Answer:
The zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3 + √29/2, x = 3 - √29/2, and x = -0.4495 (approximately).
Step-by-step explanation:
To find all the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15, we can use the Rational Root Theorem and synthetic division.
Write the polynomial function in descending order of degree: f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15.
Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±3, ±5, ±15.
Use synthetic division to test each possible zero. We start with x = 1:
1 │ 1 -2 -8 10 15
│ 1 -1 -9 1
└───────────────
1 -1 -9 1 16
x = 1 is not a zero of the polynomial function.
We continue testing the remaining possible zeros:
-1 │ 1 -2 -8 10 15
│ -1 3 5 -15
└───────────────
1 -3 -3 15 0
Since the remainder is zero, we have found a zero of the polynomial function at x = -1.
We can use synthetic division to factor the polynomial function:
(x + 1)(x^3 - 3x^2 - 6x + 15)
Now we can solve for the remaining zeros of the polynomial function by factoring the cubic equation using the Rational Root Theorem and synthetic division:
3 │ 1 -3 -6 15
│ 3 0 -18
└─────────────
1 0 -6 -3
x = 3 is not a zero of the polynomial function.
-3 │ 1 -3 -6 15
│ -3 18 -36
└────────────
1 -6 12 -21
x = -3 is not a zero of the polynomial function.
The only remaining possible rational zeros are ±1/2 and ±5/2, but testing these values using synthetic division does not yield any more zeros.
However, we can see that the polynomial function can be factored as follows:
(x + 1)(x - 3)(x^2 - 3x - 5)
We can solve for the remaining zeros of the polynomial function by factoring the quadratic equation using the quadratic formula or factoring by grouping. Either way, we find that the remaining zeros are approximately x = (3 + √(29))/2 and x = (3 - √(29))/2.
Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3 + √29/2, x = 3 - √29/2, and x = -0.4495 (approximately).
Hopefully this helps, if not I'm sorry! If you need more help, you may ask me! :]
The frequency table shows the scores from rolling a dice 10 time 1 1 2 2 3 1 4 2 5 4 6 2 find the mean
On answering the provided question, we have got that 3.3 is the average equation result after rolling the dice ten times.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
We must add up all the scores and divide by the total number of rolls in order to determine the mean.
The total of every score is:
1 + 1 + 2 + 2 + 3 + 1 + 4 + 2 + 5 + 4 + 6 + 2 = 33
There are ten rolls in total.
The mean is as a result:
mean = total scores / total rolls = 33 / 10 = 3.3
3.3 is the average result after rolling the dice ten times.
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PLEASE HELPPP AND SHOW THE WORKKKK
The answer will be as follows after answering the supplied question As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
y - y1 = m(x - x1) (x - x1)
where (x1, y1) is the location of one of the points and m is the line's slope.
We may use the slope formula to calculate the slope:
m = (y2 - y1) / (x2 - x1) (x2 - x1)
where the coordinates of the two points are (x1, y1) and (x2, y2).
m = (5 - (-3)) / (3 - (-1)) = 8 / 4 = 2
As a result, the slope of the line is 2. We can now use one of the two locations to get the equation of the line. Let's take (-1, -3) as an example:
y - (-3) = 2(x - (-1))
y + 3 = 2(x + 1)
y + 3 = 2x + 2
y = 2x - 1
As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.
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Find s9 for the series 1 + 5 + 25 + 125 +.
a. 248, 321
b. 284, 211
c. 488 281
d. 588, 451
The 9th term of the given series is 588, 451, which can be calculated using the formula for the nth term of an arithmetic progression Tn = a + (n-1)d, where a is the first term and d is the common difference.
The given series is an arithmetic progression with a common difference of 4. The formula for the nth term of an arithmetic progression is given by Tn = a + (n-1)d, where a is the first term and d is the common difference.
Therefore, for the given series, a = 1 and d = 4.
Substituting these values in the above formula, we get
T9 = 1 + (9-1)4
= 1 + 32
= 33
Now, adding 33 to each of the terms of the given series, we get
1 + 33 = 34
5 + 33 = 38
25 + 33 = 58
125 + 33 = 158
Therefore, the required 9th term of the series is 588, 451.
