which values are possible rational roots of 4x^3+9x^2-x+10=0 according to the rational root theorem?

Answer:

Step-by-step explanation:

All given numbers have digit 2 at the unit place, only one of them = 262 has digit 6 which is at the tenth place

The answer is none

Answer:

y=3/2x+11/2

Step-by-step explanation:

Hello! Sorry  I just saw this

Anyways, let's continue

first, we need to find the equation of the line with the one that is (-2,-4) and (2,2)

first, we need to find the slope

the equation for slope is y2-y1/x2-x1

so let's label the points

x1=-2

y1=-4

x2=2

y2=2

now plug it in

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

now, let's turn it into a line

the point-slope form is y-y1=m(x-x1) (m=slope)

now, plug it in

y-(-4)=3/2(x-(-2))

simplify to

y+4=3/2(x+2)

turn into y=mx+b format

y+4=3/2x+3

subtract 4 on both sides

y=3/2x-1

Now for the line that is parallel.

Parallel lines have the same slopes, so you automatically know that the new line will be y=3/2x+b

To make sure (-3,1) is a solution to the point, put 1 as y and -3 as x

1=3/2(-3)+b

1=-9/2+b

add 9/2 on both sides

b=11/2 or 5.5

now, put it into the equation

y=3/2x+11/2

Hope this helps!

Answer:

=y + 3 = -6(x +9)

Step-by-step explanation:

hope that will help you

Answer:

D

Step-by-step explanation:

The slope of the curve where it meets the right pole is sinh(7/25) ≈ 0.2748 (rounded to four decimal places). The angle between the line and the pole is 70.23° (rounded to two decimal places).

Given function is: y = 25 cosh(x/25) - 20

(a) Slope of the curve where it meets the right pole:

The slope of the curve is given by

dy/dx= 25/25sinh(x/25)= sinh(x/25)

At the right pole, the value of x=7, y=5

Hence, slope of curve at right pole= sinh(7/25)≈ 0.2748 (rounded to four decimal places)

(b) Angle between the line and the pole:

To find the angle, we first find the tangent of the angle at the pole.

tan θ = slope of curve at pole= sinh(7/25)

We know, opposite side / adjacent side = tan θ

By Pythagoras theorem, the opposite side is √(14^2 – 5^2) = 13.60147

Therefore, tan θ = 13.60147 / 5

tan θ ≈ 2.7203 (rounded to four decimal places)

θ = tan^-1(2.7203) ≈ 70.2313°≈ 70.23° (rounded to two decimal places)

The angle between the line and the pole is 70.23° (rounded to two decimal places).

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Answer:

f(n) is the function f-1(n) is the inverse of that function , basically the x and y switch places

Step-by-step explanation:

The integral of (3x^4 + x - 2 + √x^3) * x is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C represents the constant of integration.

To solve the given integral ∫(3x^4 + x - 2 + √x^3) * x, we can break it down into separate terms and integrate each term individually.

In the first term, 3x^4 * x, we can simplify it by multiplying the exponents: 3x^5. We apply the power rule for integration, which states that the integral of x^n is (x^(n+1))/(n+1). Applying this rule to our first term, we get (3/6)x^6 = x^6/2.

Moving on to the second term, x * x, we simply have x^2. Again, applying the power rule, the integral of x^2 is (x^3)/3.

In the third term, -2 * x, we have a constant multiple of x, which can be integrated as -(2/2)x^2 = -x^2.

Lastly, in the fourth term, √x^3 * x, we can simplify √x^3 as 3/x^2. Therefore, the term becomes (3/x^2) * x = 3/x.

Combining all the integrated terms, the final result of the integral is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C is the constant of integration.

In summary, the integral of (3x^4 + x - 2 + √x^3) * x is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C represents the constant of integration.

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Answer:

We can use proportional reasoning to solve some questions directly, such as which size of laundry detergent is the cheapest per load, or what the dimensions of the model car should be. We can also use proportional reasoning to estimate answers and check answers to problems involving more complicated algebra techniques.

Step-by-step explanation:

The manager can assemble packs of 3 different types of cookies in 120 different ways.

To find the number of different ways the manager can assemble packs of 3 different types of cookies, we can use the concept of combinations. Since the order of the cookies does not matter, we need to calculate the number of combinations.

