Step-by-step explanation:
According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n complex zeros (counting multiplicities).
The degree of the polynomial f(x) = 5x^6+2x^3−4x + 1 is 6, which means that it is a sixth-degree polynomial. Therefore, it has exactly 6 complex zeros (counting multiplicities).
Note that the zeros may be real or complex, and they may not all be distinct. To find the exact number of zeros and their values, we would need to use additional methods such as factoring, the rational zeros theorem, or numerical methods.
Answer:
The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root. In the case of the polynomial function f(x) = 5x^6+2x^3−4x + 1, it is a sixth-degree polynomial function, which means it has at most six complex roots. However, the Fundamental Theorem of Algebra does not tell us the exact number of roots, nor does it tell us whether the roots are real or complex.
To determine the number of real roots of the function f(x), we can use the Intermediate Value Theorem or graph the function to find the number of times it crosses the x-axis. However, determining the number of complex roots requires more advanced techniques, such as the use of the Fundamental Theorem of Algebra in combination with the Factor Theorem, Rational Root Theorem, or other methods.
Therefore, based on the Fundamental Theorem of Algebra alone, we can say that the function f(x) = 5x^6+2x^3−4x + 1 has at least one complex root, but we cannot determine the exact number or nature of the roots without additional analysis.
a fair coin 1s flipped repeatedly. what ts the probability that the fifth tail occurs before the tenth head?
The probability of having fifth tail occurring before the tenth head if a fair coin is flipped repeatedly is 0.377.
To solve this problem, we need to use the concept of negative binomial probability distribution.
The negative binomial probability distribution is a type of probability distribution that is used to describe the probability of k failures occurring before r successes in a sequence of independent and identical trials.
Let us consider the problem at hand.
We need to find the probability that the fifth tail occurs before the tenth head if a fair coin is flipped repeatedly.
Let X be the number of trials required to obtain the fifth tail. Then, X follows a negative binomial distribution with parameters r = 5 (number of successes we want) and p = 0.5 (the probability of obtaining a tail in a single flip).
The probability of obtaining the fifth tail on the kth trial is given by: P(X = k) = ᵏ-¹C₄(1 - p)ᵏ-ʳ *
where ᵏ-¹C₄ denotes the number of combinations of (k - 1) trials that yield 4 tails before the kth trial.
Since X should occur before the tenth head, k should be less than or equal to 9.
Therefore, we can calculate the required probability as follows:
P(X ≤ 9) = ∑P(X = k) for k = 5 to 9
= (⁴C₄*0.5⁵) + (⁵C₄*0.5⁶) + (⁶C₄*0.5⁷) + (⁷C₄*0.5⁸) + (⁸C₄*0.5⁹)
= (1*0.03125) + (5*0.015625) + (15*0.0078125) + (35*0.00390625) + (70*0.001953125)
= 0.376953125
Therefore, the probability that the fifth tail occurs before the tenth head if a fair coin is flipped repeatedly is 0.377.
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Help me me me help me
See pics for answers
A student is selected at random to work a problem on the
board.
What is the probability that the student selected is a female
junior?
0.15
0.25
0.20
0.50
archaeologists working at head-smashed-in-buffalo-jump have found the following bison bones: 7 right femurs, 10 left femurs, 15 various ribs, and 5 skulls. what is the minimum number of individuals (mni)?
The minimum number of individuals (MNI) of bison bones is 7.
Explanation:
The minimum number of individuals (MNI) of the bison bones discovered by archaeologists working at Head-Smashed-In-Buffalo-Jump is 5.
What is Head-Smashed-In Buffalo Jump?Head-Smashed-In Buffalo Jump is an archaeological site in Alberta, Canada. It is a cliff site used by First Nations people for bison hunting. Head-Smashed-In Buffalo Jump is a UNESCO World Heritage Site and is one of the world's oldest, largest, and best-preserved buffalo jump sites
How to calculate the minimum number of individuals (MNI) using the given bison bone data?The minimum number of individuals (MNI) of bison bones is the smallest possible number of bison from which the bones could have come. The minimum number of individuals (MNI) is calculated using the least number of right or left paired bones, such as femurs or humeri. The right femurs are the fewest paired bones with only seven out of the fifteen femurs found at the Head-Smashed-In Buffalo Jump site.
Therefore, the minimum number of individuals (MNI) of bison bones is 7.
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Finding Perpendicular Lines. Which line is perpendicular to a line that has a slope of -1/3 ?
