(x-3.5), or (x-7/2) are the factors of the polynomial, f(x) = 6x⁴ – 21x³ – 4x² + 24x – 35
Given,
The polynomial, f(x) = 6x⁴ – 21x³ – 4x² + 24x – 35
We have to find the factors of the polynomial;
Here,
This polygon's 35-factor factors, plus or minus 1, plus or minus 5, plus or minus 7, are potential zeros. Determine whether or not there is a non-zero remainder in each example using synthetic division. If none of these solutions work, try rational divisors derived from 35 and 6 such as 5/6, 7/6, 1/6 and so on.
Now,
f(x) = 6x⁴ – 21x³ – 4x² + 24x – 35
If used correctly, this method will eventually reveal one or two zeros of this poly. Of course, it would be lot simpler if you looked at the potential solutions provided to you for this issue.
I plotted this function and discovered that it crosses the x-axis at 7/2. Another root exists.
To determine whether or whether 7/2 is a root, use synth. div.
Then,
___________________________
7/2 / 6 -21 -4 24 -35
21 0 -14 35
----------- ------------------------------
6 0 -4 10 0
Since there is no remainder, the polynomial has a root of 7/2 (or 3.5). Therefore, a factor is (x-3.5) or (x-7/2).
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can someone help me!
Answer:
( x + 6, y + 4)
Step-by-step explanation:
Let's pick point S at ( -9, -4); it changes to point S' at ( -3, 0)
The x increase by 6, and the y increase by so the answer is
( x + 6, y + 4)
The Above Contour Map Is Given For A Function F(X,Y). Use It To Estimate The Value Of The Partial Derivatives Fx(2, 1) And Fy(2, 1).
We may deduce from the contour map that the estimates of the given functions are;
fx(2, 1) = 10
fy(2, 1) = 3
What exactly does the term "counter map" mean?The geographic mapping used as a form of activism against prevailing power systems is known as counter-mapping.
How Do You Interpret Contour Lines on a Map?Contour lines are described as the faint lines drawn on a map that link places of equal height above sea level. This indicates that even if you followed a contour line physically, the elevation (height of the land) would stay constant.
According to the contour map, the contour lines indicate that the coordinate (2, 1) in the x-direction has a value of 10.
Therefore; fx(2, 1) = 10
Using the same idea, we can deduce from the attached contour map that the coordinate (2, 1) in the y-direction will have a value between 0 and 6. Therefore;
Average = (0 + 6) divided by 2 = 3
Thus; fy(2, 1) = 3
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How do you prove SSS and SAS?
The triangles are congruent if all three sets of comparable sides are present. The side-side-side shortcut is a congruence technique (SSS).
Triangles are considered congruent by SAS if their two sides match up with their corresponding two sides on the other triangle, and if their included angles match up in both triangles.
We can prove two triangles, either by SSS or SAS by simply taking two triangles and checking whether the sides and the angles of the corresponding triangles are congruent or not.
By simply comparing it on the basis of their sides and angles we can easily prove the corresponding triangles by SSS or SAS.
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an urn contains four balls numbered 2, 2, 5, and 6. if a person selects a set of two balls at random, what is the expected value of the sum of the numbers on the balls?
7.500 (rounded to 4 decimals) sum of the numbers on the balls.
Suppose we select two distinct balls
Then we have the following possibilities of selecting two balls
(2,2), (2,2) ............, i.e. 2 ways to get a sum of 4...............(2+2 = 4 and 2+2 = 4)
(2,5), (2,5), (5,2), (5,2), i.e. 4 ways to get a sum of 7...............(5+2 = 7 and 2+5 = 7)
(2,6), (2,6), (2,6), (2,6), i.e. 4 ways to get a sum of 8...............(2+6 = 8 and 6+2 = 8)
(6,5), (5,6) , i.e. 2 ways to get a sum of 11...............(5+6 = 11 and 6+5 = 11)
total number of possible outcomes = 2(for a sum of 4) + 4(for a sum of 7) + 4(for a sum of 8) + 2 (for a sum of 11)
= 2 + 4 + 4+2
= 12
So, P(getting a sum of 4) = (number of ways to get a sum of 4)/total number = 2/12
similarly,
P(getting a sum of 7) = (number of ways to get a sum of 7)/total number = 4/12
P(getting a sum of 8) = (number of ways to get a sum of 8)/total number = 4/12
P(getting a sum of 11) = (number of ways to get a sum of 11)/total number = 2/12
We know that expected value E[x] = sum of all individual sum values by their respective probability
= 4*(2/12) +7*(4/12) +8*(4/12) +11*(2/12)
= 0.6667 + 2.3333 + 2.6667 + 1.8333
= 7.500 (rounded to 4 decimals)
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How old are Grade 7 students?