The formula to calculate combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where:

n is the total number of items (types of cookies)

r is the number of items to be chosen (3 in this case)

"!" denotes the factorial operation, which means multiplying a number by all positive integers less than itself down to 1.

Using this formula, let's calculate the number of combinations:

C(10, 3) = 10! / (3! * (10 - 3)!)

First, let's calculate the factorials:

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800

3! = 3 * 2 * 1 = 6

(10 - 3)! = 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, substitute the factorials into the formula:

C(10, 3) = 3,628,800 / (6 * 5,040)

        = 3,628,800 / 30,240

        = 120

Therefore, the manager can assemble packs of 3 different types of cookies in 120 different ways.

In summary, using the combination formula, we calculated that there are 120 different ways for the bakery manager to assemble packs of 3 different types of cookies out of the total 10 types of cookies available, where the order of the cookies does not matter.

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Answer:

Whats the question?

Step-by-step explanation:

Answer:

-9x - 14

Step-by-step explanation:

1/4 (4x - 8) - 2 (5x + 6) =

= 1/4 × 4x - 1/4 × 8 - 2 × 5x - 2 × 6

= x - 2 - 10x - 12

= -9x - 14

Answer:

-9x - 14

Step-by-step explanation:

Simplify by following these steps:

1/4 (4x - 8) - 2(5x + 6)

(here we distribute 1/4)

x - 2 - 2(5x + 6)

(here we distribute -2)

x - 2 - 10x - 12

Collect similar terms

-9x - 14

∴ -9x - 14

A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the numbers 2,3, and 4 representing a success. The estimated probability of success is 60%.

The randomly generated list of numbers from 0 to 4 is simulating an event, and the probability of a success depends on the presence of 2, 3, or 4 in the generated list.

The other two numbers, 0 and 1, represent failure. To calculate the probability of success, we need to divide the number of possible successful outcomes by the total number of possible outcomes.

In this case, the number of possible successful outcomes is 3 (2, 3, and 4) and the total number of possible outcomes is 5 (0, 1, 2, 3, and 4).

Therefore, the probability of success can be calculated as follows:

Probability of success = Number of successful outcomes / Total number of outcomes = 3 / 5= 0.6= 60%

Therefore, the estimated probability of success is 60%.

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Answer:

it would be d

Step-by-step explanation:

if look closly you can see that im just trooling to get a challenge done ( but no joke the awnser is d tho)

Answer:

got n=13

Step-by-step explanation:

I set it up 4n+7=59 because 4 dollars you can get a dvd and when you solve you

Answer:

f(-5) = -43

Step-by-step explanation:

Step 1: Define

f(x) = -2x² + 7

f(-5) is x = -5

Step 2: Substitute and Evaluate

f(-5) = -2(-5)² + 7

f(-5) = -2(25) + 7

f(-5) = -50 + 7

f(-5) = -43

The value of x is approximately 369.186.

To solve the equation -0.17 = (x - 390) / 390 + 7.2 / 390 for x, we can simplify the equation and isolate x.

Given:

-0.17 = (x - 390) / 390 + 7.2 / 390

First, let's simplify the right side of the equation by finding a common denominator:

-0.17 = (x - 390 + 7.2) / 390

Combine like terms:

-0.17 = (x - 382.8) / 390

Multiply both sides of the equation by 390 to eliminate the fraction:

-0.17 * 390 = x - 382.8

-66.3 = x - 382.8

Add 382.8 to both sides of the equation:

-66.3 + 382.8 = x

316.5 = x

Therefore, the value of x is approximately 316.5 (rounded to three decimal places).

Note: There seems to be an error in the given equation. The correct equation should be -0.17 = (x - 390) / 390 + 7.2 / 390, not -0.17 = (x - 390) / 390 + 7.2 / 390.

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In this problem, we are given a second-order linear homogeneous differential equation, and we need to find a particular solution Y_p for the non-homogeneous equation. The equation is Y'' - 2Y' + Y = [tex]e^(2x)(cos(x) - 35i sin(x))[/tex]

To find the particular solution  we can use the method of undetermined coefficients. Since the right-hand side of the equation is a combination of exponential and trigonometric functions, we assume that  [tex]Y_p[/tex] has a similar form.

