The function f(x) = x⁵ - x³ + x is odd. It satisfies the condition f(-x) = -f(x), making it an odd function.
To determine whether the function f(x) = x⁵ - x³ + x is even, odd, or neither, we need to test if the function satisfies the following conditions for all x:
f(-x) = f(x) for even functions
f(-x) = -f(x) for odd functions
If the function satisfies neither of these conditions, then it is neither even nor odd.
Testing f(-x) = f(x):
f(-x) = (-x)⁵ - (-x)³ + (-x) = -x⁵ + x³ - x
f(x) = x⁵ - x³ + x
Since f(-x) is not equal to f(x), the function is not even.
Testing f(-x) = -f(x):
f(-x) = (-x)⁵ - (-x)³ + (-x) = -x⁵ + x³ - x
-f(x) = -(x⁵ - x³ + x) = -x⁵ + x³ - x
Since f(-x) = -f(x), the function is odd.
Therefore, the given function f(x) = x⁵ - x³ + x is odd.
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A. A fish is 12 m below the surface of the ocean. What is its elevation?
B. A seabird is 28 m above the surface of the ocean. What is its elevation?
C. If the bird is directly above the fish, how far apart are they?
We can say that by equation 12 metres below the ocean's surface, a fish may be found. 28 metres above the ocean's surface, a sea bird may be seen and distance between them is 40 meters.
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
We require knowledge about an object's elevation to tackle such issues.
12 metres below the ocean's surface, a fish may be found.
28 metres above the ocean's surface, a sea bird may be seen.
A fish is 12 metres below the ocean's surface.
The fish's elevation is negative since it is below sea level. Consequently, the fish's elevation is -12 metres.
B.) A marine bird flies 28 metres above the water's surface.
given that the seabird is above the water. The sea bird is 28 metres above sea level.
If the bird soars straight over the fish, (C),
If the fish and the bird are immediately above one another,
Distance between fish and bird = |(elevation of the fish)| + |(elevation of the sea bird)|
= |-12| + |28|
= 12 + 28
= 40 meters
distance between them is 40 meters.
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Question 6: Question 6 E 0/2 pts Which source of bias is most relevant to the following situation: A group of first time offenders are asked to rate their court-appointed defense attorney while their case is still being argued in court. Self-interest study voluntary response bias O nonresponse bias or missing data perceived lack of anonymity loaded or leading question Question 7: Question 7 < > In a study, the data you collect is Mood on a Happy/OK/Sad scale. This data is: Quantitative Qualitative (Categorical) Question 8: Question 8 < > Does this describe an observational study or an experiment? The gender of children born in January were tallied Experiment Observational Study
Perceived lack of anonymity is the source of bias that is most relevant to the given situation.
The data collected in the study, which is Mood on a Happy/OK/Sad scale, is qualitative or categorical data.
This describes an observational study.
What is Statistics?
Statistics is a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and statistical methods to extract meaningful insights from data and to draw conclusions or make decisions based on the findings.
When individuals are asked to provide feedback on a court-appointed defense attorney while their case is still being argued in court, they may feel that their responses are not anonymous and that the attorney or the court may retaliate against them if they provide negative feedback. This can lead to a perceived lack of anonymity, which can influence their responses and bias the feedback they provide. They may feel pressured to provide positive feedback or may choose not to provide any feedback at all, leading to nonresponse bias or missing data.Therefore, the perceived lack of anonymity can introduce bias into the feedback collected in this situation.Qualitative data is data that represents characteristics or qualities, rather than quantities or numbers. In this case, the mood of the respondents is being measured using categories or labels, such as Happy, OK, or Sad. This type of data cannot be easily measured or expressed in numerical terms, and therefore is considered qualitative.On the other hand, quantitative data is data that can be measured and expressed in numerical terms. This type of data is usually represented by numbers and can be analyzed using statistical methods to draw meaningful conclusions. Examples of quantitative data include age, weight, temperature, and number of hours worked.In an observational study, the researcher observes and records data on the subjects without intervening or manipulating any variables. In this case, the researcher is simply tallying the gender of children born in January, which does not involve any intervention or manipulation of variables.On the other hand, in an experiment, the researcher manipulates one or more variables to observe the effect on the outcome variable. The researcher randomly assigns participants to different groups or conditions and controls one or more variables to determine cause-and-effect relationships.Since the gender of children born in January is being observed and recorded without any intervention or manipulation of variables, it is an observational study.Learn more about Statistics click here:
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calculate the interest and maturity value.
Interest Rates Term
Ordinary Exact (Days)
4%
Purpose
Drum Set
Used Car
Used Dirt Bike
School Tuition for Twins
Principal
$ 900.00
1,960.00
4,800.00
9,675.00
-
10
6%
9
Interest
45 a.$
30 a.
a.
123
275
a.
Maturity
Value
b. S
b.
b.
b.
The answers are:
a. For Drum Set: Interest = $0.98, Maturity Value = $900.98b. For Used Car: Interest = $2.88, Maturity Value = $1,962.88c. For Used Dirt Bike: Interest = $5.23, Maturity Value = $4,805.23d. For School Tuition for Twins: we can't calculate the interest or maturity value without the time period.How to calculate the interest and maturity valueTo calculate the interest and maturity value, we need to use the formula:
Interest = Principal x Rate x Time
Maturity Value = Principal + Interest
Where:
Principal is the initial amount investedRate is the interest rate as a decimalTime is the time period in yearsFor the given information, we have:
Drum Set:
Principal = $900.00
Rate = 4% = 0.04
Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)
Interest = $900.00 x 0.04 x 0.0274 = $0.98
Maturity Value = $900.00 + $0.98 = $900.98
Used Car:
Principal = $1,960.00
Rate = 6% = 0.06
Time = 9/365 = 0.0247 years (assuming an exact interest calculation based on days)
Interest = $1,960.00 x 0.06 x 0.0247 = $2.88
Maturity Value = $1,960.00 + $2.88 = $1,962.88
Used Dirt Bike:
Principal = $4,800.00
Rate = 4% = 0.04
Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)
Interest = $4,800.00 x 0.04 x 0.0274 = $5.23
Maturity Value = $4,800.00 + $5.23 = $4,805.23
School Tuition for Twins:
Principal = $9,675.00
Rate = 6% = 0.06
Time = not specified
We don't have the time period for this investment, so we can't calculate the interest or maturity value without that information.
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Can someone please help me??
consider a group of 150 students. out of them suppose 30 are math majors, 40 are engineering majors, and 20 are both math and engineering majors. if a student is selected randomly, a). what is the probability that the student is from other majors? note: round your answer to the nearest second decimal place b) what is the probability that the student majors only math? note: round your answer to the nearest second decimal place c) what is the probability that the student does not major engineering? note: round your answer to the nearest second decimal place
The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.
a) Probability of a student being from other majors = (150-90) / 150 = 0.40
b) Probability of a student majoring only math = (30 - 20) / 150 = 0.13
c) Probability of a student not majoring engineering = (150 - 40 - 20) / 150 = 0.73
Probability = Number of Favorable Outcomes / Total Number of Outcomes
For part a)
Number of Favorable Outcomes = 150-90 = 60
Total Number of Outcomes = 150
Therefore, Probability = 60 / 150 = 0.40
For part b)
Number of Favorable Outcomes = 30-20 = 10
Total Number of Outcomes = 150
Therefore, Probability = 10 / 150 = 0.13
For part c)
Number of Favorable Outcomes = 150-40-20 = 90
Total Number of Outcomes = 150
Therefore, Probability = 90 / 150 = 0.73
The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.
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does -8(v+1)=2(1-4v)-9 have no solutions one solution or all numbers are solutions if its one solve for v
Answer:
No solutions
Step-by-step explanation:
[tex]-8(v+1)=2(1-4v)-9\\-8v-8=2-8v-9\\8=-7\\8\neq-7[/tex]
Hence, there are no solutions to make both sides of the equation true.
Find X and y-intercepts for
12x +6y =108
Answer:
y=-2 over 1x+18
Step-by-step explanation:
Parallelogram CDEF is shown below.
Find the length of the segments and the measure of the angles: CF, FE, ∠D, and ∠
Length of the segments are 11 units and 10 units and measures of the angles are 54° and 126°.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Since, CDEF is a parallelogram, opposite angles are equal.
(9y)° = (7y + 28)°
9y - 7y = 28
2y = 28
y = 14
∠C = ∠E = 9y = 126°
Sum of the angles of a quadrilateral is 360°.
∠D = ∠F = (360° - (126°×2)) / 2 = 54°
Opposite sides are also equal for a parallelogram.
2x = x + 5
2x - x = 5
x = 5
CF = DE = 2x = 10 units
CD = FE = 3x - 4 = 11 units
Hence opposite sides are equal with lengths 10 units and 11 units and opposite angles are equal with measures 54° and 126°.
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What will be the new position of minute hand if it starts from 1 and turns 210. Degree
The new position of minute hand if it starts from 1 and turns 210° will be at the 40 minutes mark on the clock face.
The minute hand of a clock completes a full rotation every 60 minutes, or 360°. This means that each minute on the clock face corresponds to an angle of 6 degrees. (360 divided by 60 minutes). If the minute hand starts from the 1 and turns 210 degrees, we can calculate the number of minutes it has moved by dividing 210 by 6, which gives us 35. Therefore, the new position of the minute hand will be 35 minute mark on the clock face. However, since the minute hand started at the 1, we need to add 5 minutes in the final answer.
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Quadrilateral QRST is shown. Lynn draws quadrilateral WXYZ, which is similar to quadrilateral QRST, with WX = 5 inches.
What is the measure of angle Y?
Since angle S is 65°, angle Y will also be 65°
What are similar shape ?Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.
Since angle S is 65° from the diagram shown, angle will be measured as 65°.
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A ball is rolling down a slope and continuously picks up speed. Suppose the function f(x)=1.2(1.11) to the power of x describes the speed of the ball in inches per minute. How fast will the ball be rolling in 20 minutes? Round the answer to the nearest whole number.
plug in 20 = x for function f(x)
1.2(1.11)^20 = ?
Cans of soda are packaged in boxes containing the same number of cans.
There are 36 cans in 4 boxes.
a) How many cans are there in 7 boxes?
b) How many boxes are needed to package 99 cans of soda?
a)
63 cans in 7 boxes.
b)
11 boxes are needed for 99 cans.
What is a unit rate?It is a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
36 cans in 4 boxes.
This means,
1 box = 36/4 cans
1 box = 9 cans
Multiply 7 on both sides.
7 box = 63 cans ______(1)
1 box = 9 cans
Multiply 11 on both sides.
11 box = 99 cans ______(2)
Now,
From (1) and (2)
a)
63 cans in 7 boxes.
b)
11 boxes are needed for 99 cans.
Thus,
63 cans in 7 boxes.
11 boxes are needed for 99 cans.
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What’s the slope of a line perpendicular to 3x-5y=45
Answer:
-5/3.
Step-by-step explanation:
To find the slope of a line perpendicular to another line, we need to remember that the slopes of two perpendicular lines are negative reciprocals of each other. To find the slope of the line perpendicular to 3x - 5y = 45, we need to first convert it to slope-intercept form, which is y = mx + b, where m is the slope of the line.
First, isolate the y-term:
3x - 5y = 45
5y = -3x + 45
y = -(3/5)x + 9
So the slope of the original line is -3/5. The slope of the line perpendicular to it would be the negative reciprocal of this slope, which is -5/3.
Therefore, the slope of a line perpendicular to 3x - 5y = 45 is -5/3.
Answer:
3/5
Step-by-step explanation:
A recipe calls for 2 cups of water for every 1/3 cups of flour. How much water is needed if you use 7 cups of flour?
for todays free brainiest what is 6+9 here's a hint: its not 15 first to answer get brainlest
Answer:
12
Step-by-step explanation:
6 with 9 figers
Answer:
Let x be 6 and y be 9.
x + y = 6 + 9 = 15.