NEED ANSWERS ASAP!!! if an object is moving at a speed of V kilometers per hour, how many meters does it travel in M seconds? (its asking for the equation on how to solve this problem)
Can this be a biconditional statement and still be true? : “If a polygon is a square, then it has four sides.”
No, the biconditional statement isn't true because It's not necessary that if a polygon has four sides, then It will be a square.
What is Biconditional statement?
A statement that combines a conditional statement with its opposite is known as a biconditional statement. So, if and only if the other conditional is also true, the first conditional is true.
Let's elaborate the statement, “If a polygon is a square, then it has four sides.”
We know that a square has four equal sides and So, if a polygon is a square, it must have four equal sides which states that the given statement is true.
But, if we see its converse, "If a polygon has four sides, then it is a square". It is not necessary that the polygon will be a square.
eg. A parallelogram and rectangle also have four sides, So it could either be a parallelogram, rectangle or a square.
Hence, The given statement is correct but the converse of it, is not correct.
So, It can't be called a biconditional statement.
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Suppoe a merry-go-round i pinning once every 3 econd. If a point on the outide edge ha a peed of 12. 56 feet per econd, what i the radiu of the merry-go-round? (Ue 3. 14 for
The value of radius of the merry-go-round will be 6 feet.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
The longest line which can be drawn inside the circle will be the diameter.
The perimeter of the circle = 2πr where r is the radius of the circle.
The Merry cover on the round in 3 seconds thus, to cover the 2πr path it takes 3 seconds.
2πr/3 = 12.56
2πr = 37.68
r = 5.996 ≈ 6 feet.
Hence "The value of the radius of the merry-go-round will be 6 feet".
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a variable with a value of x1x2 is added to the general linear regression model to account for two predictive variables, x1 and x2 and the effect on the response variable. this type of effect is called
The given type of effect is called predictive.
What is linear regression?
When predicting a variable's value based on the value of another variable, linear regression analysis is used. The dependent variable is the one you're trying to forecast. The independent variable is the one that you are utilizing to forecast the value of the other variable.
Given:
A variable with a value of x1 x2 is added to the general linear regression model to account for two predictive variables, x1 and x2 and the effect on the response variable.
Linear regression is one of the most generally utilized predictive displaying methods.
It is spoken to by a condition = + + , where an is the catch, b is the slant of the line and e is the blunder term.
This condition can be utilized to predict the estimation of an objective variable dependent on a given predictor variable(s).
The predictor variable is the name given to an autonomous variable utilized in regression examinations.
The predictor variable gives data on a related ward variable concerning a specific result.
Hence, the given type of effect is called predictive.
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If PB = 6, what is SB?
Answer:
SB = 4
Step-by-step explanation:
The figure is the intersection of the medians of this triangle. The medians of a triangle bisect the sides of the triangle. The intersection of the medians is called the centroid. In this case, the centroid of this figure would be S.
In fact, the distance from a vertex to the centroid of the triangle is 2/3 of the distance from said vertex to the vertex's opposite side.
Create the equation SB = 2/3(PB).
.....................................SB = 2/3(6)
....................................SB = 12/3
...................................∴SB = 4
Answer:
SB = 4
Step-by-step explanation:
SB = 2/3 BP
SB = 2/3 (6)
SB = 4
Kiley, jermaine, and gunther are playing tug-of-war. Kiley and jermaine are on the same side of the rope, and gunther is on the other side. Kiley is exerting a force of 20 n, and jermaine is exerting a force of 25 n.
The positive sign indicates that Gunther pulls to the right.
A force that would result in a balanced force for the game is: 45N
First we define a reference system.
Let's assume the horizontal axis as positive towards the right.
Suppose Kiley and Jermaine pull the rope to the left, while Gunther pulls the rope to the right.
The equilibrium equation is given by:
-20-25+F=0
Where,
F: force with which Gunther pulls the rope.
Clearing F we have:
The positive sign indicates that Gunther pulls to the right.
