Factor completely 10x2 + 2x − 8

Answer: 24

Step-by-step explanation:

1. Number Them

Elf and Dwarf = 1

Hobbit = 2

Wizard = 3

Man = 4

* Elf and Dwarf are put together so that they are always sitting together

2. Multiply

1 x 2 x 3 x 4 = 24

Answer:

D

Step-by-step explanation:

I took the quiz :)

The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.

1. Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems.
maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

Now, To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 3/4), (0, 0), and (3, 0).

        z = x₁ + 2x₂ = (0) + 2(3/4)

                    = 1.5z = x₁ + 2x₂ = (0) + 2(0) = 0

                        z = x₁ + 2x₂ = (3) + 2(0) = 3

The maximum value of the objective function z is 3, and it occurs at the point (3, 0).

Hence, the optimal solution is (3, 0), and the optimal value of the objective function is 3.2.

maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

To find the optimal solution and the optimal value of the objective function,

        evaluate the objective function at each corner of the feasible region:

                                (0, 0), (3, 0), and (2, 5).

                          z = x₁ + x₂ = (0) + 0 = 0

                          z = x₁ + x₂ = (3) + 0 = 3

                           z = x₁ + x₂ = (2) + 5 = 7

The maximum value of the objective function z is 7, and it occurs at the point (2, 5).

Hence, the optimal solution is (2, 5), and the optimal value of the objective function is 7.3.

maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 1), (2, 0), and (5, 1).

                         z = 3x₁ + 4x₂ = 3(0) + 4(1) = 4

                      z = 3x₁ + 4x₂ = 3(2) + 4(0) = 6

                      z = 3x₁ + 4x₂ = 3(5) + 4(1) = 19

The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.

Learn more about linear programming

brainly.com/question/32634451

#SPJ11

Answer:

76666.6666667

Step-by-step explanation:

Answer:

-157

Step-by-step explanation:

25+(-13×14)=-157

The answer is B: 1/16

If a pack of 50 pencils cost $5.45 then a single pencil costs $0.109.  

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost of a pack of 50 pencils = $5.45.

To find the cost of one pencil,

Use ratio property,

50 pencil costs = $5.45

1 pencil costs = 5.45 / 50 =  $0.109

Cost of one pencil is $0.109.  

To learn more about Ratio on :

https://brainly.com/question/13419413

#SPJ5

(b)  The range of the function is (-∞, 1] U [1, +∞).

(d) The limit as x approaches negative infinity is 1.

(e) lim(x→1+) f(x) = 1 / 1 = 1, The limit as x approaches 1 from the positive side is 1.

(a) Sketching the graph of the function f(x) = \((x^4 - 1) / x^4:\)

To better understand the properties of the function, let's simplify it:

f(x) =\((x^4 - 1) / x^4\)

By factoring the numerator as a difference of squares, we get:

f(x) =\([(x^2)^2 - 1] / x^4\)

Now we can simplify further:

f(x) = \([(x^2 + 1)(x^2 - 1)] / x^4\)

Notice that (x² - 1) is a difference of squares and can be factored as (x - 1)(x + 1):

f(x) = \([(x^2 + 1)(x - 1)(x + 1)] / x^4\)

From this expression, we can observe the important properties of the function:

1. The function is defined for all real numbers except x = 0 since division by zero is undefined.

2. The function has vertical asymptotes at x = 0 and x = ±1.

3. The function is positive for x < -1 and x > 1, and negative for -1 < x < 0.

4. The function crosses the x-axis at x = -1 and x = 1.

To sketch the graph, you can use an online graphing tool like Desmos or Wolfram Alpha. The graph will show the vertical asymptotes, the x-intercepts, and the overall shape of the function.

(b) Domain and range of the function:

The domain of the function f(x) is all real numbers except x = 0, as division by zero is undefined.

The range of the function f(x) can be determined by analyzing the behavior of the function as x approaches positive and negative infinity. As x approaches infinity, the function approaches 1 since the higher powers dominate the fraction. As x approaches negative infinity, the function also approaches 1. Therefore, the range of the function is (-∞, 1] U [1, +∞).

