so we know the center and a point it passes through, so the distance from the center to that point on the circle is its radius
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{\frac{9}{2}}~,~\stackrel{y_2}{-16})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~\frac{9}{2} - 0~~)^2 + (~~-16 - (-10)~~)^2} \implies r=\sqrt{(\frac{9}{2} )^2 + (-16 +10)^2} \\\\\\ r=\sqrt{( \frac{9}{2} )^2 + ( -6 )^2} \implies r=\sqrt{ \frac{81}{4} + 36 } \implies r=\sqrt{ \cfrac{225}{4} }\implies r=\cfrac{15}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{0}{h}~~,~~\underset{-10}{k})}\qquad \stackrel{radius}{\underset{\frac{15}{2}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 0 ~~ )^2 ~~ + ~~ ( ~~ y-(-10) ~~ )^2~~ = ~~\left( \frac{15}{2} \right)^2\implies x^2+(y+10)^2=\cfrac{225}{4}[/tex]
Answer:
x^2 + (y + 10)^2 = 225/4
Step-by-step explanation:
To find the standard form of a circle with center (h, k) and radius r, the equation is:
(x - h)^2 + (y - k)^2 = r^2
We are given the circle's center as (0, -10) and a point on the circle as (9/2, -16). We can use this information to find the radius of the circle.
Radius (r) = Distance between center and point on the circle
r = sqrt[(0 - 9/2)^2 + (-10 + 16)^2]
r = sqrt[(81/4) + 36]
r = sqrt[(81 + 144)/4]
r = sqrt(225)/2
r = 15/2
Now we can substitute the values of (h, k, and r) into the standard form equation to get:
(x - 0)^2 + (y - (-10))^2 = (15/2)^2
Simplifying and multiplying out the terms, we get:
x^2 + (y + 10)^2 = 225/4
Therefore, the standard form of the circle is:
x^2 + (y + 10)^2 = 225/4
A bottle of orange juice contains 64 fluid ounces.how many cups of orange juice are in three bottles
A bottle of orange juice contains 64 fluid ounces. The percent of bottle of orange juice is water is 75% and there are 48 cups of orange juice are there in bottles.
Percentage:
In mathematics, a percentage is a number or a ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we divide the number by a whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".
Using this formula
Percentage = Ounces of water/Ounce bottle of orange juice
Where:
Ounces of water = 48 ounces
Ounce bottle of orange juice = 64 ounce
Let plug in the formula
Percentage = 48/64
Percentage = 0.75×100
Percentage = 75%
Therefore,
the percent of bottle of orange juice is water is 75%.
Complete Question:
A bottle of orange juice contains 64 fluid ounces. how many cups of orange juice are in three bottles. What percent of bottle of orange juice is water
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Answer:
the percent of bottle of orange juice is water is 75%.
Step-by-step explanation:
On Friday, 235 people attended a performance at the Community Playhouse. On Saturday, 260 people attended the performance. Everyone paid $12 for a ticket. Which expression represents the total receipts in dollars, for the two performances?
235+260/12
12(235+260)
12(235)+260
235+12(260)
12*235*260
Answer:
Step-by-step explanation:
Friday receipts: [tex]235 \times 12[/tex]
Saturday receipts: [tex]260 \times 12[/tex]
Total [tex]=235 \times 12 + 260 \times 12[/tex]
[tex]=12(235+260)[/tex] (since 12 is a common factor in both expressions)
To find the total receipts in dollars for the two performances, you need to multiply the number of tickets sold by the price per ticket. The formula is: total receipts = (number of tickets sold) x (price per ticket). Based on this formula, which expression do you think is correct?
The correct expression would be: 12(235+260)
You can check your answer by simplifying the expression: 12(235+260) = 12(495) = 5940. The total receipts in dollars for the two performances are $5940.
// Hope this helped! //
What is Elie's emotional feeling about God at this point in the story?
He is angry at God.
He has determined God does not exist.
He wants to maintain his faith.
He believes God is testing them.