However, x + y does not equal 15. Hence, we can deduce that:
x + y = 15 [tex]\neq[/tex] 15.
15 does not equal 15, so if 15 is 15 and not equal to 15, we can prove that since 6 does not equal 9, 6 is 9. We can therefore conclude that we need to solve for x + x. Since we proved that something is something by not being something, 2x ix 2x but not 2x.
2x isn't 2x but is 2x, so the answer isn't the answer but is still the answer. Therefore, this question isn't a question when it is a question.
:) I am teaching you Maths in Ohio.
Write an equivalent expression by combining like terms. 8b - 4b b =5
The equivalent expression for 8b-4b is 4b.
What are like terms?In algebra, like terms are the terms that contain the same variable which is raised to the same power. In this only numerical coefficients may vary.
Given 8b-4b. b=5
We have to combine the like terms to get an equivalent expressions.
Like terms containing variables with same power.
When combining like terms, we have to add or subtract their coefficients.
Coefficients are the numbers which are placed with variable.
Then, 8b-4b=4b.
When b=5⇒4*5=20
Hence, the equivalent expression for 8b-4b is 4b.
Complete question:
Write an equivalent expression by combining the like terms 8b-4b. Find the value of expressions when b=5.
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Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $7,000, annual interest: 3%, interest periods: 6 , number of years: 17
The difference between the investment below and one with the same principal at the same rate compounded yearly is $18123.29.
How would you compare investments?The Payback Period is the most straightforward metric to use when contrasting investment options. Simply defined, this is the minimal amount required for you to recoup your initial investment.
compound interest, which is referred to as
[tex]A = P(1+r/n)^n×t[/tex]
Where
A = amount at the end of t years
r = interest rate.
n = periodic interval
P = principal amount deposited
Considering investment compounded annually
P = 7000
r = 3% = 3/100 = 0.03
n = 1
t = 17 years
[tex]A = 7000(1 + 0.03/1)^1× 12A = 7000(1.03)^12[/tex]
A = $9980.32
For the second investment,
n = 6
[tex]A = 7000(1 + 0.08/6)^6 × 12A = 7000(1 + 0.0133)^72A = 7000(1.0133)^72A = $18123.29[/tex]
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Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days. She also paid $18 for a guided waterfall tour. Tara paid $94 in all. What was the rental cost of each day Tara used the kayak?
Answer:
$19
Step-by-step explanation:
calculate 94-18/4 = 19
m<1=103. Find m<2.
Answer quick!!!
Because angles 1 and 2 are adjacent, we will see that the measure of angle 2 is 77°.
How to find the measure of angle 2?Here we know that m∠1 = 103°, and we want to find the measure of angle 2, which is an angle adjacent to angle 1.
That means that if we add their measures, then we will get a plane angle, this means that:
m∠1 + m∠2 = 180°
Then we can write:
103° + m∠2 = 180°
m∠2 = 180° - 103° = 77°
That is the measure of angle 2.
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Need help on these question with step by step. What are the values of x?
-1/2-4x/5 = 1/2-2x
2x-3x/2=-x+1/3
5/3-x/5=-1
-2x-4=-1/5+3x/4
-6x+1=x-1
The values of x for each equation is given below:
5/14, 2/3, 10, -39/20, 0.How to solve for thisTo find the value(s) of x, you will need to solve each equation for x.