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Sam and terry contribute money to buy 2 litre tub of juice in the ratio of 2:3 calculate the amount of juice each one received after sharing in the ratio of 2:3
Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in the ratio of 2:3.
To solve this problem, we need to use the concept of ratio and proportion.
Let's first find the total amount of money contributed by Sam and Terry. Since the ratio of their contributions is 2:3, we can write:
Total contribution = Sam's contribution + Terry's contribution
Let's assume that Sam contributed $2x and Terry contributed $3x. Then, we have:
Total contribution = $2x + $3x = $5x
Now, we know that the total contribution is equal to the price of the juice, which is not given in the problem. So, let's assume that the price of the 2-litre tub of juice is $10. Then, we have:
Total contribution = Price of juice = $10
Therefore,
$5x = $10
Solving for x, we get:
x = $2
So, Sam contributed $4 and Terry contributed $6.
Now, to find the amount of juice each one received, we need to share the 2-litre tub in a ratio of 2:3.
The total ratio is 2+3 = 5.
So, Sam will receive 2/5 of the juice and Terry will receive 3/5 of the juice.
Therefore, Sam will receive (2/5) × 2 litres = 0.8 litres of juice, and Terry will receive (3/5) × 2 litres = 1.2 litres of juice.
In conclusion, Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in a ratio of 2:3.
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Please answer quick will give 60 points
Answer: Answers below
Step-by-step explanation:
1. $15.64
2. 5370.28 Yen
3. 13425.70 Yen
4. $100
5. 67128.51 Yen
6.$782.08
Answer: 1: 15 2: 5370 3:13400 4: 160 5: 67100 6: 780
Step-by-step explanation: These are rounded to the nearest 100th
A triangle with a height of 9 inches has an area of 36 square inches. How long is the base of the triangle Plsss show me the process of ur answer! Tyy
someone help me
please asap
Answer:
Step-by-step explanation:
[tex]a)\quad AB[/tex]
[tex]b)\quad AB[/tex]
[tex]c)\quad AC[/tex]
[tex]d)\quad BC[/tex]
[tex]e)\quad BC[/tex]
[tex]f)\quad AC[/tex]
12 Workers can do a piece of work in 30 days. Find how many workers should be added to finish the work in 24 days?
The answer is in the attachment given below ...
Thank you :)
Liam earned $328. 65 at his summer jobs. He spent $136. 60 and put the rest of the money in his savings account. Which equation and solution shows how much money, m, Liam saved?
Liam saved $192.05 from his summer jobs.
What are probability and examples?It is based on the probability that something will happen. The fundamental underpinning of theoretical probability is the justification for probability. For instance, while flipping a coin, there is a 50% probability that it will land on its head.
By deducting his outgoings from his total earnings, we can calculate how much money Liam saved:
m = 328.65 - 136.60
Condensing the phrase:
m = 192.05
Liam was able to save $192.05 as a result of his summer jobs.
The following equation and its answer demonstrate how much money Liam has saved:
m = 328.65 - 136.60
m = 192.05
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Please I need help. Using y=k/x, you get k=1.5. So applying this, the first two are correct and in inverse proportion, however the last one doesn’t seem to work. Please help
Answer:
The last one doesn't work because s and t aren't inversely proportional. If they were inversely proportional, k would remain constant.
Use the central limit theorem(CLT) to compute the expected amount of sampling error with a sample size of 25 for the population with a mean of μ= 16 and a standard deviation of σ= 5 show work.
The expected amount of sampling error with a sample size of 25 is 1.
The Central Limit Theorem (CLT): What is it?According to the Central Limit Theorem (CLT), a statistical theory, regardless of the population distribution's form, the distribution of sample means tends to resemble a normal distribution as sample size grows. This indicates that the distribution of the means of multiple samples of the same size taken from a population will be roughly normal. Since it enables us to utilise normal distribution features to draw conclusions about a population even when the population distribution is unknown or non-normal, the CLT is crucial to statistics.
Given that, μ= 16 and σ= 5.
The formula for the standard error of the mean (SEM) is:
SEM = σ / √(n)
SEM = 5 / √(25)
SEM = 1
Hence, the expected amount of sampling error with a sample size of 25 is 1.
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Which function is the inverse of f(x)= -x^3 -9?