Answer:
3
Step-by-step explanation:
you want to flip your slope so the 3 goes over the 1 like this: 3/1
And then flip the sign so the negative turns to a positive
5 gallons of gas cost $16.25 the cost per gallon is $3.25
the question what unit rate describes the number of gallons per dollar?
Answer: To find the unit rate that describes the number of gallons per dollar, we need to divide the number of gallons by the cost in dollars. In this case, we have:
Number of gallons = 5
Cost in dollars = $16.25
Dividing the number of gallons by the cost in dollars, we get:
Gallons per dollar = Number of gallons / Cost in dollars
= 5 / $16.25
= 0.3077...
Rounding to two decimal places, we get:
Gallons per dollar = 0.31
Therefore, the unit rate that describes the number of gallons per dollar is 0.31 gallons per dollar.
Step-by-step explanation:
a raffle has a grand prize of a european cruise valued at $9000 with a second prize of a rocky point vacation valued at $1300. if each ticket costs $3 and 11200 tickets are sold, what are the expected winnings for a ticket buyer?
The expected winnings for a ticket buyer is $0.8036.
The given details are:
Grand prize = $9000
Second prize = $1300
Cost of each ticket = $3
Total tickets sold = 11200
Expected winnings are calculated by finding the expected value. Expected value is calculated by multiplying each outcome by its probability and then adding the products.
The total amount collected from selling 11200 tickets will be:
Total amount collected = 11200 × $3 = $33,600
Probability of winning grand prize = 1/11200
Probability of winning second prize = 1/11200
Probability of losing = 1 - (1/11200 + 1/11200) = 1 - 2/11200 = 11200/11200 - 2/11200 = 11198/11200
Expected value = probability of winning grand prize × grand prize + probability of winning second prize × second prize + probability of losing × zero
Expected value = (1/11200) × $9000 + (1/11200) × $1300 + (11198/11200) × 0 = $0.8036
The expected winnings for a ticket buyer is $0.8036.
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Alejandra and her family are discussing how to pay for her college education. The cost of tuition at the college that Alejandra wants to attend is $9,000 per year. Alejandra's parents will pay 85% of the tuition cost every year, and she will pay the rest. Alejandra has one year to save enough money to attend her first year of college. What is the minimum amount of money she should save every month in order to reach her goal?
Responses
$637.50
$637.50
$1,350.00
$1,350.00
$112.50
$112.50
$28.12
The correct answer is $112.50. She should save $112.50 as the minimum amount every month in order to reach her goal.
To find the minimum amount of money Alejandra needs to save every month to attend her first year of college, we need to first determine the amount she needs to pay herself.
We know that her parents will pay 85% of the tuition cost, which is:
85% of $9,000 = 0.85 x $9,000 = $7,650
Therefore, Alejandra needs to pay the remaining amount:
$9,000 - $7,650 = $1,350
Since Alejandra has one year to save this amount, we need to divide $1,350 by 12 to find the minimum amount she should save every month:
$1,350 ÷ 12 = $112.50
Therefore, Alejandra should save at least $112.50 every month to reach her goal of attending college for her first year.
The correct answer is $112.50.
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a college entrance test consists of 112 questions. the test contains true/false (7 points each), fill in the blank (9 points each) and multiple choice (13 points each). there are 1172 possible points total on the test. the number of fill in the blank is 34 less than the number of true/false. how many points come from fill in the blank questions?
The test has average 80 true/false questions, 24 fill in the blank questions, and 28 multiple choice questions, with 7, 9 and 13 points respectively, totaling 1172 points.
The college entrance test consists of 112 questions in total, with different types of questions having different point values. There are 80 true/false questions, each worth 7 points, with a total of 560 points from these questions. There are also 24 fill in the blank questions, each worth 9 points, giving a total of 216 points from these questions. Finally, there are 28 multiple choice questions, each worth 13 points, for a total of 364 points from these questions. All together, the test has 1172 points available. The number of fill in the blank questions is 34 less than the number of true/false questions, meaning that there are more true/false questions than fill in the blank questions. The test is designed to assess a student's knowledge and comprehension of the subject they are taking the test for, and is made up of the three different types of questions to give a comprehensive assessment of their understanding.