(c) Partial fraction expansion of f(x):

To find the partial fraction expansion, we start with the expression we simplified earlier:

f(x) = \([(x^2 + 1)(x - 1)(x + 1)] / x^4\)

To expand this into partial fractions, we need to factor the denominator:

x⁴ = x² · x²

The partial fraction expansion will have the form:

f(x) = A/x + B/x² + C/x³ + D/x⁴

To find the values of A, B, C, and D, we can equate the numerators:

(x² + 1)(x - 1)(x + 1) = A · x³ + B · x² + C · x + D

Now we can solve for A, B, C, and D by expanding the left side and comparing the coefficients of the corresponding powers of x.

(d) Limit as x approaches negative infinity:

lim(x→-∞) f(x) = lim(x→-∞) [(x⁴ - 1) / x⁴]

Since the highest power in the numerator is x⁴, and the highest power in the denominator is also x⁴, we can apply the rule of limits for rational functions:

lim(x→-∞) f(x) = (leading coefficient of the numerator) / (leading coefficient of the denominator)

In this case, the leading coefficients are both 1:

lim(x→-∞) f(x) = 1 / 1 = 1

Therefore, the limit as x approaches negative infinity is 1.

(e) Limit as x approaches 1 from the positive side:

lim(x→1+) f(x) = lim(x→1+) [(x⁴ - 1) / x⁴]

We can again apply the limit rule for rational functions since the highest power in the numerator is x⁴, and the highest power in the denominator is also x⁴:

lim(x→1+) f(x) = (leading coefficient of the numerator) / (leading coefficient of the denominator)

Again, both leading coefficients are 1:

lim(x→1+) f(x) = 1 / 1 = 1

Therefore, the limit as x approaches 1 from the positive side is 1.

Learn more about partial fraction expansion here:

https://brainly.com/question/31707489

#SPJ11

If the marginal productivity of capital is high, then the rental rate of capital will be high, and vice versa.Therefore, in a competitive, profit-maximizing economy with constant returns to scale, the distribution of national income between labor and capital is determined by the marginal productivity of labor and capital.

In a competitive, profit-maximizing economy with constant returns to scale, the distribution of national income between labor and capital is determined by the marginal productivity of labor and capital.Let us understand the concept and terms mentioned in this problem.The distribution of national income between labor and capital is a key economic concept. This refers to the division of a country's total income between labor (workers) and capital (owners of businesses).In a competitive, profit-maximizing economy, firms aim to maximize their profits by producing goods or services that generate the highest returns at the lowest cost. This is achieved by using the factors of production such as labor and capital in the most efficient manner to produce goods and services.Constant returns to scale refer to a production function where output increases in direct proportion to an increase in all inputs. That is, if a firm doubles its inputs, it will also double its output.Marginal productivity is the additional output that is produced by adding one more unit of a factor of production while holding all other factors constant. In a perfectly competitive market, the wage rate is determined by the marginal productivity of labor. If the marginal productivity of labor is high, then the wage rate will be high, and vice versa. Similarly, in a perfectly competitive market, the rental rate of capital is determined by the marginal productivity of capital. If the marginal productivity of capital is high, then the rental rate of capital will be high, and vice versa.Therefore, in a competitive, profit-maximizing economy with constant returns to scale, the distribution of national income between labor and capital is determined by the marginal productivity of labor and capital.

To know more about marginal visit:

https://brainly.com/question/28481234

#SPJ11

Answer:

105 cm squared

Step-by-step explanation:

15×6 to get the rectangle =90

then we have a triangle left so you do 15- 9 for the base =6 and multiply that by hight (6×5=30) and since it's a triangle and not a square we have to divide that answer by 2 and we get 15. Add those together, we get 105. Hope that helped!

The area of the shape below is 105 cm².

The area of a rectangle is calculated by multiplying the length and width of the rectangle.

The area of a triangle is equal to half of the product of the triangle's base and height.

Cut the shape given into a triangle and a rectangle as given in the following figure. Then the area of the shape is the sum of the area of the triangle and the area of the rectangle. In the shape, we can clearly specify that the base of the triangle is (15-9) cm=6cm and the height is

(11-6)cm=5cm.

Thus,

The area of the rectangle in the figure is (6×15) cm²=90 cm², and

the area of the triangle in the figure is (1/2)(6×5) cm²=15 cm².

Hence, the area of the shape is 90+15 cm² = 105 cm².