A force that would result in a balanced force for the game is: 45N
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Show all your work which is the simplest form of the expression below
Answer: 2³
Step-by-step explanation:
We will use the order of operations to help us solve. This means, in this case, starting with exponents and then multiplying. We will also use the exponent rules.
Given:
[tex]\displaystyle (2^2)^4\;*\;2^{-5}[/tex]
Power rule of exponents:
[tex]\displaystyle (2^2)^4\;*\;2^{-5}=(2^{2*4})\;*\;2^{-5}[/tex]
[tex](2^{8})\;*\;2^{-5}[/tex]
Product rule of exponents:
[tex]\displaystyle (2^{8})\;*\;2^{-5} = (2^{8+-5})= (2^{8-5})[/tex]
[tex](2^{3})[/tex]
The simplified form of the expression, from the given options, is 2³.
a tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. at the start of a weekend, her win ratio is exactly $0.500$. during the weekend, she plays four matches, winning three and losing one. at the end of the weekend, her win ratio is greater than $0.503$. what's the largest number of matches she could've won before the weekend began?
Using the ratio we know that before the weekend started, she could have won as many as 164 games.
What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
A proportion is an equation that sets two ratios at the same value.
For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
So, let n be the number of victories so that:
n/2n = 1/2 and n+3/2n+4 > 503/1000
Now, cross multiply as follows:
1000n + 3000 > 1006n + 2012
n < 988/6 = 164 4/6 = 164 2/3
Therefore, using the ratio we know that before the weekend started, she could have won as many as 164 games.
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What are the 3 methods to find the mean?
The three methods to find the mean are arithmetic, geometric and harmonic .
The arithmetic mean method: This method involves adding up all the values in the set and dividing by the total number of values. This gives the average value of the set.The geometric mean method: This method involves finding the product of all the values in the set and taking the square root of that product. This gives the average value of the set when the values represent quantities that are multiplied together (such as interest rates or growth rates).The harmonic mean method: This method involves taking the reciprocal of each value in the set (1/value), adding those reciprocals up, and taking the reciprocal of that sum. This gives the average value of the set when the values represent quantities that are inversely related (such as speeds or rates).To learn more about mean, visit:
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What are 3 types of sets?
The three types of set based on the number of elements is empty set, finite set and infinite set.
In mathematics, a set is a collection of unique objects. The number of elements in a set can be finite or infinite.
An empty set is a set with no elements. It is also called a null set. For example, a set of natural numbers less than 0.
Finite set is a set containing finite number of elements, that is the number of elements in the set is countable. For example, a set of natural numbers less than 100.
Whereas infinite set is a set with infinite number of elements, that is the number of elements in the set is not countable. For example, a set of natural numbers.
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How can I calculate my height at 2?
By combining the mother's as well as father's heights in inches, you may determine the midparental height. For boys, measure 5 inches longer; for girls, measure 5 inches shorter. multiply by two.
How can you accurately anticipate a children's adult height?A person's height can be predicted by other factors besides genes. A child may occasionally be significantly taller above their relatives and parents.There is no reliable method for estimating a children's adult height.However, a number of calculations can offer a reliable approximation of a child's growth. Here is a common illustration:
In inches or millimeters, multiply the father's height by the mother's height.For boys, add 5 inches (13 centimeters), and for girls, take 5 inches (13 centimeters) away.Multiply by 2.Double with a boy's height around age 2 or even a girl's height from age 18 months to get an idea of a child's adult height.To know more about the children's adult height, here
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Are isosceles triangles equal to 180?
Yes, the isosceles triangles are equal to 180 degrees.
We know that isosceles triangles are triangles which have two equal sides. Since the sides are equal, they subtend equal angles as well.
However, the two equal angles subtended by the equal sides and one more angle which is subtended by the third side of the isosceles triangle all add up to a total of 180 degree as we know that the sum of all the angles of a triangle is always equal to 180 degrees.
Hence we can conclude that the isosceles triangles are also equal to 180 degrees like every other triangle.
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What is the final step in solving the inequality 2/5 4x 6x 4?
The final step is x < 3
What is an inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and not equal (≠) are the five inequality symbols.
Given inequality is
-2(5 - 4x) < 6x - 4
The inequality sign is less than.
