5 * x * 0.1) = 420    

x = 4000

The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.

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Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1

Answer: The given equation is

f(x) = x^{4} - 1

x- and y-intercept of the graph of the function f(x) = x^4 - 1 is

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

A graph of the above point is attached

Step-by-step explanation:

Given equation, f(x) = x^{4} - 1

let's assume the above equation with respect to y to find intercept i.e

y = x^{4} - 1 .........................(i)

Now, for the x-intercept put y = 0 in eq.(i)

So, we get,

0 = x^4 - 1

x^4 = 1

x = -1, +1

from above we get the x-intercept (1,0), (−1,0)

Now, for the y-intercept put x = 0 in eq.(i)

So, we get

y = 0^4 - 1

y = -1

from above we get the y-intercept (0, -1)

Therefore, from all above

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

Graph of the given equation f(x) = x^4 - 1 with intercept is

Answer:

Step-by-step explanation:

x is the number of students

(x+5) is the number of students and chaperons

$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have

2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)

The inequality "90 greater-than 2.50 (x + 5) "

90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign

90 ≥ 2.50(x+5)

Al aplicar operaciones de aritmética básica, tenemos que la mitad de 980 es igual a 490.

En esta pregunta tenemos un número par de tres dígitos que termina en cero. De acuerdo con la teoría numérica, un número de base 10 de más de un dígito que tenga un número par relacionado con números impares como último dígito, tendrá un número impar si es dividido por 2.

Ahora bien, si tenemos un número par con más de un dígito que termina en cero, entonces tendrá un número par que termina en 0 si es dividido por 2.

Si dividimos 980 por 2, entonces tenemos 490 como resultado:

980/2 = 98/2 × 10 = 49 × 10 = 490

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Given :

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}[/tex]

[tex] \: [/tex]

Let's solve by using midpoint formula :

[tex] \: [/tex]

[tex] \bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}[/tex]

[tex] \: [/tex]

[tex] \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}[/tex]

[tex] \: [/tex]

[tex] \: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}[/tex]

[tex] \: [/tex]

[tex]\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}[/tex]

[tex] \: \: [/tex]

[tex] \underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓[/tex]

Hope Helps! :)

Answer:

-2

Step-by-step explanation:

When x = 1, 3x² + 2x - 7 = -2.

The value of x comes out to be 6 from the algebraic equation.

Solving the Given Algebraic Equation for x:

Given algebraic equation is,

3x + 12 = 8x - 18

⇒ 12 = 8x - 3x -18

8x - 3x - 18 = 12

5x - 18 = 12

5x = 12 + 18

5x = 30

x = 30 / 5

x = 6

What is an algebraic equation?

A mathematical statement in which two expressions are put equal to one another is known as an algebraic equation. One or more variables, coefficients, and constants make up an algebraic equation in most cases. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.

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Answer: [tex](x,y)=\{(-1,1), (0,4) \}[/tex]

Step-by-step explanation:

[tex]3x^2 +6x+4=-3x^2 +4\\\\6x^2 +6x=0\\\\x^2 +x=0\\\\x(x+1)=0\\\\x=-1, 0\\\\x=-1 \longrightarrow y=1\\\\x=0 \longrightarrow y=4\\\\\therefore (x,y)=\{(-1,1), (0,4) \}[/tex]

The solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given quadratic equations are given as below:-

y = 3x² + 6x + 4

y = -3x² + 4

Equate the equations and solve for the value of x.

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

x² + x = 0

x ( x + 1 ) = 0

x = 0 and x = -1

At x=0 and x=-1 the values of y are calculated as below:-

y = -3x² + 4

y = 0+ 4 = 4

y = -3 + 4 = 1

Therefore, the solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).

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Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).

The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.

In step 5 where the multiplication property of equality is applied, we would have:

sin(A) = CD/b

Multiply both sides by b

sin(A) × b = CD/b × b

b(sin A) = CD

CD = b(sin A)

This same property is applied to sin B = CD/a to get CD = a(sin B).

Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).

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Answer:

it's answer came 20000o

Answer:

hey its me again so the answer is 11.

I'm sure because I did this.

Answer:

2

Step-by-step explanation:

You have the correct answer selected: 2.

The reason for this is that when there are exponents inside and outside of the parenthesis like this, they are multiplied.