Answer:
Based on the given information, it is most likely that Elie is angry at God. Throughout the story, Elie witnesses the atrocities of the Holocaust and the brutal treatment of Jews, which challenges his faith in God. He struggles to reconcile the suffering he sees with the idea of a just and loving God. Elie's anger towards God is evident in several instances, such as when he witnesses the hanging of a young boy and questions how God could allow such cruelty to happen. Additionally, he feels that God has abandoned him and his fellow prisoners, particularly when he is forced to watch the slow death of his father. Overall, Elie's emotional feeling about God is one of anger and disillusionment.
use a calculator and find value of x- 1.5(0.55)^x= 2
Using a calculatοr οr spreadsheet, we can find that x is apprοximately 3.977 after several iteratiοns.
We can use trial and errοr οr iterative methοd tο find the value οf x.
What is Trial and Errοr Methοd ?Trial and Errοr Methοd is a prοblem-sοlving strategy that invοlves testing variοus sοlutiοns until the cοrrect οne is fοund. It is a simple but time-cοnsuming apprοach that invοlves attempting different sοlutiοns and checking their οutcοmes until the desired result is achieved. This methοd is οften used when there is nο clear οr οbviοus sοlutiοn tο a prοblem, and it requires patience, persistence, and the ability tο learn frοm mistakes.
Trial and Errοr Methοd:
We can substitute different values οf x intο the equatiοn until we get a value that is very clοse tο 2.
Using the calculatοr and by trial and errοr, we can find that x is apprοximately 3.977.
Iterative Methοd:
We can use an iterative methοd tο find the value οf x that satisfies the equatiοn. The iterative fοrmula fοr this prοblem is:
x_{n+1} = lοg[tex](2 + 1.5(0.55)^{x_n})[/tex] / lοg(0.55)
where x_n is the nth apprοximatiοn οf x.
Starting with x_0 = 3, we can use this fοrmula tο get better and better apprοximatiοns οf x. Using a calculatοr οr spreadsheet, we can find that x is apprοximately 3.977 after several iteratiοns.
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15. The equation of a circle is x² + y2 = 64. A point on the circle has coordinates (x. √28). Determine the possible
values of x. You must show work to receive credit.
Answer:
±6
Step-by-step explanation:
To find the possible values of x for a point on the circle with equation x² + y² = 64, we can substitute the given y-coordinate of √28 into the equation and solve for x:
x² + (√28)² = 64
x² + 28 = 64
x² = 64 - 28
x² = 36
Taking the square root of both sides, we get:
x = ±6
Therefore, the possible values of x for a point on the circle with coordinates (x, √28) are x = 6 and x = -6.
Help please!! Lot of points
In 2004, a forest covered an area of 1500 km^2. Since then, this area has decreased by 4.25% each year. Let t be the number of years since 2004. Let y be the area that the forest covers in km^2. Write an exponential function showing the relationship between y and t.
An exponential function showing the relationship between y and t is:
y(t) = 1500(e)^(-0.0425t)
How to write exponential models?The general form of expression of an exponential growth function is:
y = P(e)^(rt)
where;
y is the Amount you want the account/price/population/etc. to equal
P is the principal, or the amount you start with.
e is a specific irrational number approximately 2.718.
We are given:
In 2004, a forest covered an area of 1500 km². Thus:
y(0) = 1500 km²
r = -4.25% = -0.0425
y(t) = P(e)^(rt)
Thus:
A = y(0) = 1500
Thus:
y(t) = 1500(e)^(-0.0425t)
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2065 Old Q.No. 10 A sum of money put out a compound interest increased by Rs. 180 at the end first year and Rs. 188 10 at the end of second year. Find the rate percent and [5] the sum. Ans: 4.5% p.a., Rs. 4,000
If a sum of money put out a compound interest increased by Rs. 180 at the end first year and Rs. 188 10 at the end of second year. The rate is 4.5% and the sum is $4,000.
How to find the rate?Let the sum of money be x.
After the first year, the amount becomes x+180.
After the second year, the amount becomes (x+180)+188.10 = x+368.10.
Let the rate of interest be r, expressed as a decimal.