To learn more about area visit- https://brainly.com/question/27683633?referrer=searchResults

#SPJ2

Answer:

heres the graph

Step-by-step explanation:

The opposite angles of the cyclic quadrilateral are equal to 180 degrees which are supplementary angles.

If the quadrilateral is inscribed in a circle then the quadrilateral is known as a cyclic quadrilateral.

A quadrilateral can be inscribed in a circle, if and only if, the opposite angles in that quadrilateral are supplementary.

We know that the sum of the opposite angles of the cyclic quadrilateral is equal to 180 degrees.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

More about the cyclic quadrilateral link is given below.

https://brainly.com/question/15061291

#SPJ1

Answer:

Step-by-step explanation:

(a+2,b)=(4,5)

Since the points are equal we can equate them to find a

Comparing a + 2 to 4

We have

a + 2 = 4

Send 2 to the right side of the equation

a = 4 - 2

We have the final answer as

Hope this helps you

Step-by-step explanation:

Here,

according to the question,

(a+2, b)=(4,5)

since, they are equal, equating with their corresponding elements we get,

(a+2)=4

or, a= 4-2

Therefore, the value of a is 2.

Also you can find value of b in same way,

b=5.

Therefore, the value of a abd b are 2 and 5 respectively.

Hope it helps...

72 miles Sophie bike last week. we get the answer by making and solving equation.

Let's take x miles, Sophie swam

from the question we get,

she runs ⇒3 × x = 3x miles

she biked ⇒ 3 × 3x = 9x miles

Then by solving, ⇒3x + 9x + x = 104

                          ⇒ 13x = 104

                          ⇒ x = 8

therefore, we get

9x = 9 × 8

    = 72 miles

lastly, we get that she biked 72 miles last week.

There are two types of equations: identities and constraints. The ID applies to all values ​​of the variable. Constraint expressions apply only to specific values ​​of variables. Equations are written as two expressions joined by an equal sign.

There are three main forms of linear equations. Point-slope format, standard format, and slope-intercept format.

Learn more about the equation here: https://brainly.com/question/2972832

#SPJ1

Answer:

i can't see that

Step-by-step explanation:

plzz sent me a clear photo

Answer:

1. 1

2. 1  ⋅  10 ^24

3. 1000000000

4. 1

5. 1  ⋅  10 ^20

6. 1  ⋅  10 ^30

7. 1  ⋅  10 ^27

8. 10000

9. 0.01

10. 0.0001

11. 0.1

Hopefully these are right, I simplified all of the problems...sorry if they are wrong

Step-by-step explanation:

Answer:

Let xxx be the number of days Addison can afford to rent.

The cost of renting the car for xxx days is 20*x.

The cost of driving 100 miles is 0.10*100 = 10.

The total cost of renting the car and driving is 20*x + 10.

Addison wants to spend at most $80, so we have the inequality 20*x + 10 <= 80.

Solving for xxx, we get x <= 3.

Therefore, Addison can afford to rent the car for at most 3 days.

We can drag the particles in mass/grams measurement to the corresponding descriptions as follows:

1.  1.6744 × 10⁻²⁴: Two electrons and 0ne proton

2. 5.021 × 10⁻²⁴: Two protons and one neutron

3. 5.0224 × 10⁻²⁴: One proton and two neutrons

4. 3.3484  × 10⁻²⁴: One electron, one proton, and one neutron

To match the measurements to the descriptions first note that one neutron is 1.6749 × 10⁻²⁴. One proton is equal to  1.6726 × 10⁻²⁴ and one electron is equal to  9.108 × 10⁻²⁸.

To obtain the right combinations, we have to add up the particles to arrive at the constituents. So, for the figure;

1.6744 × 10⁻²⁴, we would

Add 2 electrons and one proton

= 2(9.108 × 10⁻²⁸) + 1.6726 × 10⁻²⁴

= 1.6744 × 10⁻²⁴

The same applies to the other combinations.

Learn more about electrons and protons here:

https://brainly.com/question/1481324

#SPJ1

The normal price of each chair is

The percentage off the normal price is

The percentage of the present price of each chair will be

To calculate the present value of one chair, we will use the formula below

By substituting the values, we will have

Since Mr .Krabs bought 4 chairs, the amount he spent will be

By substituting the values, we will have

Therefore,

The amount Mr.Krabs spent is = $6.30

The sets in which the number 6/7 is an element are: A. real numbers, D. rational numbers, and F. integers.

To determine which sets contain the number 6/7 as an element, we need to understand the definitions of the sets and their characteristics.

A. Real numbers: The set of real numbers includes all rational and irrational numbers. Since 6/7 is a rational number (it can be expressed as a fraction), it is an element of the set of real numbers.

B. Whole numbers: The set of whole numbers consists of non-negative integers (0, 1, 2, 3, ...). Since 6/7 is not an integer, it is not an element of the set of whole numbers.

C. Natural numbers: The set of natural numbers consists of positive integers (1, 2, 3, ...). Since 6/7 is not an integer, it is not an element of the set of natural numbers.

D. Rational numbers: The set of rational numbers consists of all numbers that can be expressed as fractions of integers. Since 6/7 is a rational number, it is an element of the set of rational numbers.

E. Irrational numbers: The set of irrational numbers consists of numbers that cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. Since 6/7 can be expressed as a fraction, it is not an element of the set of irrational numbers.

F. Integers: The set of integers consists of positive and negative whole numbers (..., -3, -2, -1, 0, 1, 2, 3, ...). Since 6/7 is not an integer, it is not an element of the set of integers.

Therefore, the sets in which the number 6/7 is an element are: A. real numbers, D. rational numbers, and F. integers.

Learn more about integer here:

https://brainly.com/question/490943

#SPJ11

Answer:

The amount is $239.43

Step-by-step explanation:

The amount she will earn after 5 years is given by

A= p(1+r/n)^(nt)

P = $200

r = 0.036

n = 12*5 = 60

t = 5

A= 200(1+0.036/60)^(300)

A= 200(1+0.0006)^(300)

A= 200(1.0006)^300

A= 200(1.19715)

A= 239.43

The amount is $239.43

Answer:

She will earn $1,126.32 from interest.

Step-by-step explanation:

I did it on edmentum and this was the right answer

Using the circumference of the circle, it is found that:

About 7.1 feet of railing needs to be replaced.

The circumference of a circle of radius r is given by:

\(C = 2\pi r\)

It is equivalent to 360º.

In this problem, the diameter is of 30 feet, hence the radius is 15 feet, so:

\(C = 2\pi (15) = 30\pi\)

Then, considering that the circumference is equivalent to 360º, the length to be replaced is given by:

\(L = \frac{27}{360} \times 30\pi = 7.1\)

About 7.1 feet of railing needs to be replaced.

More can be learned about the circumference of a circle at https://brainly.com/question/25846963

Answer: 7.1

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

Answer:

√5, 2, −13/5,−2, −9/4

Step-by-step explanation:

You basically just Calculate all of the numbers and order them from greatest to least, that's it.

\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 4700\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &11 \end{cases} \\\\\\ 4700=Pe^{0.04\cdot 11} \implies 4700=Pe^{0.44}\implies \cfrac{4700}{e^{0.44}}=P\implies 3027\approx P\)

Answer:

yes

Step-by-step explanation:

Answer:

The question is incorrect. please provide a diagram.

The given points H, I, J, and K form a parallelogram.

The slopes of the sides can be calculated using the formula:

Slope = (change in y) / (change in x)

Slope of side HI:

= (1 - (-2)) / (7 - 4) = 3 / 3 = 1

Slope of side IJ:

= (4 - 1) / (4 - 7) = 3 / (-3) = -1

Slope of side JK:

= (1 - 4) / (1 - 4) = (-3) / (-3) = 1

Slope of side KH:

= (-2 - 1) / (4 - 1) = (-3) / 3 = -1

Now, let's calculate the lengths of the sides:

Length of side HI:

= √(7-4)² + (1+2)²

= √9 + 9

= √18

Length of side IJ:

= √(4-4)² + (4-1)²

= √0+ 9

= √9

=3

Length of side JK:

= √(4-1)² + (4-1)²

= √9 + 9

= √18

Length of side KH:

= √(4-1)² + (-2-1)²

= √9 + 9

= √18

Based on the slopes and lengths, we can identify the type of quadrilateral: The given points H, I, J, and K form a parallelogram.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ1

The answer is 3

Hope this Helped :T

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

To learn more about linear equations refer to:

https://brainly.com/question/2030026

#SPJ1