Determine the number of rational zeros using rational zero theorem
f(x)=4x^(4)-x^(3)+3x^(2)-4x-6

Answer:

The FOIL method is a technique used to multiply two binomials. The word "FOIL" is an acronym that stands for "First, Outer, Inner, Last." I will dive in it briefly for u!

Step-by-step explanation:

To use the FOIL method, you multiply the first term of the first binomial with the first term of the second binomial. Then, you multiply the outer terms (first term of the first binomial and the second term of the second binomial), followed by the inner terms (second term of the first binomial and the first term of the second binomial), and finally the last terms (second term of both binomials). You then combine the like terms to simplify the result.

The FOIL method is especially useful when multiplying polynomials, which are expressions with one or more terms involving variables with various powers. For example, to multiply the binomials (x + 3) and (x - 2), you would use the FOIL method as follows:

First: x × x = x²

Outer: x × (-2) = -2x

Inner: 3 × x = 3x

Last: 3 × (-2) = -6

Combine the like terms: x² - 2x + 3x - 6 = x² + x - 6

Thus, the product of (x + 3) and (x - 2) is x² + x - 6.

Answer:

The FOIL method is a mnemonic device used to multiply two binomials. It stands for "First, Outer, Inner, Last" and it is a step-by-step process that helps to remember the order of operations for multiplying binomials. When multiplying two binomials, the FOIL method involves multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms, and then adding the resulting terms together to simplify the expression.

The FOIL method is used in polynomial algebra because it is an efficient way to multiply two polynomials of degree one, also known as binomials. When multiplying two binomials, we can use the FOIL method to distribute each term in the first binomial to each term in the second binomial, resulting in a new polynomial expression. This method allows us to simplify polynomial expressions and solve equations by factoring, which is a crucial skill in algebra and calculus.

In summary, the FOIL method is a mnemonic device used to multiply two binomials by remembering the order of operations for each term. This method is commonly used in polynomial algebra because it is an efficient way to simplify polynomial expressions and solve equations by factoring.

Answer:

25.62 grams of cocoa

Step-by-step explanation:

To find the number of grams of cocoa in Keith's chocolate bar, we need to multiply the weight of the chocolate bar in grams by the percentage of cocoa in decimal form.

First, we convert the percentage to a decimal by dividing it by 100:

42% = 42/100 = 0.42

Next, we multiply the weight of the chocolate bar by the percentage of cocoa:

0.42 x 61 = 25.62

Therefore, the chocolate bar contains 25.62 grams of cocoa, rounded to the nearest tenth.

Answer:

25.62

Step-by-step explanation:

42 / 100 × 61

= 0.42 × 61

= 25.62

The equation of the axis of symmetry is x = 5/2

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

y = x^2 - 5x + 1

The above equation si a quadratic equation

Differentiate the equation

SO, we have

y' = 2x - 5

Set the differentuated equation to 0

This gives

2x = 5

Evaluate

x =5/2

Hence, the equation is x =5/2

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Below is the code required to Create a dice rolls application that displays 5 rolls of two dice in Java.

Here is a Java program that displays 5 rolls of two dice:

import java.util.Random;

public class DiceRolls {

   public static void main(String[] args) {

       Random random = new Random();

       int rolls = 5;

        for (int i = 0; i < rolls; i++) {

           int die1 = random.nextInt(6) + 1;

           int die2 = random.nextInt(6) + 1;

           int sum = die1 + die2;

           System.out.println("Roll " + (i+1) + ": " + die1 + " + " + die2 + " = " + sum);

       }

   }

}

Explanation:

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Arc length formula is L = ∫a^b √[1 + (dy/dx)^2] dx . The arc length of a curve is the length of the curve between two points, and it can be calculated using the arc length formula in calculus.

The arc length formula can be used to find the length of a curve in terms of the function that describes the curve.

The arc length formula is given by:

L = ∫a^b √[1 + (dy/dx)^2] dx

where L is the arc length of the curve, a and b are the endpoints of the curve, dy/dx is the derivative of the function that describes the curve with respect to x, and ∫ represents the integral of the function over the interval from a to b.