Then, using the formula for compound interest, we have:
(x+180) = x(1+r)
(x+368.10) = (x+180)(1+r) = x(1+r)² + 180(1+r)
Subtracting the first equation from the second, we get:
188.10 = x(1+r)² - x(1+r) + 180(1+r)
8.10 = x(r+r²) + 180r
Simplifying this equation, we get a quadratic in r:
r² + r(180/x) - 8.1/x = 0
Using the quadratic formula, we can solve for r:
r = [-180/x ± sqrt((180/x)² + 4(8.1/x))]/2
r = [-180/x ± sqrt((32400/x²) + (32.4/x))]/2
r = (-90/x) ± sqrt((8100/x²) + (8.1/x))
Since r must be positive (since the amount increased), we take the positive root:
r = (-90/x) + sqrt((8100/x²) + (8.1/x))
Substituting the given values of the increase and solving for x, we get:
180 = x[(1+(-90/x)+sqrt((8100/x²)+(8.1/x))) - 1]
180 = x(-90/x + sqrt((8100/x²)+(8.1/x)))
180 = -90 + xsqrt((8100 + 8.1x)/x³)
270 = xsqrt((8100 + 8.1x)/x³)
72900 + 729. x = 729. x²
x² - x(100.1) + 720000 = 0
(x-400)(x-1800) = 0
x = 400 or x = 1800
Since x cannot be negative, we take x = 400.
To find the rate of interest, we use the first equation:
x+180 = x(1+r)
180 = x*r
r = 180/x
r = 180/ 400
r = 0.45 = 4.5% per annum.
Therefore, the sum of money is Rs. 4,000.
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Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $6. If you roll a 2, 3, 4 or 5, you win $2. Otherwise, you pay $7.
Answer:
what do you want to ask dear?
Step-by-step explanation:
describe the usefullnes and limitations of these pieces it data in defining who you are as a person or as a student. in what ways do they help give a clear picture
Statistical scores and rankings in school can be useful for a variety of purposes, such as measuring academic performance, making admissions decisions, and providing feedback for improvement.
Describe types of data and their uses.The usefulness of statistical scores or rankings in school can vary depending on the context and purpose of their use.
GPA (Grade Point Average) is a common metric used to measure a student's academic performance over time. It is calculated by assigning numerical values to letter grades and averaging them. GPA can be useful for college admissions, scholarships, and job applications, as it provides a quick snapshot of a student's overall academic performance.
SAT and ACT scores are standardized tests used by colleges and universities as part of their admissions process. These scores are designed to measure a student's readiness for college-level work and are often used in combination with other factors, such as GPA and extracurricular activities, to make admissions decisions.
Test scores, such as those from quizzes, exams, or assignments, provide feedback to both students and teachers about the effectiveness of their teaching and learning strategies. These scores can be useful in identifying areas where a student may need additional support or where a teacher may need to adjust their teaching methods.
Class ranking compares a student's academic performance to their peers in the same graduating class. This ranking can be useful for college admissions and scholarships, as it provides a way to differentiate between students with similar GPAs.
Overall, statistical scores and rankings in school can be useful for a variety of purposes, such as measuring academic performance, making admissions decisions, and providing feedback for improvement. However, it is important to keep in mind that these scores should be viewed as one piece of information among many and should not be relied upon as the sole indicator of a student's abilities or potential.
[tex]$$\textbf{Formula:}$$[/tex]
[tex]GPA = \frac{\sum_{i=1}^n (credit_i \times grade_i)}{\sum_{i=1}^n credit_i}[/tex]
SAT and ACT scores = Combination of scores from various sections of the test
Class ranking = Student's position in the graduating class based on their GPA or other academic performance metrics
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Complete Question:
People use data and statistics to help them make important policy decisions, to identify
problems in an organization, and to predict outcomes. In this unit, you studied various
ways to analyze and represent data sets to determine how to best interpret the data.
You also learned how to critically examine the data and account for outside factors that
may influence the patterns you see in the data.
Think about the many statistical scores or rankings you receive in school, such as GPA,
SAT and ACT scores, test scores, and class ranking. Describe the usefulness and
limitations of these pieces of data in defining who you are as a person or as a student.
In what ways do they help give a clear picture? What are they not conveying?
helppppppppppppppppppppppppppppppppppppppp
Answer: X = 12, Y = 60°
Step-by-step explanation:
We are given a parallelogram. We know one degree measure, and one given side. To find X, create an equation, x + 3 = 15. Solve. X = 12. Since this is a parallelogram, Y must equal 60°, since parallelograms have two sets of equal degree measures.
1. A study of 200 advertising firms revealed their income after taxes:
•Income after Taxes
•Number of Firms
*Under $1 million=95
$1 million to $20 million=74
$20 million or more=31
What is the probability an advertising firm selected at random has under $1 million or
$1 million to $20 million in income after taxes?
