The missing root is -24 - 5i.
To find the missing root of the polynomial function f(x) = x^3 - x^2 + 24x + 26, we can use the fact that the sum of all the roots of a polynomial equation is equal to the negation of the coefficient of the second-to-last term divided by the coefficient of the leading term.
In this case, the coefficient of the second-to-last term is 24, and the coefficient of the leading term is 1. Therefore, the sum of all the roots is -24/1 = -24.
We already know that -1 and 1 + 5i are roots, so we can subtract them from the sum to find the missing root:
Missing root = -24 - (-1) - (1 + 5i) = -24 + 1 - 1 - 5i = -24 - 5i.
Note that the missing root is a complex number, indicating that the polynomial has at least one complex root.
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You start driving west for 20 miles, turn left, and drive south for another 14 miles. At the end of driving, what is your straight line distance from your sta
rting point? Round to the nearest tenth of a mile.
The straight-line distance from your starting point at the end of driving is approximately 24.4 miles.
To find the straight-line distance from your starting point, we can use the Pythagorean states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The distance you drove west and turned left forms two sides of a right triangle, and the straight-line distance from the starting point will be the hypotenuse.
Given:
Distance driven west = 20 miles
Distance driven south = 14 miles
Using the Pythagorean:
Hypotenuse² = (Distance driven west)² + (Distance driven south)²
Hypotenuse² = 20² + 14²
Hypotenuse² = 400 + 196
Hypotenuse² = 596
To find the length of the hypotenuse (straight-line distance), we take the square root of both sides:
Hypotenuse = √596
Hypotenuse ≈ 24.4 miles (rounded to the nearest tenth)
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Which describes the value of a?
Answer:
(c) 0 < a < 1
Step-by-step explanation:
You want to know the value of 'a' in y = a·cot(x) that will cause a vertical compression without reflection.
Vertical scalingWhen a function value is multiplied by a factor greater than 1, its graph is expanded vertically. When that factor is less than 1, the graph is compressed, as in the attachment.
If the scale factor is negative, the graph will be reflected across the x-axis.
Here, you want compression without reflection. That requires a positive scale factor less than 1.
0 < a < 1
Log2x + log4x + log16 = 7
the solution to the equation log2x + log4x + log16 = 7 the logarithms using the properties of Logarithms is x ≈ 53.408.
To solve the equation log2x + log4x + log16 = 7, we can simplify the logarithms using the properties of logarithms.
First, we can use the property loga + logb = log(ab) to combine the logarithms:
log2x + log4x + log16 = log(2x * 4x * 16)
Next, we simplify the expression inside the logarithm:
log(2x * 4x * 16) = log(32x^3)
Now, our equation becomes:
log(32x^3) = 7
To eliminate the logarithm, we can rewrite the equation in exponential form:
32x^3 = 10^7
Simplifying further:
32x^3 = 10,000,000
Now, we can solve for x by dividing both sides of the equation by 32:
x^3 = 10,000,000 / 32
x^3 = 312,500
To find the value of x, we take the cube root of both sides:
x = ∛312,500
x ≈ 53.408
Therefore, the solution to the equation log2x + log4x + log16 = 7 is x ≈ 53.408.
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I need help, I was trying to solve it but I got lost.
Answer: [tex]x\approx 6.2[/tex]
Step-by-step explanation:
Detailed explanation is attached below.
A bag contains seven balls labeled 1 through 7. One ball will be randomly picked. What is the probability of picking an off number? Write your answer as a fraction in simplest form.
Answer:
The odd numbers between 1 and 7 are 1, 3, 5, and 7. There are four of them.
The total number of balls in the bag is 7.
Therefore, the probability of picking an odd number is:
number of odd numbers / total number of balls = 4/7
So the probability of picking an odd number is 4/7
Find the volume of the sphere use three
Answer: 2916 cubic feet
Step-by-step explanation:
V=(4/3)*3*(9^3)
V=(4/3)*3*729
V=2916
What is P(Not A | Not B )?