Let's assume [tex]Y_{P}[/tex] = A [tex]e^(2x) (cos(x) + B e^(2x) (sin(x))[/tex] + B [tex]e^(2x) (sin(x)),[/tex], where A and B are constants to be determined.

Next, we differentiate twice and substitute it into the original equation to find the values of A and B. After simplifying the equation, we equate the coefficients of the terms on both sides.

By solving the resulting equations, we can determine the values of A and B. Once we have A and B, we substitute them back into the assumed form  to obtain the particular solution.

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The solution to the system of inequalities is the region above the line y = -3x – 1 and the region above the line y = 3x – 2.

To solve the system of inequalities, we first graph the lines y = -3x – 1 and y = 3x – 2 on the coordinate plane. The line y = -3x – 1 has a negative slope and y-intercept at -1. It is a straight line that goes downward from left to right. The line y = 3x – 2 has a positive slope and y-intercept at -2. It is a straight line that goes upward from left to right.

The inequality y > -3x – 1 represents all the points above the line y = -3x – 1, and the inequality y > 3x – 2 represents all the points above the line y = 3x – 2. The solution to the system of inequalities is the region that satisfies both conditions, which is the region above both lines.
In summary, the solution to the system of inequalities is the region above the line y = -3x – 1 and the region above the line y = 3x – 2.

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The Deposit Fees 15% VAT amount on goods sold at a VAT-inclusive price of R1,500 would be approximately R195.65.

To answer the questions using the provided information, we'll refer to TABLE 2 for the deposit fees.1.2.1 The minimum amount one will pay when making a deposit of notes and coins:

Notes: R2.25 per R100 or part thereof

Coins: R5 per R100 or part thereof

Therefore, the minimum amount one will pay depends on the value of the deposit. For notes, it will be R2.25 per R100 or part thereof, and for coins, it will be R5 per R100 or part thereof.

1.2.2 To determine if Mr Mbhalati's statement is valid, let's calculate the deposit fees for his deposit of notes and coins.

Deposit of notes:

Deposit amount: R1,500

Deposit fee for notes: R2.25 per R100 or part thereof

Calculation:

Deposit fee = (Deposit amount / 100) * Deposit fee per R100

= (1500 / 100) * 2.25

= 33.75

Deposit of coins:

Deposit amount: R500

Deposit fee for coins: R5 per R100 or part thereof

Calculation:

Deposit fee = (Deposit amount / 100) * Deposit fee per R100

= (500 / 100) * 5

= 25

Total deposit fee = Deposit fee for notes + Deposit fee for coins

= 33.75 + 25

= 58.75

Therefore, Mr Mbhalati's statement is not valid. The total deposit fee for his deposit of notes to the value of R1,500 and R500 in coins would be R58.75, not R180.

1.2.3 To calculate the 15% VAT on the amount of goods sold at a VAT-inclusive price:

Amount from the sale of goods: R1,500

Calculation:

VAT amount = (Amount from the sale of goods / (100 + VAT rate)) * VAT rate

= (1500 / (100 + 15)) * 15

= (1500 / 115) * 15

≈ 195.65

Therefore, the Deposit Fees 15% VAT amount on goods sold at a VAT-inclusive price of R1,500 would be approximately R195.65.

1.2.4 One method Mr Mbhalati can use to send money to a person who does not have a bank account is by using a money transfer service like Western Union or MoneyGram. These services allow individuals to send money to recipients who can collect it in cash from designated locations, even if they don't have a bank account.

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Answer:

proper fraction

Step-by-step explanation:

Mixed number   has a whole number and a fraction  a  b/c

Improper fraction  has a numerator that is greater than the denominator a/b  where a is greater than b  a>b

Proper fraction  has a numerator that is less than the denominator a/b  where a is less than b  a<b

Answer:

Proper fraction

Step-by-step explanation:

Numerator is less than the denominator, making it a proper fraction.

Answer:

Step-by-step explanation:

First get y alone

So add 4x to each side

Then divide by 3 on each side

(a) Domain refers to the set of all possible values that the independent variable (x) can take in the given equation or function. (b) Intercepts represent the points where a curve intersects the x-axis or the y-axis. The x-intercepts occur when the value of y is equal to zero, while the y-intercepts occur when the value of x is equal to zero.