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Which fractions are less than 1/2 ? choose all the correct answers
The fractions less than [tex]\frac{1}{2}[/tex] are:
a. [tex]\frac{2}{5}[/tex]
d. [tex]\frac{1}{6}[/tex]
e. [tex]\frac{3}{8}[/tex]
To see why, we can compare each fraction to [tex]\frac{1}{2}[/tex], which is equivalent to [tex]\frac{4}{8}[/tex]:
[tex]\frac{2}{5}[/tex] < [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 40, we get [tex]\frac{16}{40}[/tex] < [tex]\frac{20}{40}[/tex].[tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] > [tex]\frac{1}{2}[/tex], because when we convert both fractions to have a common denominator of 8, we get [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] and [tex]\frac{1}{2}[/tex] = [tex]\frac{4}{8}[/tex], and [tex]\frac{3}{4}[/tex] > [tex]\frac{4}{8}[/tex].[tex]\frac{4}{5}[/tex] > [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 40, we get [tex]\frac{32}{40}[/tex]> [tex]\frac{20}{40}[/tex].[tex]\frac{1}{6}[/tex] < [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 24, we get [tex]\frac{4}{24}[/tex] < [tex]\frac{6}{24}[/tex].[tex]\frac{3}{8}[/tex] < [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 8, we get [tex]\frac{3}{8}[/tex] < [tex]\frac{4}{8}[/tex].[tex]\frac{5}{6}[/tex] > [tex]\frac{4}{8}[/tex], because when we convert both fractions to have a common denominator of 12, we get [tex]\frac{10}{12}[/tex] > [tex]\frac{6}{12}[/tex].The complete question is:-
Which fractions are less than 1/2 ? choose all the correct answers
a. 2/5 b. 6/8 c. 4/5 d. 1/6 e. 3/8 f. 5/6
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a 6 foot ladder is leaning against a wall. if the top of the ladder slides down the wall at a rate of 2 feet per second, how fast is the bottom moving along the ground when the bottom of the ladder is 2 feet from the wall?
When the bottom of the 6-foot ladder is 2 feet from the wall, the bottom is moving along the ground at 1 foot per second.
To find the rate at which the bottom of the ladder moves along the ground, we can use the Pythagorean theorem and related rates. Let x be the distance from the bottom of the ladder to the wall, and y be the height of the ladder on the wall. The Pythagorean theorem is x² + y² = 36.
Differentiating both sides with respect to time (t) gives 2x(dx/dt) + 2y(dy/dt) = 0. We are given that dy/dt = -2 ft/s, and we need to find dx/dt when x = 2 feet.
To find y, we can use the Pythagorean theorem: 2² + y² = 36, so y² = 32, and y = 4√2. Plugging these values into the differentiated equation, we get 2(2)(dx/dt) + 2(4√2)(-2) = 0. Solving for dx/dt, we find that dx/dt = 1 ft/s.
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I need some help pretty please
The solution to the inequality is: x > 22/5 or x < 6/5
What is inequality?
Inequality is a mathematical concept used to compare two quantities or values, indicating that one value is greater than, less than, or not equal to another value. Inequalities are represented using inequality symbols such as > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).
To solve the inequality |14 - 5x| > 8, we can break it down into two cases:
Case 1: 14 - 5x > 8
In this case, we solve for x:
14 - 5x > 8
-5x > 8 - 14
-5x > -6
x < 6/5
However, we need to check if this solution satisfies the original inequality:
|14 - 5x| = |14 - 5(6/5)| = |14 - 6| = 8
Since the absolute value of the expression is exactly 8, the solution x < 6/5 does not satisfy the inequality |14 - 5x| > 8.
Case 2: 14 - 5x < -8
In this case, we solve for x:
14 - 5x < -8
-5x < -8 - 14
-5x < -22
x > 22/5
Again, we need to check if this solution satisfies the original inequality:
|14 - 5x| = |14 - 5(22/5)| = |14 - 22| = 8
Since the absolute value of the expression is exactly 8, the solution x > 22/5 satisfies the inequality |14 - 5x| > 8.
Therefore, the solution to the inequality is:
x > 22/5 or x < 6/5
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2. Describe the solution to this system of equation below. Justify your thinking.
3. Look at the system of equation.Solve the system algebraically. Show all of your work.
A student is asked to find the vertex of a parabola whose equation is as follows: y = 3 * (x + 4) ^ 2 - 2 The student concludes the vertex is at (4, - 2) . the student correct? If not, what do you think the student did wrong? Explain with as much relevant mathematical detail as possible. Please use at least 3 sentences total in your answer
Step-by-step explanation:
the general equation of a parabola is
y = a(x – h)² + k.
(h, k) is the vertex of the parabola.
comparing it to
y = 3(x + 4)² - 2
we see that (h, k) = (-4, -2).
the student made a sign mistake. it is "- h" in the squared factor. so, "+4" indicates "-4" as "h".
but the student simply used "+4".
helpppo enough points algebra 2 (3 variable problem)
Therefore, the football team scored 4 touchdowns, 2 field goals, and 1 safety in the game.
What is equation?An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on. An equation is often written with an equal sign (=) between the two expressions. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used extensively in mathematics, physics, engineering, and many other fields to describe relationships between different quantities.
by the question.
Let's denote the number of touchdowns scored by "T", the number of field goals scored by "F", and the number of safeties scored by "S".
From the problem, we know:
[tex]T + F + S = 8 (they scored points 8 times)\\7T + 3F + 2S = 38 (the total score was 38 points)\\T = F + S[/tex] (they scored as many touchdowns as they did field goals and safeties combined)
Substituting the third equation into the first, we get:
[tex]F + S + F + S = 8\\2F + 2S = 8\\F + S = 4[/tex]
We now have a system of three equations:
[tex]T + F + S = 8\\7T + 3F + 2S = 38\\T = F + S[/tex]
Substituting the third equation into the first two, we get:
[tex]7(F + S) + 3F + 2S = 38\\8(F + S) = 21[/tex]
Solving for F + S, we get:
[tex]F + S = 21/8[/tex]
However, we also know that F + S = 4, so there must be a mistake somewhere. Looking back at the problem, we see that the statement "they scored as many touchdowns as they did field goals and safeties combined" implies that T = F + S + 1 (since a touchdown is worth 7 points and a field goal and safety combined are worth 4 points). Substituting this into the first two equations, we get:
[tex](F + S + 1) + F + S = 8\\7(F + S + 1) + 3F + 2S = 38[/tex]
Simplifying, we get:
[tex]2F + 2S = 6\\10F + 9S = 31[/tex]
Solving for F and S, we get:
[tex]F = 2\\S = 1[/tex]
Substituting these values back into the equation T = F + S + 1, we get:
[tex]T = 4[/tex]
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What is the measure of arc c e d? 106° 108° 148° 212°
The measure of angle CED in a circle is 212°
The measurement of angles is done using basic geometric tools such as protractors and compasses. This tool helps to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles. Angles are measured in three ways: degrees, radians, and revolutions.
In the given figure:
∠ EBD = 160°
and ∠ CBE = 52°
We have to tell the measure of arc CED.
Since m( arc EBD) = 160° and m( arc CBE ) = 52°
From the figure:
m( arc CED ) = m( arc CBE ) + m( arc CBE)
= 160° + 52°
= 212°
Therefore, measure of angle CED = 212°.
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A) 142
B) 146
C) 138
D) 132
E) 144
Answer:
it is 146 i no what work your doing i do i
m/3 = 4
solve m.
Please show your work
Equations with fractions
Can someone please show me step by step how to answer this, thank you.
Answer:
x=7
Step-by-step explanation:
The equation can be represented as following:
[tex](\frac{x}{14} +3\frac{1}{2})=2(\frac{x}{21} +1\frac{2}{3})[/tex]. If we open the parenthesis, we can get as following:
[tex]\frac{1}{14}x +3\frac{1}{2}=\frac{2}{21}x +3\frac{1}{3} \\[/tex], which then subtract [tex]2\frac{2}{21} x[/tex] from both sides to get the following:
[tex]\frac{7}{2}-\frac{1}{42} x=\frac{10}{3}[/tex];
subtract [tex]\frac{7}{2}[/tex] from both sides to get [tex]\frac{-1}{42} x=\frac{-1}{6}[/tex], and multiply both sides by -42 to get our final answer of x=7
Are these triangles similar, congruent, or neither? What theorem supports the answer?
options:
Similar: SSS
Similar: SAS
Similar: AA
Congruent: SAS
Congruent: ASA
Congruent: AAS
Neither
Answer:
Similar: SAS
Step-by-step explanation:
The triangles are not congruent( they're not the equal) but the are similar because they form vertical angles that are congruent and their corresponding side lengths are in proportion
I'm reallyy confused on whats going on
Answer:82.13
Step-by-step explanation: you break it down into different shapes then add it.