The calculated value of the conditional probability P(Not A | Not B) is 0.8125
How to calculate the probability P(Not A | Not B )?From the question, we have the following parameters that can be used in our computation:
The table of values
The probability P(Not A | Not B ) is calculated as
P(Not A | Not B ) = (Not A and Not B)/(Not B)
Using the above as a guide, we have the following:
(Not A and Not B) = 0.65
(Not B) = 0.80
Substitute the known values in the above equation, so, we have the following representation
P(Not A | Not B ) = 0.65/0.80
Evaluate
P(Not A | Not B) = 0.8125
Hence, the probability P(Not A | Not B) is 0.8125
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Write a polynomial function in factored form that has roots at x=7, x=-10, and x=3. Each root should have a multiplicity of 1.
The polynomial function in factored form with roots x = 7, x = -10, and x = 3, each with a multiplicity of 1, is [tex]f(x) = x^3 - 76x + 210.[/tex]
To write a polynomial function in factored form with the given roots, we can use the factored form equation:
f(x) = (x - r1)(x - r2)(x - r3)...
Where r1, r2, r3 represent the roots of the polynomial.
Given the roots x = 7, x = -10, and x = 3, we can write the factored form equation as:
f(x) = (x - 7)(x + 10)(x - 3)
Expanding this equation will give us the polynomial function in factored form:
[tex]f(x) = (x - 7)(x + 10)(x - 3)[/tex]
[tex]= (x^2 - 7x + 10x - 70)(x - 3)[/tex]
[tex]= (x^2 + 3x - 70)(x - 3)[/tex]
[tex]= x^3 - 3x^2 + 3x^2 - 9x - 70x + 210[/tex]
[tex]= x^3 - 76x + 210[/tex]
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What is the mode of the data set below? 0, 4 , 3, 4, 0, 9, 1
The mode of the data is 0
What are the measures of central tendency?Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.
It provides an accurate description of the entire data.
The three major measures of central tendency are given as;
ModeMeanMedianThe mode is defined as the measure of central tendency representing the most occurring number in a given data set
From the information given, we have;
0, 4 , 3, 4, 0, 9, 1
Then, the mode is 0
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What are the values of the trigonometric ratios for this triangle?
sin θ =
cos θ =
tan θ =
4/3 3/5 4/5 5/3 5/4 3/4
Answer:
Sin θ = 3/5 cos θ = 4/5 tan θ= 3/4
perla has 150 meters of fencing material and wants to form a rectangular pen with an area of 1300 square meters
a. let w= the width of the pen and L=length. Write a system of equations to determine w and L.
b.Solve the system and interpret your answer in the context of the problem.
Answer:
Step-by-step explanation:
can someone help me with this i need help to pass math
The angle that has been formed and is shown as x is shown as 52.1°.
What is the angle x?In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. The tangent function is denoted as tan.
We can see that we need to find the tangent of the angle;
Tan x = 36/28
x = Tan-1(36/28)
x = 52.1°
Thus it is clear from the calculation that we have done above that the angle that is marked x is 52.1°.
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What should be the third row in the following series of shapes
Answer:
The answer is number 2
Suppose that 100 unique names are put into a hat and drawn at random without replacement. How many different ways can you draw all of the names from the hat? Remember that "without replacement" means that the names are not returned to the hat after they are chosen. Write your answer in factorial notation.
The solution is: 100! different ways can you draw all of the names from the hat.
Here, we have,
if we have n object, and as we know that arrangement given by = n!. (Permutation)
A permutation is a mathematical technique for determining the number of possible arrangements in a sentence where the order of arrangements is important. A common math problem involves choosing some items in a particular order from a set of items.
A permutation also called an "order number" or "sequence", is the rearrangement of the elements of an ordered list so that they correspond one-to-one with themselves. (Faculty; Ouspensky 1937, p. 18). Permutations are said to be ordered combinations. The number of permutations r of n objects acquired simultaneously is determined by the following formula: P(n,r)=n!(n-r)!
Hereafter taking each unique name, we will arrange it in raw, so we can say this problem is equivalently permutation problem, So we can say the way of drawing all names can be done in 100! Way.
So ANSWER IS 100!
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What is the area of the rectangle part of the shape below?