2 times 2 is 4. That's why (8^2)^2 = 8^4

Answer:

p = 2

Step-by-step explanation:

[tex](8^{2}) ^{p}[/tex] = [tex]8^{4}[/tex]

  [tex]8^{2p}[/tex] =    [tex]8^{4}[/tex]

   [tex]8^{p}[/tex] = [tex]8^{\frac{4}{2}[/tex]

    p = 2

Answer:

CIRCLE

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The rules that define the piecewise function graphed are as follows:

y = x + 2, y = 5.

A piecewise function is a function that has different definitions, depending on the input.

In this problem, for x between 0 and 3, a linear function is given, with slope given as follows:

m = (5 - 2)/(3 - 0) = 1.

The y-intercept is of 2, as y = 2 when x = 0, hence the definition is:

[tex]y = x + 2, 0 \leq x \leq 3[/tex]

For x greater than 3, the function is constant at y = 5, hence the definition is:

y = 5, x > 3.

Hence, the rules that are used to define the piecewise function graphed are as follows:

y = x + 2, y = 5.

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Answer:   About the building of his bed

Answer:

116

Step-by-step explanation:

zinc : copper

4      :     11

11 = 319

zinc = 4 / 11 * 319

Zinc = 116

Answer:

[tex]2\sqrt{6} +4[/tex]

Step-by-step explanation:

Let x be that unknown number.

From the information given from the question, we can deduce:

[tex]x^{2} -8=8x[/tex]

From here, we can solve for x to find what is the number.

[tex]x^{2} -8=8x\\x^{2} -8x-8=0[/tex] (Quadratic Equation)

From here we can use the Quadratic Formula to solve for x.

[tex]x=\frac{-b+/-\sqrt{b^{2} -4ac} }{2a}[/tex]

In this case,

a = 1, b = -8 , c = -8

We substitute a, b and c to find x.

[tex]x=\frac{-(-8)+/-\sqrt{(-8)^{2}-4(1)(-8) } }{2(1)} \\= 2\sqrt{6} +4[/tex]

(Reject the negative solution)

Answer: Option (1)

Step-by-step explanation:

[tex]3x^3 - 6x^2 + 30x-20=-20\\\\3x^3 - 6x^2 + 30x=0\\\\3x(x^2 - 2x+10)=0\\\\[/tex]

So, either [tex]x=0[/tex] or [tex]x^2 -2x +10=0[/tex]

For the second case, we know x=0.

For the second case, we can use the quadratic formula.

[tex]x=\frac{2 \pm \sqrt{(-2)^2 - 4(1)(10)}}{2}\\\\x=1 \pm 3i[/tex]

An appropriate numerical summary is descriptive statistics.

It should be noted that a numerical summary means a number used to describe specific characteristics of a data set.

In this case, descriptive statistics can be used. This is used to describe the data set.

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Answer:

Step-by-step explanation:

A=6x²

[tex]\frac{dA}{dt} =6\times 2x \times \frac{dx}{dt} \\\frac{dA}{dt}=12x \frac{dx}{dt}[/tex]

Answer:

E

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

Consider the triangle on the left

3rd angle = 180° - 60° - 90° = 180° - 150° = 30°

the 3rd angle of the triangle on the left = 30° ( vertically opposite angle ), so

∠ 1 = 180° - 30° - 65° = 180° - 95° = 85°

The plotting of the inequalities was done using geogebra online graphing calculator. The graph is attached.

Inequalities are the mathematical expressions in which both sides are not equal. It should be noted that in inequality, unlike in equations, we compare two values.

The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Inequality is an expression used to show the nonequal comparison of numbers and variables.

Given the system of inequalities:

3y > 2x + 12

3y - 2x > 12   (1)

2x + y < -5    (2)

Plotting the inequalities using GeoGebra online graphing calculator. The graph is attached

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Answer: b and e

Step-by-step explanation:

b - the slope is positive

the slope is 8 not negative 8 because, 4+4/2-1 = 8/1 = 8 since subtracting 4 and -4 makes it 4+4

e - it is possible for x to be positive and for y to be negative

The length of AC is 12 units . Option D

The formula for area of a kite is given thus;

Area = [tex]\frac{p * q}{2}[/tex]

Where p and q are the lengths

Area of kite = 48 square units

BD, q = 8 units

AC , p = unknown

Substitute the values

[tex]48 = \frac{AC * 8}{2}[/tex]

Cross multiply

[tex]AC * 8 = 48 * 2[/tex]

[tex]8AC = 96[/tex]

[tex]AC = \frac{96}{8}[/tex]

[tex]AC = 12[/tex] units

Thus, the length of AC is 12 units . Option D

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Answer:option 4

Step-by-step explanation: