(1) The quotient of the polynomial is x² + 3x - 5 and the remainder is -8.
(2) The quotient of the polynomial is x² - 2x + 1 and the remainder is 0.
The factored form is (x + 5)(x - 1)².
What is the solution of the long division of the polynomial?
1. To divide f(x) = x³ + x² - 11x + 10 by x - 2, we can use polynomial long division:
x² + 3x - 5
------------------
x - 2 | x³ + x² - 11x + 10
- x³ + 2x²
-------------
-x² - 11x
+ x² - 2x
---------
-9x + 10
-9x + 18
-------
-8
Therefore, the quotient is x² + 3x - 5 and the remainder is -8.
Since there is a remainder it will be difficult to factor the polynomial.
2. Using long division, we get:
x² - 2x + 1
-------------------------
x + 5 | x³ + 3x² - 9x + 5
- x³ - 5x²
----------
-2x² - 9x
-2x² - 10x
----------
x + 5
x + 5
------
0
Therefore, we have: g(x) = (x + 5)(x² - 2x + 1)
To factor the quadratic expression x² - 2x + 1, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where;
a = 1,
b = -2, and
c = 1.
Substituting these values, we get:
x = (-(-2) ±√((-2)² - 4(1)(1))) / 2(1)
= 1
Therefore, the factorization of g(x) is:
g(x) = (x + 5)(x - 1)²
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According to a poll, 80% of Americans report being afflicted by stress. Suppose a random sample of 1,200 Americans is selected. Complete parts (a) through (d) below.
a. What percentage of the sample would we expect to report being afflicted by stress?
The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%
How to calculate the percentage afflicted by stress?The percentage of a data set is when part of the data is represented per 100 with a symbol of %.
It was stated in the question that 80% of Americans report being afflicted by stress.
Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.
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What is the answer b2+c2+c3
Answer:
8
Step-by-step explanation:
well because since you have to add u add 3+b
Answer:
This would be adding like terms togeather. So c3 plus c2 equals c5. So b2+c5 is your awnser.
Step-by-step explanation:
In a rotation, the pre-image and image will stay
Answer:
Rotation" means turning around a center. The distance from the center to any point on the shape stays the same. Every point makes a circle around the center. In a rotation, the Preimage and Image are the same size
Step-by-step explanation:
Answer:
i don't understand
Step-by-step explanation:
can you put the rest of the question in the ch,at or something so i can answer the question easyer
A contractor drew this diagram to find the area of a right-triangular shaped patio.
The length of railing b is 104 feet. The measure of angle A is 28°.
What is the area of the patio rounded to the nearest square foot?
Answer:
Step-by-step explanation:
sin28=0,27
cos28=0.88
so b=0.88c
and a =0.27c and from here is easy
Simplify 2x - 4) + 7(x + 2).
9x + 6
9x - 4
09x - 6
How far does the tip of a minute hand on a clock travel in 15 minutes if the distance from the center to the tip is 8cm? Leave your answers in terms of pi or round your answer to the nearest tenth.
SHOW WORK
The tip of the minute hand on a clock travels a distance of 4π inches in 15 minutes.
How to find the distance of the tip minute handThe distance traveled by the tip of a minute hand on a clock can be calculated using the circumference formula.
The circumference of a circle is given by the formula:
C = 2πr C is the circumference, π is pi (approximately 3.14159) and r is the radius.
The distance from the center of the clock to the tip of the minute hand is the radius is 8 centimeters.
The circumference of the circle traced by the tip of the minute hand is:
\(\text{C} = 2\pi \text{r}\)
\(= 2\pi (8)\)
\(= 16\pi \ \text{centimeters}\)
Since the minute hand travels the full circumference of the circle in 60 minutes, in 15 minutes it will cover 15/60 = 1/4 of the circumference.