Answer:
The Answer is 80√3 or 138.56 to 2d.p
Step-by-step explanation:
sin 60=L/8
L=sin60×8
L=4√3
Area of rectangle =L×W
A=20×4√3
A=80√3=138.56 to 2d.p
8cm into kilometres
Answer:
[tex]\huge\boxed{\sf 0.00008\ km}[/tex]
Step-by-step explanation:
Statement:To convert cm to km, we need to divide by 100,000.Solution:= 8 cm
= 8 / 100,000 km
= 0.00008 km[tex]\rule[225]{225}{2}[/tex]
Answer:
0.00008
80 cm is 0.0008 so you know I just assumed
Zoe is doing a survey to find the time her classmates spend playing video games. She asks the following question:
Which student spends the most time playing video games?
Part A: Describe the data you would expect her to collect from this question.
Part B: Explain whether this is a statistical question. If this is not a statistical question, then modify the question to make it statistical.
i need help
Answer:
Part A: The data that Zoe would expect to collect from this question is the amount of time each student spends playing video games. She could collect this data by asking each student how many hours per week they spend playing video games.
Part B: This is not a statistical question because it is asking for a specific answer. A statistical question would be asking for a distribution of the data, such as the average amount of time students spend playing video games or the range of times students spend playing video games.
To make this question statistical, Zoe could ask the following question:
How much time do students in my class spend playing video games per week?
This question is statistical because it is asking for a distribution of the data. Zoe could then collect the data and use it to create a histogram or other graph to show the distribution of the data.
Teams in the National Football League in America are divided into two conferences: the AFC and the NFC. Some teams have animals as their mascots, and others do not. The following two-way table displays this data.
how many teams are in the NFC
The total number of teams that are in the NFC from the given two way frequency table is: 16 teams
How to Interpret a two way frequency table?A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data
From the attached two way table, we see that:
Total number of animals = 15
Total number of non-animals = 17
Total Number of NFC = 16
Total number of AFC = 16
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Teams in the National Football League in America are divided into two conferences: the AFC and the NFC. Some teams have animals as their mascots, and others do not. The following two-way table displays this data.
How many teams are in the NFC?
The total number of teams that are in the NFC from the given two way frequency table is: 16 teams
How to Interpret a two way frequency table?A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data
From the attached two way table, we see that:
Total number of animals = 15
Total number of non-animals = 17
Total Number of NFC = 16
Total number of AFC = 16
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Recipe for fruit punch orange juice 6 cups pineapple juice 3 cups cranberry juice one cup Felicia has 32 fluid ounces of pineapple juice does she have enough pineapple juice to make one recipe?
PART- A
A-Yes she has just enough pineapple juice.
B-yes she has more than enough pineapple juice.
C- No she needs 8 more fluid ounces of pineapple juice.
D- No she needs 16 more fluid ounces of pineapple juice.
PART B- Jared also wants to make fruit punch. He has 8 pints of each Orange juice, pineapple juice, and cranberry juice. Which of the following are true…
A- he doesn’t have enough of each type of juice to make 1 recipe.
B- He has enough of each type of juice to make 1 recipe.
C- he has enough of each type of juice to make 2 recipes.
D- he has enough of each type of juice to make 3 recipes.
The statement which is true is he has enough of each type of juice to make 1 recipe, the correct option is B.
We are given that;
Orange juice cup= 6
Pineapple juice cup=3
Now,
PART A: To answer this question, we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Felicia has pineapple juice in fluid ounces. We can use the fact that 1 cup = 8 fluid ounces to convert Felicia’s amount of pineapple juice to cups:
32 fluid ounces = 32 / 8 cups = 4 cups
The recipe requires 3 cups of pineapple juice, so Felicia has more than enough pineapple juice. The correct answer is B.
PART B: we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Jared has each type of juice in pints. We can use the fact that 1 pint = 2 cups to convert Jared’s amounts of juice to cups:
8 pints = 8 * 2 cups = 16 cups
Jared has 16 cups of each type of juice. The recipe requires 6 cups of orange juice, 3 cups of pineapple juice, and 1 cup of cranberry juice. This adds up to 10 cups of juice for one recipe. So, Jared has enough of each type of juice to make one recipe and have some left over. However, he does not have enough of each type of juice to make two recipes, since that would require 20 cups of juice in total. T
Therefore, by unitary method the answer will be He has enough of each type of juice to make 1 recipe.