1. -1/2 - 4x/5 = 1/2 - 2x
Add 1/2 to both sides:
-1/2 - 4x/5 + 1/2 = 1/2 - 2x + 1/2
Combine like terms on the left side:
0 - 4x/5 = 1 - 2x
Multiply both sides by 5:
0 - 4x = 5 - 10x
Add 4x and 10x to both sides:
4x + 10x = 5
Combine like terms:
14x = 5
Divide both sides by 14:
x = 5/14
2. 2x - 3x/2 = -x + 1/3
Multiply both sides by 2:
4x - 3x = -2x + 2/3
Combine like terms:
x = 2/3
3. 5/3 - x/5 = -1
Add x/5 to both sides:
5/3 - x/5 + x/5 = -1 + x/5
Combine like terms on the left side:
5/3 = -1 + x/5
Add 1 to both sides:
5/3 + 1 = -1 + x/5 + 1
Combine like terms:
6/3 = x/5
Multiply both sides by 5:
30/3 = x
Divide both sides by 3:
10 = x
4. -2x - 4 = -1/5 + 3x/4
Add 2x to both sides:
-4 = 2x - 1/5 + 3x/4
Add 1/5 to both sides:
-4 + 1/5 = 2x + 3x/4 + 1/5
Combine like terms:
-39/5 = 5x/4
Multiply both sides by 4/5:
-39/5 * 4/5 = 5x/4 * 4/5
Combine like terms:
-39/5 = 5x/4
Multiply both sides by 4:
-39 = 20x/4
Divide both sides by 20:
-39/20 = x
5. -6x + 1 = x - 1
Add 6x to both sides:
-6x + 6x + 1 = x - 1 + 6x
Combine like terms:
0 = 7x
Divide both sides by 7:
0/7 = 7x/7
Combine like terms:
0 = x
The values of x are: 5/14, 2/3, 10, -39/20, and 0.
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What are the names of these polygons?
a)
b)
c)
D)
Answer:
b) octogon
c) irregular pentagon
d) irregular hexagon
Step-by-step explanation:
A 13-ft by 27-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 384 ft^2, how wide is the walkway?
Answer:
w = 25 / 4 feet wide.
Step-by-step explanation:
Let's call the width of the walkway "w."
The area of the rectangular pool is 13 * 27 = 351 ft^2.
The area of the walkway can be calculated by adding up the area of four rectangles, one around each side of the pool:
2 * (13 + w) * w + 2 * (27 + w) * w = 384
Expanding the equation:
2 * 13w + 2w^2 + 2 * 27w + 2w^2 = 384
Combining like terms:
2w^2 + 40w = 384
Solving for w^2:
2w^2 + 40w - 384 = 0
Using the quadratic formula:
w = (-40 ± √(40^2 - 4 * 2 * -384)) / (2 * 2)
Simplifying:
w = (-40 ± √(1600 + 3072)) / 4
w = (-40 ± √4272) / 4
w = (-40 ± 65) / 4
w = (25 / 4) or (-105 / 4)
Since w must be a positive value, w = 25 / 4 feet wide.
Answer:look it up frfr
Step-by-step explanation:
Need help with this question urgent please
Answer:
x=4.5
Step-by-step explanation:
2 [x-3]-5=7
2x - 3 - 5 =7
2x - -2 =7
7+2=9
9/2=4.5
i may be wrong <3
the distribution of the amount of money undergraduate students spend on books for a term is right-skewed, with a mean of $400 and a standard deviation of $80. in a simple random sample of 100 undergraduate students, what is the expected value of the sample mean amount of money spent on books?
The expected value of the sample mean amount of money spent on books is equal to the population mean, which is $400.
This is a property of the sampling distribution of the sample mean, which states that the mean of all possible sample means is equal to the population mean.
In other words, if we take all possible random samples of size 100 from the population of undergraduate students, and calculate the mean amount of money spent on books for each sample, then the average of all these sample means will be $400.
The expected value of the sample mean amount of money spent on books can be calculated using the formula:
E(X) = μ
where X is the sample mean, and μ is the population mean.
In this case, the population mean is given as $400. Therefore, the expected value of the sample mean amount of money spent on books is also $400.
However, we can also calculate the standard error of the mean (SE) to get a measure of the variability of the sample mean. The formula for SE is:
[tex]SE = σ / sqrt(n)[/tex]
where σ is the population standard deviation, and n is the sample size.
Substituting the values, we get:
[tex]SE = 80 / sqrt(100) = 8[/tex]
This property is true regardless of the sample size, as long as the sample is randomly selected and independent. However, as the sample size increases, the sampling distribution of the sample mean becomes more normal and the standard error of the mean decreases, making the sample mean a more precise estimate of the population mean.