(c) Symmetry relates to the shape of a curve with respect to a specific axis or point. A curve can exhibit symmetry about the x-axis, y-axis, or the origin. If a curve is symmetric, its equation will exhibit certain patterns.

(d) Asymptotes are lines that a curve approaches but never intersects. They can be horizontal, vertical, or oblique. Asymptotes provide information about the behavior of a curve as x approaches infinity or negative infinity.

(e) Intervals of increasing and decreasing refer to the portions of the curve where its slope is positive (increasing) or negative (decreasing). These intervals can be determined by examining the sign of the derivative of the function.

(f) Local extrema are points on a curve where the function reaches a maximum or minimum value within a specific interval. They can be identified by analyzing critical points or points where the derivative of the function is zero or undefined.

(g) Concavity refers to the curvature of a curve. It can be concave up (opening upwards) or concave down (opening downwards). The concavity of a curve can be determined by examining the second derivative of the function.

(h) Points of inflection are points on a curve where the concavity changes. They are identified by finding the values of x where the second derivative of the function changes sign.

(i) Sketching the curves involves utilizing the information from the above points to plot the shape of the curve accurately. It involves identifying the key features such as intercepts, symmetry, asymptotes, intervals of increasing and decreasing, local extrema, concavity, and points of inflection to draw the curve as accurately as possible within the given domain or interval.

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Answer:

Your answer would be B and C.

Answer:

Prime factorisation of the numbers -

[tex] \\ \sf \: 35 = 7 \times \underline5 \\ \\ \sf \: 20 = \underline5 \times 4 \\ \\ \sf \: 15 = 3 \times \underline5 \\ [/tex]

As, we can see that the 5 is common in the both three numbers. So,

GCF, greatest common factor (35, 20, 15) = 5

Step-by-step explanation:

divide the figure into one square and one rectangle. Than use the length and width for each of your two shapes and combine them to find the area.

Answer:

46.92+18.06=64.98

Step-by-step explanation:

the shape can be divided to a rectangle = 4.6*10.2

then for the second shape

do 8.9-4.6 and you will get 4.3

multiply 4.3*4.2 for the second shape

In order for a set of numbers to represent three sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem. Only option C represents three sides of a triangle.

Now let's check each option to see which one satisfies the triangle inequality theorem:

a. 5, 3, and 2

The sum of 5 and 3 is 8, which is greater than 2. The sum of 5 and 2 is 7, which is also greater than 3. The sum of 3 and 2 is 5, which is not greater than 5. Therefore, this set of numbers does not represents three sides of a triangle.

b. 9, 5, and 15

The sum of 9 and 5 is 14, which is less than 15. Therefore, this set of numbers does not represent three sides of a triangle.

c. 8, 10, and 6

The sum of 8 and 10 is 18, which is greater than 6. The sum of 8 and 6 is 14, which is also greater than 10. The sum of 10 and 6 is 16, which is greater than 8. Therefore, this set of numbers represents three sides of a triangle.

d. 4, 6, and 10

The sum of 4 and 6 is 10, which is less than 10. Therefore, this set of numbers does not represent three sides of a triangle. Therefore, only option C represents three sides of a triangle.

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Answer:

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Company (2) is $7.4 cheaper.

Step-by-step explanation:

From the tables given in the picture,

Let the equation representing the rental 'y' and distance traveled 'x' is represented by,

y = mx + b

For company (1),

Here m = per mile rental charges = Slope of the graph

b = Initial charges

Since slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through (30, 53.55) and (60, 87.15) will be,

m = [tex]\frac{87.15-53.55}{60-30}[/tex] = $1.12 per mile

So the equation will be,

y = 1.12x + b

Since this line passes through (30, 53.55),

53.55 = 1.12(30) + b

b = 53.55 - 33.6

b = 19.95

So the expression representing charges for the company (1) will be,

y = 1.12x + 19.95

For company (2),

Per mile charges = slope of the line

m = [tex]\frac{78-56.75}{50-25}[/tex]

m = $0.85 per mile

Equation for the charges will be,

y = 0.85x + b

Since this line passes through (25, 56.75),

56.75 = 0.85(25) + b

b = 56.75 - 21.25

b = 35.5

Therefore, equation representing total charges for company (2) will be,

y = 0.85x + 35.5

By comparing per mile charges,

Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile

Steven plans to drive 85 km in rental truck.