To use the formula, we first find the derivative of the function that describes the curve, dy/dx. Then we plug this expression into the arc length formula and integrate the expression over the interval from a to b to find the arc length of the curve.

The arc length formula is useful in many applications, such as physics, engineering, and geometry, and it allows us to find the length of a curve even when it is not a straight line.

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Answer:ob

Step-by-step explanation:

The conversion of 65 kilos in pounds is equivalent to approximately 143.3 pounds.

Its name derives from the Latin word "poundus" meaning "weight". The £ symbol comes from an ornate L in Libra. The pound was a unit of currency as early as 775AD in Anglo-Saxon England, equivalent to 1 pound weight of silver.The approximation we use for kilograms (kg) to pounds (lb) is 1 kg = 2.2 lb. To convert from kilogram to pound, we multiply by 2.2. To convert from pound to kilogram, we divide by 2.2.

To convert 65 kilograms to pounds, you can use the conversion factor of 1 kilogram = 2.20462 pounds.

Therefore,65 kilograms = 65 x 2.20462 pounds= 143.3003 pounds (rounded to 4 decimal places)

So, 65 kilograms is equivalent to approximately 143.3 pounds.

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One of the molar concentration units is the millimolar. The symbol or abbreviation mM stands for millimolar. 1 millimolar equals 1 mol/meter³ in terms of measurement units. In terms of molar, 1 millimolar is equivalent to 0 point 001 molar.

The term "molar concentration" (also known as "molarity," "amount concentration," or "substance concentration") refers to the amount of a substance per unit volume of solution and is used to describe the concentration of a chemical species, specifically a solute, in a solution.

The number of moles per liter, denoted by the unit symbol mol/L or mol/dm3 in SI units, is the most widely used unit for molarity in chemistry. One mol/L of a solution is referred to as one molar, or 1 M.

Because most solutions' volumes only slightly vary with temperature due to thermal expansion, the use of molar concentration in thermodynamics is frequently inconvenient. Typically, temperature correction factors are introduced to solve this issue, or a concentration measure that is not temperature dependent, like molality, is used.

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The area of the shaded region is 5π  

The sector of a circle refers to the region enclosed by two radii of a circle and the arc between them. It is a part of the whole circle, and its area can be calculated using the following formula:

where θ is the central angle (in degrees) of the sector, r is the radius.  

Here we have

The length of arc FG = 5/3 π  and measure of ∠FEG = 50°

As we know Arc Length = θ × (π/180) × r  

=> Length of arc FG = 50 × (π/180) × r

From the given data,

=> 50 × (π/180) × r = 5π/3

=> 5 × (1/18) × r = 5/3

=>  (1/6) × r = 1

=> r = 6 units  

Hence, the radius of the circle is 6 units

By using the formula,

Area of a Sector of Circle = (θ/360°) × πr²

Area of shaded region = (50/360) × π(6)²  

= (5/36) × π(36)

= (5/36) × π(36)

= 5π  

The area of the shaded region is 5π  

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The second graph, first quadrant of coordinate plane titled Marie's round of golf could represent Marie's situation.

A coordinate plane is a two-dimensional plane made up of the x-axis and y-axis, two perpendicular number lines. Using the coordinates (x, y), which stand for the horizontal and vertical distances from the origin (the point where the x- and y-axes cross), it is possible to find locations in a two-dimensional space. The first quadrant, second quadrant, third quadrant, and fourth quadrant of the coordinate plane are designated in order anticlockwise.

Given that, she stayed at the first hole for the first 30 minutes. Then she drove away from the first hole for the next 2 hours.

The situation is best described by the graph 2, first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from 0 comma 0 to one half comma 0, a line segment from one half comma 0 to 2 and a half comma 5, and a line segment from 2 and a half comma 5 to 4 and a half comma 0.

Hence, the second graph could represent Marie's situation.

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Answer:

the answer is the graph shone below

i took the test and  IT WAS RIGHT  

Step-by-step explanation:

have a good day!