Answer:
B. [tex]\sqrt[3]{-x-9}[/tex]
Step-by-step explanation:
Switch x and y, and then solve for y.
[tex]y = -x^3-9\\x=-y^3-9\\x+9=-y^3\\-x-9=y^3\\\sqrt[3]{-x-9} =y[/tex]
If a, b, c, and d are real numbers, which of the following is a statement of the addition property of equality?
The correct statement is a=b implies that ac=bc.
What is addition property ?If the real numbers a and b are such that a=b, then their values are equal.
The result of adding c to both sides of the formula a=b is:
a+c = b+c
This is so that the equality of an equation is not altered by adding the same value to both sides.
As a result, if a=b, we can infer that a+c=b+c, meaning that if two real numbers are equal, adding the same value to both would also produce two identical numbers. One of the core characteristics of equality, this holds true for all real numbers.
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meters and feet are two different scales for measuring distance. Five meters is approximantly 16.41 ft, and 12 m is approximently 39.37ft. write an equation that shows the approximate distance in feet as a function of the distance in meters
Step-by-step explanation:
16.41 ft / 5 m = 'unit rate' (or conversion factor) = 3.282 ft/ m
then # ft = 3.282 ft / m * # meter (approximately )
The function f(x)=4x-8 is reflected accross the y axis resulting in a new function write the equation of g(x)
Tableau DA 3-2: Exercise, Computing cost per equivalent unit and assigning costs to output LO P1
The equivalent unit of production- Weighted Average Method is given in the attached image.
What is the equivalent unit of production- Weighted Average Method?The equivalent units of production (EUP) in the weighted average method refer to the units of output that have been partially completed during a period, and are expressed in terms of fully completed units.
In the weighted average method, the costs incurred during the period are combined with the costs of beginning work in process (BWIP) to determine the cost per equivalent unit. This cost per equivalent unit is then used to assign costs to the units completed and transferred out and to the units still in process at the end of the period.
The EUP in the weighted average method is calculated by adding together the units completed during the period with the equivalent units of work done on the units that are still in process at the end of the period.
The equivalent units are calculated by multiplying the number of partially completed units by the percentage of completion for the period.
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Write tan x in terms of cos x.
The written form of tan x in terms of cos x as required to be determined in the task content is; tan x = (√( 1 - cos² x) ) / cos x.
What is tan x in terms of cos x?As evident from the task content; it is required that tan x be written in terms of cos x.
Hence, recall from trigonometric identities that;
tan x = sin x / cos x
However, since sin² x = 1 - cos² x from ( sin²x + cos²x = 1)
It follows that; sin x = √( 1 - cos² x)
Hence, it can be written that;
tan x = (√( 1 - cos² x ) ) / cos x.
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On his 25th birthday, Matthew started an annuity for his retirement. He deposits $630 each month into an account earning 8% annual interest compounded monthly. He determines that he will be able to retire once he has $1,000,000 in his retirement account. Determine how old Matthew will be when he is able to retire.
Matthew who started an annuity on his 25th birthday by depositing $630 monthly into an account earning 8% annual interest compounded monthly will become 55 years old when the retirement account will be $1,000,000.
What is an annuity?An annuity involves a series of payments made periodically.
The annuity attracts an interest rate compounded periodically.
Compounding involves charging interest on accumulated interest and the principal for each compounding period.
I/Y (Interest per year) = 8%
PV (Present Value) = $0
PMT (Periodic Payment) = $630
FV (Future Value) = $1,000,000
Results:
N = 368.641 months
= 30 years and 9 months
Sum of all periodic payments = $232,470
Total Interest = $767,530
Matthew's current age = 25 years
55 years old (25 + 30)
Thus, Matthew will be 55 years old when his retirement (annuity) account grows to $1,000,000.
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8. Theo went to a bakery on Saturday morning. He bought a cup of hot chocolate and some bagels. The hot
chocolate cost $3.50 and each bagel costs $0.75 each.
(a) Write a linear function, that models the total cost, c, in dollars, of Theo's order based on the number of
bagels, b, he buys.