Step-by-step explanation:
To find the probability of an advertising firm selected at random having under $1 million or $1 million to $20 million in income after taxes, we need to add the number of firms in each of these two categories and divide the result by the total number of firms.
Number of firms with under $1 million in income after taxes = 95
Number of firms with $1 million to $20 million in income after taxes = 74
Total number of firms = 95 + 74 + 31 = 200
Therefore, the probability of an advertising firm selected at random having under $1 million or $1 million to $20 million in income after taxes is:
(95 + 74) / 200 = 0.845
So the probability is 0.845 or 84.5%.
Please help with this math problem!!
The given equation has no solution.
What is a Quadratic equation?
A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic. Equations using quadratics is another name for it. The quadratic equation has the following general form: ax2 + bx + c = 0, where x is an unknown variable and a, b, and c are numerical coefficients. A quadratic equation is one like x2 + 2x + 1 for instance.
Given equation:
4r² + 3r + 15 = 9
we can simplify it as :
4r² + 3r = 9 - 15
4r² + 3r = - 6
4r² + 3r + 6 = 0
Now, we will use Quadratic formula which is given by :
r = [ -b + √b² - 4ac ] / 2a
Substituting values as a = 4, b = 3 and 6.
we get,
r = [ -3 + √3² - 4(4)(6) ] / 2(4)
= [ -3 + √(-87)]/8
since, its determinant (b² -4ac) is negative, hence the given equation has no roots.
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Reread "Nothing Gold Can Stay."
Nature's first green is gold,
Her hardest hue to hold.
Her early leaf's a flower;
But only so an hour.
Then leaf subsides to leaf.
So Eden sank to grief,
So dawn goes down to day.
Nothing gold can stay.
Which words best help the poet convey a mood of thoughtfulness and sadness?
Question 4 options:
hardest hue to hold
early leaf's a flower
first green is gold
only so an hour
The phrase "hardest colour to hold" from Robert Frost's poem "Nothing Gold Can Stay," is the line that the poet uses to best encapsulate his thoughtfulness and sadness. The Option A is correct
What is meant by the phrase "hardest colour to hold"?These lines convey a message that goodness and beauty are transient and challenging to cling onto. As the reader considers the fleeting nature of life and the transitory nature of the things we hold dear, this concept may cause them to feel melancholy and reflective.
Although phrases such as "just so an hour," "early leaf's a flower," and "first green is gold" also emphasized an impermanence and fleetingness, but the phrase "hardest colour to hold" makes this point the most strongly.
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-3y-4x= -11
3y-5x= -61
x=
y=
In response to the query, we can state that As a result, the following is equation the system of equations' solution: x = 8 \sy = -7
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 can use the substitution or elimination methods to find the values of x and y in this system of equations. We shall apply the elimination approach in this case:
-3y - 4x = -11 (equation 1) (equation 1)
3y - 5x = -61 (equation 2) (equation 2)
By combining equations 1 and 2, we may remove the y variable:
-3y -4x + 3y - 5x = -11 - 61
Streamlining the left side:
-9x = -72
-9 divided by both sides:
x = 8
Knowing that x = 8 allows us to solve for y by introducing this number into either equation. Consider using equation 1:
-3y - 4(8) = -11
Simplifying:
-3y - 32 = -11
32 more on both sides:
-3y = 21
By -3, divide both sides:
y = -7
As a result, the following is the system of equations' solution:
x = 8 \sy = -7
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Randy and Corey are discussing a lesson they learned in Math. Randy says that "All trapezoids are parallelograms." Corey disagrees. Who do you think is correct, Randy or Corey? Explain why you think Randy or Corey is correct.
Cory's statement is correct. A Trapezoid cannot be Parallelogram.
What is Trapezium?A trapezium is a polygon with a single pair of parallel sides. Trapezoid parallel bases are another name for these parallel sides. The other two non-parallel sides are known as trapezoidal legs.
A parallelogram is a quadrilateral having two pairs of parallel sides. The length and size of a parallelogram's opposed sides and opposite angles are equal. Its inner angles add up to 360°.
According to the given information:
Randy's claim is that "all trapezoids are parallelograms." Nonetheless, Cory disagrees with the statement "A Trapezoid is not a Parallelogram."
Corey's assertion is correct.
Because a trapezium is a quadrilateral with exactly one set of parallel opposed sides.
A parallelogram is a quadrilateral having opposite pairs of sides that are parallel.