The weight of gallon of water is 8.345 pounds according to density of water.

The gallon is a unit of volume and we need to find the weight of one gallon of water. So, the weight and volume are related to each other by the formula -

Density = mass/volume

Now, we know the volume and need the density of water in pounds per gallon.

The density of water is 8.345 pounds per gallon.

So, keeping the values in formula

Mass = density × volume

Mass = 8.345 × 1

Performing multiplication on Right Hand Side of the equation

Mass = 8.345 pounds

The weight of water is 8.345 pounds.

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Variance in statistics is the squared difference between a random variable's expected value and its mean value.

Data points' variance from the mean is a measure of how they vary. A variance, according to Layman, is a measurement of how widely apart a set of data (numbers) are from their mean (average) value.

Finding the expected difference of deviation from the actual number is what is meant by variance. As a result, variance is influenced by the data set's standard deviation.

Data is more dispersed from its mean the higher the variance value, and less dispersed from mean if the variance value is low or minimal. As a result, it is referred to as a measure of data spread from mean.

[tex]Var(X) = E[(X-\mu)^2][/tex]  

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Work Shown:

5/32 divide 25/4

(5/32) * (4/25)

(5*4)/(32*25)

(5*4)/(8*4*5*5)

(1)/(8*5)

1/40

Answer:

Option 2

 x     y

−3     0

−1      3

 0     4

 3     0

4 3

Step-by-step explanation:

For a relation x →  y to be a function, there can be one and only one value of y for a value of x

Looking at the tables we see that option 1 is out since all x values are 2 andthere are multiple values of y

The last option is out because for x = 0 there are two values of y=-2 and y = 2

Correct choice is the second option which has a unique y value for each value of x

Answer:

option 2 im doing it rn

Step-by-step explanation:

For the given rectangle, the angles are:

1 = 72°

2 = 36°

3 = 18°

4 = 144°

What is a rectangle?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length. A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

The given figure is a rectangle.

The angle 3 = 18°

This is because they are alternate angles.

In triangle ADC,

 ∠DAC = 180 - ( 18 + 90) = 72°

The angles  ∠DAC and  ∠BCE are alternate angles.

∠BCE and 1 are congruent angles.

1 = 72°

2 = 180 - ( 72+72) = 36°

From triangle BDC,

∠CDE = 180 - (72+90) = 18

So 4 = 180 - ( 3+∠CDE ) = 180 - (18+18) = 144°

Therefore for the given rectangle, the angles are:

1 = 72°

2 = 36°

3 = 18°

4 = 144°

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The width he need to make the pasture with the given rectangle is 4x³y⁶.

Area of a rectangle is the product of its length and width.

If a rectangle has length L units and width of W units, then

Area = L × W squared units.

We are given that;

Area= 20x6y5

Length= 5x³y4

We can start by using the formula for the area of a rectangle:

Area = length x width

We know that the area of the rectangular pasture is 20x6y5, and we know the length is 5x³y4. So we can plug in these values and solve for the width:

20x6y5 = (5x³y4) x width

To solve for width, we can divide both sides by 5x³y4:

width = 20x6y5 / (5x³y4)

Simplifying the expression on the right-hand side, we can divide each term in the numerator by 5x³y4:

width = (4x³y¹) x (4y5)

Simplifying further, we can add the exponents of the common factor y:

width = 4x³y⁶

Therefore, the farmer would need to make the width of the rectangular pasture will be 4x³y⁶.

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75% of 500 is determined using bar model as 375.

To use a bar model to find 75% of 500, you can follow these steps:

3 parts x 25% per part = 75%

Finally, to find the value of 75% of 500, you can multiply 500 by 75% in decimal form (0.75):

500 x  0.75 = 375

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Answer:

Below

Step-by-step explanation:

tan x  = 110 /11

Arctan( tan x) = arctan(110/11)

   x     =   84.3°

The error in the solution is that, In step 2, the Distributive Property was applied incorrectly.