Semi circle-a=pie times radius squared. radius is 3 so 3 squared is 9 and you multiply that by pie which is 28.26 and half is 14.13.
rectangle=6times 6=36
rectangle=14 times 3=32
add that all up and you should get 82.13
Look at the second Model It. How does using the partial quotients strategy help you find the quotient of 2,125 ÷ 4?
Finding a quotient of [tex]2,125/4[/tex] is [tex]531.25[/tex] with the use of partial quotients is possible.
What are fractional quotients?A fraction's quotient is the whole integer that results from simplifying the fraction. The division is the fraction's decimal form if the simplified fraction yields a non-whole number. The answer to a division issue involving two fractions can also be found in the quotient.
What makes it a quotient?Latin's "how many times" is the meaning of the word "quotient." It makes perfect sense: by dividing two numbers, you can determine "how many time" the second number enters the first. The number being divided is referred to as the payout, and the number being divided by it is referred to as the divisor.
40)2125(531.25
20
-------
12
-12
------
5
-4
--------
10
-8
--------
20
-20
----------
00
----------
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consider a product with 500 components. each component has a defect probability of 0.015%. what is the defect probability of the final product?
Using the probability multiplication we know that the defect probability of the final product will be 7.5%.
What is probability?Simply put, the probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
The higher the likelihood, the more likely it is that the event will take place.
So, the probability formula is:
P(E) = Favourable events/Total events
So, in the given situation, the number of components integrated:
500
Defect probability of each component:
0.015%
Then, the defect probability of the final product:
= 500 * 0.015
= 7.5%
Therefore, using the probability multiplication we know that the defect probability of the final product will be 7.5%.
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Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. Choose the best answer for residuals plot (a). O The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. O The fanned pattern indicates that the linear model is not appropriate. The model's predicting power increases as the values of the explanatory variable increases. O The scattered residuals plot indicates an appropriate linear model.
Each of the residual plots indicates the appropriateness of the linear model that was fit to the data. The appropriate answer for residuals plot (a) is: the fanned pattern indicates that the linear model is not appropriate.
The model's predicting power decreases as the values of the explanatory variable increase.
A residual is the difference between the actual y value and the predicted y value, which is determined by the regression equation or linear model. A scatterplot of residuals is often used to evaluate the appropriateness of a linear model in a regression analysis, as well as to check for other things like non-linear relationships or non-constant variance.
Residuals scatterplots assist in detecting various types of patterns or lack of patterns that may be present in data. Patterns in a residual plot indicate that the linear model does not fit the data well, whereas the lack of pattern in a residual plot indicates that the linear model is appropriate.In this problem, the residual plot (a) has a fanned pattern. This means that the linear model is not appropriate. Furthermore, the model's predicting power decreases as the values of the explanatory variable increase. This means that the model may overestimate or underestimate the response variable as the values of the explanatory variable rise.
Therefore, we can conclude that the fanned pattern on residual plot (a) indicates that the linear model is not appropriate.
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nationally, the proportion of red cars on the road is 0.12.a statistically-minded fan of thephiladelphia phillies (whose team color is red) wonders if phillies fans are more likely todrive red cars.one day during a home game, he takes an srs of 210 cars parked at citizensbank park (the phillies home field) while a game is being played, and counts 35 red cars.(there are 21,000 parking spaces.)is this convincing evidence that phillies fans prefer redcars more than the general population?support your conclusion with a test of significance
Yes,the statement "phillies fans prefer redcars more than the general population" is convincing evidence
The sample provides convincing evidence that Phillies fans are more likely to drive red cars than the general population.
This can be supported through a test of significance.
What is a test of significance?A statistical test is referred to as a significance test or a hypothesis test. The test is used to determine if there is enough evidence to reject a null hypothesis that a specific condition is true.
A hypothesis test is typically used to determine if there is enough evidence to support or reject a claim about a population parameter based on a sample statistic.
In this scenario, the proportion of red cars in the population is 0.12. The sample size is 210 cars parked at Citizens Bank Park, with 35 of them being red.
To test whether Phillies fans prefer red cars more than the general population, the following null and alternative hypotheses can be used:
Null hypothesis:
The proportion of red cars driven by Phillies fans is equal to the proportion of red cars in the general population.
Alternative hypothesis:
The proportion of red cars driven by Phillies fans is greater than the proportion of red cars in the general population.
Using a one-tailed test and a significance level of 0.05, we can compute the test statistic as follows:
Z = (0.17 - 0.12) / √(0.12 * 0.88 / 210) = 1.77
The critical value for a one-tailed test with a 0.05 significance level and 209 degrees of freedom is 1.65. Since the test statistic (1.77) is greater than the critical value (1.65),
We reject the null hypothesis and conclude that there is sufficient evidence to support the claim that Phillies fans are more likely to drive red cars than the general population.
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The line plot shows the size (in inches) of several different frog species. What is the difference between the shortest and longest species of frog?
The difference between the shortest and longest species of frog is [tex]3^{3\\}[/tex].
A line plot is a graph that shows data as checkmarks or points over a number line, indicating the frequency of each value.
When displaying information that changes over time, a line graph, also referred to as a line chart or a line plot, is frequently used. It can be visualized using a series of points connected by straight lines. The "x-axis" and the "y-axis" are two of its axes.
is a graph where the lines connecting the various data points are used. A line graph shows numerical values over a predetermined period of time. The shortest and longest frog species differ in terms of [tex]3^{3}[/tex].
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Square and pentagon each have 9 in sides are their perimeters the same
No they wouldn't be the same because, the perimeter is adding all sides.
The square has 4 sides so you would add 9, four times.
9 + 9 + 9 + 9 = 36
And a pentagon has 5 sides so you would add 9, five times.
9 + 9 + 9 + 9 + 9 = 45
So, they are not the same.
The polygons below are similar. Find the value of x
The value of x is 6m. Polygons can be regular or irregular, depending on whether all their sides and angles are congruent or not.
To find the value of x in the similar polygons shown in the figure, we can use the fact that corresponding sides of similar polygons are proportional. A polygon is a two-dimensional closed shape with three or more straight sides and angles. It is formed by connecting consecutive line segments, which are called sides, at their endpoints. The point where two sides of a figure meets is called a vertex. A polygon can have any number of sides, but it must have at least three. Polygons include triangles, quadrilaterals, pentagons, hexagons, and many more.
Since the polygons are similar so, the ratio of sides will be equal:
[tex]\frac{5}{10} = \frac{x}{12}[/tex]
x = 6 m.
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Please help !!!!!!!!!!!
The simplified expressions are, 6. [tex]16^{\frac{1}{2} }[/tex] = 4, 7. [tex]125^{\frac{1}{3} }[/tex] = 5, 8. [tex]36^{\frac{1}{2} }[/tex] = 6, 9. [tex]27^{\frac{1}{3} }[/tex] = 3,10. [tex]49^{\frac{1}{2} }[/tex] = 7.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical operations and structures using symbols and letters to represent numbers and quantities. It involves manipulating mathematical expressions and solving equations to find unknown values.
In algebra, the basic operations include addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions can also include variables, which represent unknown quantities, and coefficients, which are the constant values that appear in front of variables.
The study of algebra begins with the basic concepts of arithmetic, such as addition, subtraction, multiplication, and division, and then progresses to more advanced topics, such as equations, inequalities, functions, matrices, and abstract algebra. Algebraic concepts are widely used in other areas of mathematics, including geometry, trigonometry, calculus, and number theory
[tex]16^{\frac{1}{2} }[/tex] = 4
[tex]125^{\frac{1}{3} }[/tex] = 5
[tex]36^{\frac{1}{2} }[/tex] = 6
[tex]27^{\frac{1}{3} }[/tex] = 3
[tex]49^{\frac{1}{2} }[/tex] = 7
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A square table has a side length of 15ft. what is the measure of the diagonal
The measure of the diagonal of the square table is 15 * [tex]\sqrt{2}[/tex] feet (approximately 21.21 feet).
What is the measure of the diagonal?The diagonal of a square is the line segment that links two opposed corners of the square. The Pythagorean theorem asserts that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the square is the hypotenuse of a right triangle with two legs of length 15ft each (since the sides of a square are equal in length). So, we can use the Pythagorean theorem as follows:
[tex]diagonal^2[/tex] = [tex]15^2 + 15^2[/tex]
[tex]diagonal^2[/tex] = 450
diagonal = [tex]\sqrt{450}[/tex]
Using a calculator or simplifying by factoring out perfect squares, we get:
diagonal = [tex]\sqrt{(225 * 2)}[/tex] = 15 * [tex]\sqrt{2}[/tex]
Therefore, the measure of the diagonal of the square table is 15 * [tex]\sqrt{2}[/tex] feet (approximately 21.21 feet).
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