Charges for company (1),

y = 1.12x + 19.95

y = 1.12(85) + 19.95

y = $115.15

Charges for company (2),

y = 0.85x + 35.5

y = 0.85(85) + 35.5

y = $107.75

Difference in charges of both the companies = 115.15 - 107.75 = $7.4

Therefore, company (2) is $7.4 cheaper.

The optimal solution for the given linear programming problem is z = 2, x₁ = 0, x₂ = 2, x₃ = 0, x₄ = 6, x₅ = 2, x₆ = 0 and x₇ = 0.

To solve the given linear programming problem using the simplex method, we need to convert it into standard form. The standard form of a linear programming problem involves introducing slack, surplus, and artificial variables as necessary.

The original problem is:

Minimize z = x₁ + 2x₂ + 3x₃ - x₄

Subject to:

2x₁ - x₂ + x₃ - 2x₄ ≤ 6

-x₁ + 2x₂ + x₃ + x₄ ≤ 8

2x₁ + x₂ + x₃ + x₄ ≥ 2

0 ≤ x₁ ≤ 3

1 ≤ x₂ ≤ 4

0 ≤ x₃ ≤ 2

2 ≤ x₄ ≤ 5

To convert the problem into standard form, we introduce slack variables and convert inequalities to equations:

Minimize z = x₁ + 2x₂ + 3x₃ - x₄

Subject to:

2x₁ - x₂ + x₃ - 2x₄ + x₅ = 6

-x₁ + 2x₂ + x₃ + x₄ + x₆ = 8

2x₁ + x₂ + x₃ + x₄ - x₇ = 2

x₁, x₂, x₃, x₄, x₅, x₆, x₇ ≥ 0

0 ≤ x₁ ≤ 3

1 ≤ x₂ ≤ 4

0 ≤ x₃ ≤ 2

2 ≤ x₄ ≤ 5

Now we can set up the initial simplex tableau:

   BV   x₁   x₂   x₃   x₄   x₅   x₆   x₇   RHS

----------------------------------------------

  x₅    2   -1    1   -2    1    0    0    6

  x₆   -1    2    1    1    0    1    0    8

  x₇    2    1    1    1    0    0   -1    2

Next, we perform iterations of the simplex method until we reach the optimal solution. The iteration process involves finding the entering variable, the leaving variable, and updating the tableau.

Iteration 1:

Entering variable: x₂ (the most negative coefficient in the objective row)

Leaving variable: x₆ (minimum ratio test)

Pivot on row 2, column 3:

   BV   x₁   x₂   x₃   x₄   x₅   x₆   x₇   RHS

----------------------------------------------

  x₅    2    0    1   -2   -1    1    0    2

  x₂   -0.5   1    0    0    0.5 -0.5  0    2

  x₇    1    0    0    1   -1    1    -1   6

Iteration 2:

Entering variable: x₃ (the most negative coefficient in the objective row)

Leaving variable: x₇ (minimum ratio test)

Pivot on row 3, column 4:

   BV   x₁   x₂   x₃   x₄   x₅   x₆   x₇   RHS

----------------------------------------------

  x₅    2    0    1   -2   -1    1    0    2

  x₂   -0.5   1    0    0    0.5 -0.5  0    2

  x₄    1    0    0    1   -1    1    -1   6

The tableau is now in its final form, and we have reached the optimal solution:

z = 2

x₁ = 0

x₂ = 2

x₃ = 0

x₄ = 6

x₅ = 2

x₆ = 0

x₇ = 0

Therefore, the optimal solution for the given linear programming problem is:

z = 2

x₁ = 0

x₂ = 2

x₃ = 0

x₄ = 6

x₅ = 2

x₆ = 0

x₇ = 0

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Answer:

60/2=t

Step-by-step explanation:

Simple algebra. You need to divide the total by the per minute to find the length in time that it will take. t=30.