Equations are mathematical expressions consisting of two or more variables and constants on two sides connected by an equal to sign.

Solution of the equation is the value of the variable that the equation holds true.

Given equation is,

8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

Using the multiplication property of equality, multiplying whole equation by 2,

(2 × 8) - a = 6 (4 - 5a)

16 - a = 6 (4 - 5a)

Distributive property states that, for three numbers or expressions, a, b and c,

a (b + c) = ab + ac

Applying that,

6 (4 - 5a) = (6 × 4) - (6 × 5a) = 24 - 30a

But the student didn't multiply 6 with 5a, and thus he got 24 - 5a in step 2.

Hence the incorrect step is step 2 because of incorrect use of distributive property.

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Your question is a bit confusing. The complete question with an image is given below.

A student provided the steps for solving an equation. Which statement describes the error in the solution?

Equation : 8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

x² −20x+100

Explanation

You have to factor the expression in order to get your answer.

Do this by expanding out the expression: (x-10)(x-10).

Then factor by multiplying each of the components! Use the FOIL acronym to help you. FOIL stands for First, Outer, Inner, Last. Meaning multiply the first numbers of the expressions together, then the outers, then the inner two numbers, then the last two numbers of the expression.

Multiply x and x to get x² multiply x and -10 to get -10x, multiply -10 and x to get -10x, multiply -10 and -10 to get 100. Add them all together: x² −10x−10x+100 . Then combine like terms.

here.

Answer: 16 lbs.

Step-by-step explanation:

If there are 7 packages and all of the packages weigh the same, then you would divide the number of packages by the total weight of the packages.

112÷7=16. 16 would be the weight of each package individually.

So, the answer is C;16 lbs.

a) The probability of finding oil is 0.70, or 70%.

b) The new probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, which is  1.00 or 100% .

(a) The probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, since both of these outcomes are considered positive for the oil company:

P(find oil) = P(high-quality oil) + P(medium-quality oil) = 0.50 + 0.20 = 0.70

Therefore, the probability of finding oil is 0.70, or 70%.

(b) To interpret the soil test, we can use Bayes' theorem:

P(Ai | S) = P(S | Ai) * P(Ai) / P(S)

where P(Ai | S) is the updated probability of finding oil given the soil test, P(S | Ai) is the probability of observing the soil test result given that there is oil of the corresponding quality, P(Ai) is the prior probability of finding oil of the corresponding quality, and P(S) is the probability of observing the soil test result regardless of the presence of oil.

Using the given probabilities, we can calculate:

P(S) = P(high-quality oil) * P(S | high-quality oil) + P(medium-quality oil) * P(S | medium-quality oil) + P(no oil) * P(S | no oil)

= 0.50 * 0.20 + 0.20 * 0.80 + 0.30 * 0.20

= 0.26

Now we can calculate the updated probabilities for each quality of oil:

P(high-quality oil | S) = P(S | high-quality oil) * P(high-quality oil) / P(S)

= 0.20 * 0.50 / 0.26

= 0.3846 or 0.38 (rounded to two decimal places)

P(medium-quality oil | S) = P(S | medium-quality oil) * P(medium-quality oil) / P(S)

= 0.80 * 0.20 / 0.26

= 0.6154 or 0.62 (rounded to two decimal places)

P(no oil | S) = P(S | no oil) * P(no oil) / P(S)

= 0.20 * 0.30 / 0.26

= 0.2308 or 0.23 (rounded to two decimal places)

The oil company should interpret the soil test as providing evidence for the presence of medium-quality oil, since the updated probability for this outcome is higher than the updated probability for high-quality oil. The revised probabilities for finding oil are:

P(find high-quality oil | S) = P(high-quality oil | S) = 0.38

P(find medium-quality oil | S) = P(medium-quality oil | S) = 0.62

P(find no oil | S) = P(no oil | S) = 0.23

Therefore, the new probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, which is:

P(find oil | S) = P(find high-quality oil | S) + P(find medium-quality oil | S)

= 0.38 + 0.62

= 1.00 or 100% (rounded to two decimal places)

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Answer:

x = 5.88

Step-by-step explanation:

by simplifying both sides of the equation, then isolating the variable.