The trapezoid does not satisfy the parallelogram criterion. As a result, a trapezium cannot be a parallelogram.
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SOMEONE PLEASEEEE HELP
“the graph shows a line and two similar triangles. what is the equation of the line”
A - y=3x+3
B - y=3/4x+3
C - y=4/3x+3
D - 4x+3
Answer:
Step-by-step explanation:
The line contains the points (0,3) and (6,11).
first find the slope with slope formula.
m=(11-3)/(6-3)
=8/2
=4.
you know the y-intercept is 3, so use slope-intercept form
y=4x+3
ILL GIVE BRAINLY PLEASE HURRY Recall that the first two lines of the poem "The New Colossus" allude to the ancient Greek statue of Colossus of Rhodes.
Not like the brazen giant of Greek fame,
With conquering limbs astride from land to land;
What does this allusion represent?
Question 5 options:
a place where wars were often fought
a place where outsiders were not welcome
a place where everyone was welcome
a place where citizens were unhappy
The allusion represents a symbol of strength and power, as the Colossus of Rhodes was a giant statue made of bronze that was built to commemorate the island's successful resistance to a siege.
What is allusion?Allusion is a figure of speech that makes a reference to a person, place, thing, event, or idea from history, literature, mythology, or another source. It is used to create an implied comparison without explicitly stating it. Allusions can be used to express feelings, suggest ideas, or draw attention to a certain concept. An allusion can be subtle, humorous, or even ironic. Allusions can also add depth and complexity to a piece of writing, or draw attention to a specific idea or point.
The statue is meant to represent the strength and power of the island, and its ability to protect itself from outside forces.
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Find x. Round your answer to the nearest tenth of a degree.
The value of x is obtained as 37.49°. The solution has been obtained by using the concept of trigonometry.
What is trigonometry?
The study of the sides, angles, and connections of the right-angle triangle is known as trigonometry which is a branch of mathematics.
In the figure, we are given length of perpendicular as 14 and length of hypotenuse as 23.
We are also given an angle 'x'
We know that sin theta = [tex]\frac{opposite side}{hypotenuse}[/tex]
Here, theta = x
Using this, we get
⇒ sin x = [tex]\frac{14}{23}[/tex]
⇒ x = [tex]sin^{-1} (\frac{14}{23})[/tex]
⇒ x = 37.49°
Hence, the value of x is obtained to be 37.49°.
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1. Calculate the values below when a = 5, b = 3 and c = 9:
Answers:
1. 3a + b = _______
2. 4a + 2b = _______
3. 5a + 3b – c = _______
1. 18
2. 26
3. 25
1. 3×5+3= 18
2. 4×5+2×3= 26
3. 5×5+3×3-9= 25
When a number and letter are next to each other mean multiply (Example)
5a = 5×a
(NEED HELP ASAP)
Write your answer as an integer or as a decimal rounded to the nearest hundredth.
Answer:
0.48
Step-by-step explanation:
By the law of sines, the ratio of the sides of a triangle to the sine of the angles opposite the side must be the same
Therefore
[tex]\dfrac{EG}{\sin90} =\dfrac{ FG}{\sin E}\\\\\\\dfrac{\sqrt{69}}{\sin 90} = \dfrac{4}{\sin E}}\\\\\\\sin 90 = 1\\\\\dfrac{\sqrt{69}}{1} = \dfrac{4}{\sin E}\\\\\sqrt{69} = \dfrac{4}{\sin E}\\\\\sin E = \dfrac{4}{\sqrt{69}}\\\\\\= 0.481543\\\\= 0.48 \text{ rounded to the nearest hundredth}[/tex]
What is the correct shortcut?
For the rectangle given the correct option is B) HL.
What is a rectangle?
A quadrilateral with parallel sides that are equivalent to one another and four equal vertices is known as a rectangle. It is also known as an equiangular rectangle for this reason.
A rectangle is given with parallel sides equal.
Two opposite angles are 90°.
A diagonal is drawn.
The given information describes a rectangle, which is a special case of a parallelogram with all angles equal to 90°.
In a rectangle, the diagonals are congruent and bisect each other.
Therefore, the correct option is (HL) hypotenuse-leg, which is a special case of the congruence rule for right triangles.
If we consider the right triangle formed by one of the diagonals and one of the sides of the rectangle, we can see that we have a right triangle with hypotenuse equal to the diagonal and leg equal to one of the sides of the rectangle.