(b) Explain what the statement below means in the context of the problem.
c(6)=8
a) The total cost, c, in dollars, of Theo's order based on the number of
bagels, b, he buys is: c = 0.75b + 3.5
b) The statement c(6) = 8 represents that the number of bagels bought was 6 which resulted in a total cost of $8
How to solve Linear Equation Word Problems?The general expression for a linear equation in slope intercept form is:
y = mx + b
Where:
m is slope
b is y-intercept
a) Let the number of bagels bought be b
Cost of each bagel = $0.75
Cost of chocolate = $3.50
Thus:
Total cost is:
c = 0.75b + 3.5
b) c(6)=8
This means the number of bagels bought was 6 which resulted in a total cost of $8
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Combine the like terms to create an equivalent expression.
7+4c+2d+3=7+4c+2d+3=7, plus, 4, c, plus, 2, d, plus, 3, equals
Answer:
4c + 2d + 10
Step-by-step explanation:
The expression given is mostly already simplified, and the like terms that have variables are already combined.
As for 7 and 3, they are like terms because neither of them are attached to a variable.
Combining these like terms:
7 + 3 = 10The equivalent expression is now 4c + 2d + 10.
Find the mean of the first five natural numbers
Answer:
The first five natural number are 1, 2, 3, 4 and 5. Hence, the mean of the five natural numbers is 3.
Answer:
3
Step-by-step explanation:
[tex]\frac{1+2+3+4+5}{5}[/tex] = [tex]\frac{15}{5}[/tex] = 3
The natural numbers are also called the counting numbers. They are the set of numbers: 1, 2, 3, ....
Helping in the name of Jesus.
seppect you are a news fesorter following ten oriminal srials (a) It the bras wten in Jagat, what is the probebsty that al the defendants would be found guity? (found your ansmer to three deomal place
The probability of all the defendants being found guilty is 1/16. Answer: 1/16.
As per the given information, there is a criminal trial happening in Jagat, and the question is about finding the probability of all the defendants being found guilty. Here's how to solve it:The total number of possible outcomes is 2, since each defendant can either be found guilty (G) or not guilty (NG).So, n(S) = 2 * 2 * 2 * 2 = 16 (since there are 4 defendants)The probability of all the defendants being found guilty can be found as:Probability = Number of favorable outcomes / Total number of possible outcomes Since there are 16 possible outcomes, let's calculate the number of favorable outcomes:All the defendants being found guilty (G G G G) is just one such outcome. Hence, the number of favorable outcomes is 1.The probability can be calculated as:Probability = Number of favorable outcomes / Total number of possible outcomes= 1/16 Hence, the probability of all the defendants being found guilty is 1/16. Answer: 1/16.
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now that we have determined that the problem deals with combinations, calculate the number of ways that six letters can be grouped from nine letters total. fill in the blanks below with the correct numbers. provide your answer below:
Answer : There are 84 different ways that six letters can be grouped from nine letters total.
Now that we have determined that the problem deals with combinations, we can use the formula for combinations to calculate the number of ways that six letters can be grouped from nine letters total. The formula for combinations is:
C(n,k) = n! / (k! * (n-k)!)
Where n is the total number of items, and k is the number of items being chosen. In this case, n = 9 and k = 6. Plugging these values into the formula gives us:
C(9,6) = 9! / (6! * (9-6)!)
C(9,6) = 9! / (6! * 3!)
C(9,6) = 362880 / (720 * 6)
C(9,6) = 362880 / 4320
C(9,6) = 84
Therefore, there are 84 different ways that six letters can be grouped from nine letters total.
Answer: 84.
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20. What is the value of x to the nearest tenth? The diagram is not drawn to scale. (1 point)
x
x=14.4
x 12.7
x=3.0
x=2.2
Using similar triangle theorem, to calculate the ratios of the length, the value of x is 14.4 units
What is similar triangle theoremThe similar triangle theorem, also known as the AA (angle-angle) similarity theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar. That is, the corresponding sides of the triangles are in proportion, and the ratios of the corresponding sides are equal. In other words, if ΔABC ~ ΔDEF, then:
AB/DE = BC/EF = AC/DF
This theorem can be used to solve problems involving similar triangles, such as finding unknown side lengths or angles.
To find the value of x, we need to apply similar triangle theorem.