Applying distributive property on the left side
-10 + 8x < 6x -4
Subtract 6x from both sides
-10 + 8x - 6x < 6x -6x - 4
-10 + 2x < - 4
Add 10 on both sides:
-10 + 2x + 10 < - 4 + 10
2x < 6
Divide both sides by 2:
2x/3 < 6/3
x < 3
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A rectangle piece of lawn i 55 m and 98 m long find the length of the fence around it
Step-by-step explanation:
draw a rectangle with width 98 and height 55 there are two of each side, so 98 + 98 + 55 +55 = 306
Answer:
306m
Step-by-step explanation:
You need to find the perimeter of the rectangle. To do that, you just add the side lenghts. So, this is your lawn with the side lengths:
55m
_____________
| |
| |
| |
98m | | 98m
| |
| |
| |
_____________
55m
You just add them together!
55 + 55 + 98 + 98 = 306
so you need 306 meters of fencing
What is the slope y =- 5x 3?
Parallel lines are two straight lines that never cross. For this to happen, the lines have to have the same slope.
In this case, the equation given is in what's called "slope-intersect" form. The general form of the slope intercept formula is y=mx + b where m is the slope of the line and b is the point on the Y-axis where the line crosses.
The equation given is y=5x+3 and since the 5 is in the place of m from the general equation, 5 is the slope. Since parallel lines have the same slope, 5 is the answer.
Slope-Intercept Form:
When we're given a linear equation we can immediately see if it's in the slope-intercept form if it follows the format y=mx+b. As long as y does not have a coefficient the slope and y-intercept are the values of m and b.
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in a certain large population of adults, the distribution of iq scores is strongly left-skewed with a mean of 122 and a standard deviation of 5. suppose 200 adults are randomly selected from this population for a market research study. the distribution of the sample mean of iq scores is (a) left-skewed with mean 122 and standard deviation 0.35. (b) exactly normal with mean 122 and standard deviation 5. (c) exactly normal with mean 122 and standard deviation 0.35. (d) approximately normal with mean 122 and standard deviation 5. (e) approximately normal with mean 122 and standard deviation 0.35.
The correct answer is e) approximately normal with a mean 122 and standard deviation 0.35.
In this case, the distribution of the sample mean of IQ scores will be approximately normal because the sample size of 200 is sufficiently large. This is known as the Central Limit Theorem, which states that the distribution of the sample mean will be approximately normal as long as the sample size is large enough, regardless of the shape of the distribution of the population.
The mean of the sample mean distribution will be 122, which is the same as the mean of the population. The standard deviation of the sample mean distribution will be smaller than the standard deviation of the population because it is calculated using the sample size rather than the population size.
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How do you solve 3 to the power of 1?
To answer, let's use the exponent rules to solve the power of 1.
What is exponent rule?Exponents, often known as powers, specify how many times the base number must be multiplied.
Exponent rules are principles that are used to simplify expressions using exponents. These principles are also useful in simplifying formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.
Negative exponents Rule: [tex]a^{-m} = 1/a^m[/tex]
Product Rule: [tex]a^m * a^n = a^{(m+n)}[/tex]
Quotient Rule: [tex]a^m/a^n = a^{(m-n)}[/tex]
Power of a Power Rule: [tex](a^m)^n = a^{mn}[/tex]
Here, given that, 3 to the power of 1
The number 3¹ may be expressed as 3 to the power of 1, according to the exponent rule.
The base number in this formula is 3, while the power number is 1, and we know that any integer increased to that same power of that one equals the original number.
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cm 2 What is the area of the rectangle? Enter the answer in the box. 9 cm 4 cm
Answer:
Let,
length of rectangle ( L) =9cm
breadth of rectangle (b) =4cm
Area of rectangle=L×b
=9×4
=36cm^2
i need help im confused
f(-4) = -18, f(-2) = -10, f(6) = 12 and f(-1) = -6 using the piecewise function.
What are piecewise functions?A function defined by numerous sub-functions, where each sub-function applies to a distinct interval in the domain, is known in mathematics as a piecewise-defined function (also known as a piecewise function, a hybrid function, or definition by cases). Instead of being a property of the function itself, piecewise definition is a means to express the function.