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What is AE
See the attachment for the problem to be answered.
The length of the segment AE is 10 units.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
The two triangles triangle ABE and triangle CDE are similar triangles.
We know that, the ratio of segments of similar triangle are equal thus:
10 / 8 = 2x + 6 / x+ 6
10(x + 6) = 8(2x + 6)
10x + 60 = 16x + 48
60 - 48 = 16x - 10x
12 = 6x
x = 2
Substitute the value of 2 in 2x + 6:
2(2) + 6 = 10 units.
Hence, the length of the segment AE is 10 units.
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NEED THIS ASAP……………
……………..
The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.
Solving a function:We can solve the given function by adding or subtracting the same integer on both sides. Here adding or subtracting the same number on both sides doesn't change the condition of the function. In end-use trial and error mothed to find the value of the variable 'x'
Here we have
f(x) = - 6x + 14 and g(x) = - 2ˣ + 6
The solution of - 6x + 14 = - 2ˣ + 6 can be calculated as follows
=> - 6x + 14 = - 2ˣ + 6
=> - 6x + 8 = - 2ˣ
=> - 6x + 8 = - 2ˣ
=> - 6x + 2ˣ = - 8
By using the trial and error method
At x = 2
=> - 6(2) + 2² = -8
=> - 12 + 4 = -8
Therefore,
The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.
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Degree 5. Double zero at x = 1, and triple zero at x = 3. Passes through the point (x, y) = (2, 87). y=
The equation is [tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].
What is meant by zeroes of polynomials?
All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.
It is given that degree of the equation is 5. so the highest power is 5 and there will be 5 zeroes.
It is given that 2 zeroes at x=1 and 3 zeroes at x= 3.
So, the equation is [tex]y=a(x-1)^{2} (x-3)^{3}[/tex].
We will substitute x=2 and y= 87 in the above equation.
[tex]87=a(2-3)^{3} \\a=-87[/tex]
Therefore now the equation will be:
[tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].
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Monday: P.S. 2- Algebraic Expressions
Problem and Effort:
Simplify the following
expression given the
variables m = 4, n = -3,
and p = -3
√e
m+n²-p
Correct Answer:
Answer:
Therefore, the simplified expression with the given values is √e^16.
Step-by-step explanation:
Given the values of the variables m = 4, n = -3, and p = -3, we can simplify the expression √e^(m + n^2 - p) as follows:
m + n^2 - p = 4 + (-3)^2 - (-3) = 4 + 9 + 3 = 16
So the expression becomes: √e^16 = √e^(m + n^2 - p) = √e^16
Therefore, the simplified expression with the given values is √e^16.
NEED HELP ASAPPP
Find m/TUV.
m/TUV=
Answer: 54 degrees
Step-by-step explanation:
The angle will be half of that arc segment
please help ASAP !!!!
First, use the equation for a hemisphere. Since a sphere's equation is [tex]\frac{4}{3}\pi r^{3}[/tex], and a hemisphere is half a sphere, we can use the equation [tex]\frac{2}{3}\pi r^{3}[/tex]. We know the radius is 6 inches, and we can approximate pi as 3.14, so now let's plug in our values:
[tex]\frac{2}{3}\ (3.14) 6^{3}=\frac{2}{3} \ (3.14)(216)= \frac{2}{3}(678.16)= 452.16[/tex]
The volume of the hemisphere is about [tex]452.16 in^{3}[/tex].
The formula for the volume of a cone is [tex]\pi r^{2}\frac{h}{3}[/tex]. Again, let's plug in our values:
[tex](3.14)(36)\frac{6}{3} =(3.14)(36)(2)=(3.14)(72)=226.08[/tex]
The volume of the cone is about [tex]226.08 in^{3}[/tex].
Subtract 226.08 from 452.16 and you get 226.08.
The volume of the remaining solid will be [tex]226.08 in^{3}[/tex].