Since the diagonals are congruent and the sides of the rectangle are equal, we have a case of HL congruence.
Option (a) AAS (angle-angle-side) and option (c) SSS (side-side-side) do not apply to this situation since we only have information about one side and one diagonal of the rectangle.
Option (d) "Not equal and congruent" is not a valid answer choice as congruent objects, by definition, must be equal.
Therefore, option B is the correct answer.
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3. Gavin loves to cook. He's even considering a culinary career as a chef as one of his options. He has to plan his classes for next year and has a chance to go to the vocational school and take culinary as his shop class. He knows it would give him great experience, but none of his friends plan to go to the vocational school. What should he do?
Answer:
The decision of whether Gavin should take culinary as his shop class at the vocational school depends on his personal goals and priorities.
If Gavin is seriously considering a culinary career as a chef, then taking culinary classes at the vocational school could provide him with valuable skills and knowledge that could help him achieve his career goals. In this case, he should prioritize his personal goals over his friends' plans and choose the vocational school option.
On the other hand, if Gavin is not sure about his career goals and values spending time with his friends, then he may want to choose a different shop class that is offered at his high school. It is important to note that culinary skills can be learned outside of school as well, through internships, volunteering, or cooking at home.
Ultimately, Gavin should weigh his personal goals and priorities against the potential benefits and drawbacks of each option and make a decision that is best for him.
Find the root(s) of f (x) = (x- 6)2(x + 2)2. -6 with multiplicity 1 -6 with multiplicity 2 6 with multiplicity 1 6 with multiplicity 2 -2 with multiplicity 1 -2 with multiplicity 2 2 with multiplicity 1 2 with multiplicity 2 Find the root(s) of f (x) = (x + 5)3(x - 9)2(x + 1). -5 with multiplicity 3 5 with multiplicity 3 -9 with multiplicity 2 9 with multiplicity 2 -1 with multiplicity 0 -1 with multiplicity 1 1 with multiplicity 0 1 with multiplicity 1
The root(s) of f (x) are
6 with multiplicity 2
-2 with multiplicity 2.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
We are given to find the roots of the following polynomial function :
f (x) = (x- 6)²(x + 2)²
We know that
the roots of a polynomial f(x) are given by the equation f(x) = 0.
Therefore, the roots of the given polynomial are given by
(x- 6)² =0 => x =6,6
(x + 2)² =0 , x =-2, -2
Thus, the required roots are
6 with multiplicity 2 and -2 with multiplicity 2.
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Two vessels are pulling a broken-down ship toward a boathouse with forces of 750lb and 630lb. The angle between the forces is 34.5°. Determine the magnitude of the equilibrant force.
The magnitude of the equilibrant force is 938.893 lb
How to find the equilibrant forceWe can use the concept of vector addition to solve this problem. The equilibrant force is the force that is needed to balance out the two given forces, so that the net force on the broken-down ship is zero.
Let's represent the two given forces as vectors A and B, with magnitudes of 750 lb and 630 lb, respectively. The angle between them is 34.5 degrees.
|C|^2 = |A|^2 + |B|^2 - 2|A||B|cosθ
where
θ is the angle between the two forces.
Substituting the given values, we get:
|C|^2 = (750 lb)^2 + (630 lb)^2 - 2(750 lb)(630 lb)cos(34.5°)
Simplifying this expression, we get:
|C|^2 = 562500 + 396900 - 945000 * cos(34.5°)
|C|^2 = 881520.0752
Taking the square root of both sides, we get:
|C| ≈ 938.893 lb
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Find the coordinates of the orthocenter of AXYZ with vertices X(-9,5), Y(-6, 8), and Z(-6,3).
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F(x)= 2ax^2 + bx + 3 has a relative extremum at the point (-1,2)
At the relative extremum
a = 1/2 and b = 2What is a relative extremum?
A relative extremum is a relative minimum or maximum of a function.
Since the function F(x) = 2ax² + bx + 3 has a relative extremum at the point (-1,2). This implies that dF(x)/dx = 0 at the extremum.