When the domain may be divided into intervals on which the property holds, the phrase "property holding piecewise for a function" is used, which is separate but related. This is a characteristic of the function itself, as opposed to the idea mentioned above.
f(-4) = 4(-4)-2 = -18 ∵-4≤-1
f(-2) = 4(-2)-2= -10 ∵-2≤-1
f(6) = [tex]\frac{1}{2}*6 + 9 = 12[/tex] ∵6>-1
f(-1) = 4(-1)-2 = -6 ∵-1≤-1
f(-4) = -18, f(-2) = -10, f(6) = 12 and f(-1) = -6 using the piecewise function.
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Students are making lemonade from a p
owdered lemon drink mix. Rahul mixes 14 cups of water and 5 cups of powdered lemon mix. Aisha mixes 11 cups of water and 4 cups of powdered lemon mix. Use Rahul and Aisha’s percent of powdered lemon mix to determine whose mix will be more lemony.
Answer:
Aisha mix will be more lemony
Step-by-step explanation:
Find Rahul's percentage of the powdered lemon mix by
Finding the total number of cups
14 + 5 = 19 total cups
Then take
5 divided by 19, times 100% = 26.3%
Find Aisha's percentage of the powdered lemon mix by
Finding the total number of cups
11 + 4 = 15 total cups
Then take
4 divided by 15, times 100% = 26.6% or 27%
Answer: Ariana uses 85% drink mix, and Andres uses 90% drink mix. Therefore, Andres's drink will taste more lemony.
Step-by-step explanation:
Ariana uses 17 cups of mix out of the 20 total cups which is 85%
Andres uses 10 cups of mix out of the 11 total cups which is around 90%
Step-by-step explanation:
4x - 2 = 9x + 18. Which number do you subtract from both sides, the 4x or the 9x? Explain why.
How do you write 6 more than a number?
“6 more than twice m” can be written in the mathematical form as 2m+6.
The question is saying that we have to write “6 more than twice m” as an algebraic expression or into a mathematical expression.
As in the question, it is mentioned that we have to take the number m as a variable.
So, we are going to use this ‘m’ for solving this question.
Let the number be m.
Then, twice of m will be similar to 2 times m or m multiplied by 2.
Therefore, twice m will be 2m.
Now, the question is saying that 6 more than twice m.
“6 more than” means 6 is added to that specific number.
Hence, 6 more than that number which is twice of m will be 2m+6.
Hence, “6 more than twice m” can be written in the mathematical form as 2m+6.
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The table shows how a leading automobile dealer plans to spend its advertising dollars for this year. If this company plans to increase its budget by 5% next year, approximately how much will it spend on social media ads?
Advertising Budget: $81,000
48.5% Television
23% Magazines
20% Newspapers
7% Radio
1% Billboards
0.5% Social Media
A.
Using the concept of percentage, social media budget will cost $425.25
PercentageThis is the expression of a ratio or fraction in percentage form. This is done by multiplying a ratio by 100.
The original advertising budget is $81,000 and they plan to increase it by 5%.
Let's calculate the 5% increase in the budget.
5% of 81000 =
5 / 100 = x / 81000
0.05 = x / 81000
x = 81000 * 0.05
x = 4050
The budget for next year will 81000 + 4050 = 85050
In the breakdown for the advertising budget, social media budget got 0.5%
Let's find 0.5% of 85050
0.5% * 85050
0.5 / 100 = x / 85050
0.005 = x / 85050
x = 0.005 * 85050
x = 425.25
The social media budget is $425.25
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How many 5-letter combinations can be created from the letters in the word "friendly"? assume that the order of the letters does not matter.
a. 56
b. 120
c. 6,720
d. 40,320
Number of combinations = 56 combinations can be created from the letters in the word "friendly"
Points to remember
nCₐ = n!/(r!(n - r)!)
The given word is "FRIENDLY"
F R I E N D L Y is a 8 letter word.
To find the number of combinations
5 letters can be selected from 8 letter = 8C₅
8C₅ = 8!/(8 - 5)!5!
= 8!/3!5!
= (8 * 7 * 6* 5!)/(1 * 2 * 3 * 5!)
= 8 * 7
= 56
5 letter combinations can be created from the letters in the world “friendly = 56
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A principal of $3000 is invested at 7.25% interest, compounded annually. How much will the investment be worth after 10 years?
Use the calculator provided and round your answer to the nearest dollar.
Answer:
$6,232.89 or $6,232.90
Step-by-step explanation:
A=P(1+(r/n))^nt
A= 3000(1+(.075/12))^12*10
A= 3,232.89
3,232.89+3000= 6,232.89