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3. (x + 5)2 - y ; x = -2 and y = 1
4. 3x + 4y2 ; × =-3 and y = 5
if anyone could help me with these thank you so much
Answer:
Question 3: 5
Question 4: 91
Step-by-step explanation:
[tex](x+5)2-y[/tex]
[tex]x = -2[/tex]
[tex]y =1[/tex]
[tex](-2 + 5)2 - 1[/tex]
[tex](3)2-1[/tex]
[tex]6-1 = 5[/tex]
[tex]3x +4y^2[/tex]
[tex]x = -3[/tex]
[tex]y=5[/tex]
[tex]3(-3)+4(5)^2[/tex]
[tex]-9 + 100[/tex]
[tex]=91[/tex]
What type of angles are angle 1 and angle 8 ?
Answer:
Angles 1 and 8 are alternate exterior angles.
100 Points! Algebra question. Describe the end behavior of the graph in the function. Photo attached. Thank you!
two books are proportional in size One book is two inches thick and fourteen inches long the second book is 1.5 inches thick how long is the second
Answer:
The length of the second book is 10.5 inches, while the first book's thickness is in a ratio of 2:1.5, which simplifies to 4:3. Similarly, the length of the first book is also in a ratio of 4:3 with the second book. Hence, we can calculate the second book's length as 14 divided by 4, multiplied by 3, which equals 10.5 inches.
Can I have help finding the area
Step-by-step explanation:
One rectangle 10 x 6 = 60 cm^2
Two sqaures 2 * 4x4 = 32 cm^2 Total = 92 cm^2
Describe the transformations from the parent y=1/x :
y=3/x+5 -3
The transformations to the parent function are given as follows:
Vertical stretch by a factor of 3.Translation left 5 units.Translation down 3 units.How to obtain the transformations?The parent function for this problem is given as follows:
y = 1/x.
The transformed function for this problem is given as follows:
y = 3/(x + 5) - 3.
Hence the transformations to the parent function are given as follows:
Vertical stretch by a factor of 3. -> multiplication by 3 in the numerator.Translation left 5 units, as x -> x + 5.Translation down 3 units, as y -> y - 3.More can be learned about transformations at https://brainly.com/question/28687396
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What is the area of this figure?
Answer:
70cm^2
Step-by-step explanation:
10×5=50cm^2 is the area of the rectangle
18-10=8 is the height of the triangle
8×2.5=20
20÷2=10 is area of half the triangle
10+10=20cm^2 is the area of the triangle
50cm^2+20cm^2=70cm^2
5. When
is the heart fully formed?
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
We can start by finding the value of the expression inside the tangent function: tan(1/2 (0 + π/2)) = tan(π/4) = 1
Now we can substitute this value into the original equation and simplify:
y = -3 + tan(1/2 (0 + π/2))
y = -3 + 1
y = -2
The vertical shift of the graph is the constant term in the equation, which is -2. Since this value is negative, the graph is shifted downwards. Therefore, the correct answer is (A) 3 units down
A coffee house blended 16 pounds of espresso flavored
coffee beans with 10 pounds of vanilla flavored coffee
beans. The 26 pound mixture cost $229. A second mixture
included 14 pounds of espresso flavored coffee beans and 11
pounds of vanilla flavored coffee beans. The 25 pound
mixture cost $219.50. Find the cost per pound of the
espresso and vanilla flavored coffee beans.
Answer:
Use systems of equations to solve.
Let x represent the cost per pound of the espresso coffee beans and
y represent the cost per pound of the vanilla coffee beans.
6x + 5y = 77.50
20x + 13y = 234.50, both of these are given.
Rewrite these equations so you can eliminate one of the variables;
60x + 50y = 775, Multiply both sides of the equation by 10
60x + 39y = 703.5, Multiply both sides of the equation by 3
Now Subtract equation 2 from equation 1,
11y = 71.5
y = 6.5
Solve for x,
6x + 5(6.50)= 77.50
x = 7.50
Therefore, the cost per pound of the espresso coffee beans is $7.50, and
the cost per pound of the vanilla coffee beans is $6.50.