Answer:

Step-by-step explanation:

the answer is c

after distributing 13 to the expression within the Parentheses we get the equation 13*19 - 13x which can then be further simplified to 247 - 13x

Answer:

K=27/2

Step-by-step explanation:

Hope this helps!

Answer: k = 27/2 = 13 1/2 = 13.5

Step-by-step explanation: Brainliest? That answer is right. I just solved it

Answer:

Step-by-step explanation:

The total amount of space taken up on the sign by the letters in Hannah's name is between 3 and 4 whole numbers.

If each letter takes up 5/8 inch of space, then the total amount of space taken up by all 6 letters in Hannah's name is:

6 letters × 5/8 inch per letter = 30/8 inches = 3 6/8 inches = 3 3/4 inches

To find the range of whole numbers between which 3 3/4 inches falls, we can convert 3 3/4 to an improper fraction:

3 3/4 = (4 × 3 + 3)/4 = 15/4

Now we can find the two whole numbers that 15/4 is between by dividing 15 by 4:

15 ÷ 4 = 3 with a remainder of 3

So 15/4 is between 3 and 4, specifically:

3 < 15/4 < 4

Therefore, the total amount of space taken up on the sign by the letters in Hannah's name is between 3 and 4 whole numbers.

A fraction is a mathematical concept that represents a part of a whole. It is typically written in the form of one number (the numerator) over another number (the denominator), separated by a horizontal line. For example, 3/4 is a fraction where the numerator is 3 and the denominator is 4.

The numerator represents how many parts of the whole we are referring to, and the denominator represents the total number of equal parts that make up the whole. So, 3/4 represents 3 out of 4 equal parts of a whole. Fractions are used to represent quantities that are not whole numbers, such as 1/2, 3/5, and 7/8.

Fractions are used in many different areas of math and everyday life, such as in measurement, cooking, and finance. They are also an important concept in understanding other mathematical ideas like decimals and percentages.

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herefore, the area of the triangle is approximately 2.58 square yards.

Area = (1/2) * a * c * sin(B)

where B is the angle opposite to the side of length b, and a and c are the lengths of the other two sides.

In this case, we have:

B = 47 degrees (given)

a = 2 yards (given)

c = 4 yards (given)

To use the formula, we first need to find the length of the third side, b, using the Law of Cosines:

[tex]b^{2}[/tex] = [tex]a^{2}[/tex]+ ^[tex]c^{2}[/tex] - 2accos(B)

b^2 = 2^2 + 4^2 - 224cos(47)

b^2 ≈ 13.37

b ≈ 3.657

Now we can substitute the values into the formula for the area:

Area = (1/2) * a * c * sin(B)

Area = (1/2) * 2 * 4 * sin(47)

Area ≈ 2.58 square yards

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Answer: 2016

Step-by-step explanation: Since you need to find the area of everything u need to multiply it all h*ft*w (height*width*wide) so 18*14*8=2016

Completing the square is a mathematical technique used to manipulate quadratic equations into a standard form that makes them easier to solve

The general form of a quadratic equation is:

ax^2 + bx + c = 0

To complete the square, you need to add and subtract (b/2a)^2 to the left side of the equation. This is because (b/2a)^2 is equal to (b/2a) times itself, which means it is a perfect square.

Here is the formula for completing the square:

ax^2 + bx + c = 0

ax^2 + bx = -c

a(x^2 + (b/a)x) = -c

a(x^2 + (b/a)x + (b/2a)^2 - (b/2a)^2) = -c

a(x + b/2a)^2 = -c + (b/2a)^2

The equation is now in the standard form:

a(x + b/2a)^2 = (4ac - b^2)/4a

By taking the square root of both sides, you can solve for x:

x = (-b +/- sqrt(b^2 - 4ac))/2a

This is the quadratic formula, which gives you the values of x that make the equation equal to zero.

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