Taking the ratios of sides from the two triangles;
13.5 / 6.2 = x / 6.6
Cross multiply both sides and solve for x
x = (13.5 * 6.6) / 6.2
x = 14.4 units
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In the following two questions, find the area of each figure.
As a result, the right triangle x value of 65° is the answer to the given triangle issue.
What does a triangular actually mean?Triangles are categorised as polygons because they have four edges or more. Its shape is simple and symmetrical. The characters ABC make a square angle that is a triangle. When the edges are still not collinear, Euclidean geometry yields a single rectangle or square. Due to their three edges and three corners, triangles are considered polygons. The corners of a triangle are where its three edges meet. Angles in a trapezoid add up to 360 °.
Here,
Given:
Triangle is 90 degrees because of its right orientation.
The total of the triangle's angles is 180 degrees.
Thus,
=> x + 25° + 90° = 180°
=> x + 115° = 180°
=> x = 180° -115°
=> x = 65°
Thus, the value of x is 65°.
As a result, the answer to the provided triangle problem is
Right triangle's x number is 65 degrees.
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A number from 1-54 is chosen at random. Find each probability as a fraction (in simplest form), decimal, and percent.
P(odd or at most 14)
a: 7/27, 0.2593, 25.93%
b: 17/27, 0.62, 62%
c: 7/27, 0.25, 25%
d: 17/27, 0.6296, 62.96%
-------------------------------------
A card is chosen at random from a standard deck. Find each probability as a fraction in simplest form.
P(king)
a:1/52
b: 1/13
c: 4/52
d: 13/52
-----------------------
A card is chosen at random from a standard deck. Find each probability as a fraction in simplest form.
P(spade or heart)
Group of answer choices
a: 1/26
b: 1/2
c: 26/52
d: 2/52
------------------------
i dont need any explanations, so just the answers please ^^
Answer:
P(odd or at most 14)
Answer: (a) 7/27, 0.2593, 25.93%
P(king)
Answer: (d) 13/52
P(spade or heart)
Answer: (b) 1/2
A right rectangular container is 10 cm wide and 24 cm long and contains water to a depth of 7cm. A stone is placed in the water and the water rises 2. 7 cm. Find the volume of the stone
The volume of the stone is 1032 cm³.
The volume of the stone can be calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 2.7 cm. Therefore, the volume of the stone is V = 10 x 24 x 2.7 = 648 cm³.
The volume of the water in the container is calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 7 cm. Therefore, the volume of the water in the container is V = 10 x 24 x 7 = 1680 cm³.
The difference between the volume of the water and the volume of the stone is the volume of the water displaced by the stone, which is V = 1680 - 648 = 1032 cm³. Therefore, the volume of the stone is 1032 cm³.
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The value of a second-hand car is £8000
Each year it loses 20% of it value at the start of this year. work out its value an year ago
pls pls help quick
Answer:
£10,000
Step-by-step explanation:
100%-20%= 80% --> 0.8
£8000 divided by 0.8 = £10,000
Which line is perpendicular to the line y = -3x + 2
Answer:d
Step-by-step explanation:
real cube root of 64
The real cube root of 64 is 4.
What is Real cube root ?The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.
the prime factorization using the exponent found in the previous step. We can write the number 64 as:
64 = 2^2 * 2^2 * 2^2
Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:
∛2 = 1.259921...
Step 5: Multiply the factors together to get the final result:
∛64 = ∛(2^2 * 2^2 * 2^2) = ∛2^6 = (∛2)^2 = 1.259921...^2 = 4
Therefore, the real cube root of 64 is 4.
On the other hand we can easily find out by, the real cube root of 64 is 4, because 4 multiplied by itself three times gives 64:
4 * 4 * 4 = 64
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The real cube root of 64 is 4.
What is a Real cube root?
The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.
the prime factorization using the exponent found in the previous step. We can write the number 64 as:
64 = 2² * 2² * 2²
Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:
∛2 = 1.259921...
Step 5: Multiply the factors together to get the final result:
∛64 = ∛(2² * 2² * 2²) = ∛2⁶ = (∛2)² = (1.259921...)² = 4
Therefore, the real cube root of 64 is 4.
On the other hand, we can easily find out by, the real cube root of 64 is 4 because 4 multiplied by itself three times gives 64:
4 * 4 * 4 = 64
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