So, F(x) = 2ax² + bx + 3
dF(x)/dx = d(2ax² + bx + 3)/dx
= d2ax²/dx + dbx/dx + d3/dx
= 4ax + b
dF(x)/dx = 0
⇒ 4ax + b = 0
⇒b = -4ax at x = -1
b = -4a(-1)
= 4a
Since the function F(x) = 2ax² + bx + 3 has a relative extremum at the point (-1,2), we have that
F(-1) = 2a(-1)² + b(-1) + 3
= 2a - b + 3
F(-1) = 2
⇒2a - b + 3 = 2
⇒2a - b = 2 - 3
2a - b = -1
Now, b = 4a
So, substituting b into the equation, we have that
2a - b = -1
2a - 4a = -1
-2a = -1
a = -1/-2
a = 1/2
So, b = 4a
= 4(1/2)
= 2
So,
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Give a graph of a function that will satisfy all of the following properties.
f''(x) > 0 on (-infinity, -2)
f''(-2) = f'(-1) =f'(1) = f''(2) = 0 = f'(3)=0
f''(x) > 0 on (4, infinity)
Note that you have a lot of freedom with this. You can come up with many different graphs that will satisfy these properties.
One example of a graph that satisfies these properties is a cubic polynomial with the equation y=ax³+bx²+cx+d.
What is cubic polynomial?A cubic polynomial is a mathematical expression composed of terms that are raised to the third power. It is written as ax³ + bx² + cx + d, where a, b, c and d are constants and x is a variable. Cubic polynomials are used in many applications, such as approximating functions, solving equations, and finding the roots of polynomials. They can also be used to model physical phenomena, such as the motion of objects.
This graph will have a positive second derivative on the intervals (-infinity, -2) and (4, infinity). At the points -2, -1, 1, 2, and 3, the second derivative will be zero, the first derivative will be zero at -1, 1, and 3, and the function will be zero at 1.
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The number of bags of chips sold in a month is tracked and follows a normal distribution. After 2 years the mean is found to be 2.4 million, with a standard deviation of 0.3 million. What is the chance (percentage) that between 1.8 and 2.1 million bags are sold on a random month?
Answer:
The normal distribution has the same mean as the original distribution and a variance that equals the original variance divided by, the sample size.
Step-by-step explanation:
school library House 12345 books in English language 7842 books in French 32178 books in Arabic and 7116 books in other languages what is the ratio of the books in other languages to the rest of the books in the library
The ratiο οf bοοks in οther languages tο the rest οf the bοοks in the library is 204 : 1505.
What is Ratiο?A ratiο is a way οf cοmparing twο quantities by expressing the relatiοnship between them in terms οf their relative sizes. It is usually written in the fοrm οf a fractiοn οr using a cοlοn (:).
The tοtal number οf bοοks in the library is:
12345 + 7842 + 32178 + 7116 = 59481
The tοtal number οf bοοks in languages οther than English, French, and Arabic is:
7116
The ratiο οf bοοks in οther languages tο the rest οf the bοοks in the library is:
7116 : (59481 - 7116) = 7116 : 52365
Simplifying this ratiο by dividing bοth numbers by their greatest cοmmοn factοr gives:
7116 : 52365 = 204 : 1505
Therefοre, the ratiο οf bοοks in οther languages tο the rest οf the bοοks in the library is 204 : 1505.
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4x
Given a square with sides of length 4.x, diagonal of length d, perimeter P, and area A,
4x
Part: 0 / 8
d
4x
4x
(a) Write P as a function of x.
(b) Write A as a function of .x.
(c) Write A as a function of P.
(d) Write P as a function of A.
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a popup
(e) Write d as a function of .x.
(f) Write x as a function of d.
(9) Write P as a function of d.
(h) Write A as a function of d.
a. P as a function of x is P(x) = 16x
b. A as a function of x is A(x) = 16x²
c. A as a function of P is A(P) = P²/16
d. P as a function of A is P(A) = 4√A
e. d as a function of x is d(x) = √2 4x
f. x as a function of d is x(d) = d/√2
g. P as a function of d is P(d) = 4d/√2
h. A as a function of d is A(d) = d²/2
What do you mean by a function?A relationship between a collection of inputs-outputs is known as a function. Just one output is linked to each input in a function, which connects inputs.
Each function has a range, a co-domain, and a domain. A function is often written as f(x), where x stands for the input. y = f is a function's universal representation (x).
Here in the square,
Area = a²
= (4x) ²
=16x²
Perimeter = 4a
=4 × 4x
=16x
Diagonal = √2 a
= √2 4x
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