The distance traveled by the tip of the minute hand in 15 minutes is:
\(\text{Distance} = \huge \text(\dfrac{1}{4}\huge \text) \times C\)
\(= \huge \text(\dfrac{1}{4}\huge \text) \times (16\pi)\)
\(= 4\pi \ \text{centimeters}\)
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Answer:
4π cm ≈ 12.6 cm
Step-by-step explanation:
The clock can be modelled as a circle, where the radius (r) is equal to the length of the minute hand: r = 8 cm.
A clock face is divided into 12 equal sectors (numbered 1 to 12).
It takes 60 minutes for the minute hand to complete one revolution of the clock. Therefore, each sector represents the passing of 5 minutes.
This means that 15 minutes equals 3 sectors, which is a quarter of the circle.
To find the distance the tip of the minute hand travels in 15 minutes, we need to find a quarter of the circumference of a circle with radius 8 cm.
The formula for the circumference of the circle is C = 2πr, where r is the radius. Therefore, the equation to find the distance the tip of the minute hand travelled in 15 minutes is:
\(\sf Distance=\dfrac{2 \cdot \pi \cdot 8}{4}\)
Simplifying, we get:
\(\sf Distance=\dfrac{16 \cdot \pi}{4}\)
\(\sf Distance=4 \pi\)
Therefore, the minute hand will travel 4π cm or approximately 12.6 cm (to the nearest tenth) in 15 minutes.
A game of Blackjack or “21” is played with a regular deck of cards. The aim of the game is to have cards that add up to 21. The cards are not replaced to the deck once they have been drawn. If you draw two cards in a row, what is the probability of getting 21, when first card you get is an ace and the second card is a queen?
The probability of getting 21, when first card is an ace and the second card is a queen = 0.024133.
The term blackjack means that you get a value of 21 with only two cards.
Number of cards in a deck of cards = 52
There are 4 types of cards in a deck of cards - spades, clubs, hearts, and diamonds, out of which spades and clubs are black in colour.
Given that first card is Ace and second one is a Queen.
Odds of getting an Ace are 4/52, odds of the next being Queen is 16/51.
P(blackjack)=4×16/(52/2).
where P is used for probability .
Probability: Probability is simply how likely something is to happen. Whenever we are unsure about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events governed by probability is called statistics.
Probability of getting an ace followed by a queen card: 4/52 * 16/51 = 0.024133.
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Find the equation of the tangent line to the function f(x) = 3x3 - x + 2 at a =0
Answer:
y=(9a^2-1)x-6a^3+2
Step-by-step explanation:
Can someone help me
Answer:
Y = -½x + 3/2
Y = -3x + 5
Y = 1/4x - 3¼
Step-by-step explanation:
Parallel implies they have the same gradient
Perpendicular implies the gradient is a negative reciprocal of the other.
Jasmine has a circular swimming pool with a radius of 4.2 meters. What is the circumference of the pool? Use 3.14 for π
. Round to the nearest hundredth if necessary.
__ m
If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.
The "Circumference" of a circle is known as the distance around the boundary of a circle.
The circumference of a circle is given by the formula : 2 × π × radius,
where π (pi) is a mathematical constant approximately equal to 3.14,
We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :
⇒ Circumference = 2 × 3.14 × 4.2 meters,
⇒ Circumference ≈ 26.4 meters,
Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.
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how many ft is equal to 1.66m
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
In each rule , copy the chart and fill in the missing parts
Answer:
7. 14
15. 30
28. 56
32. 64
18 36
x 2x
1/2y. y
2x. 4x
x+3 2x+9
Step-by-step explanation:
each out is double the in
Could anyone explain this question in detail?
Answer:
h and k are simply variables that stand in for the x and y of a point. Math books could have easily have used x1, x2 y1 y2, etc, but h and k is the convention.
anyway, this is a guess n check question. Substitute the x value of the point for h, and y value for k, and whichever one gives you a true equation is the right one.
Answer:
Step-by-step explanation:
y = a(x-h)²+k is the “vertex-form equation” for a vertical parabola with vertex (h,k).
Since a>0, the parabola opens upwards. (If a<0, it opens downwards. If a=0, it is not a parabola at all.)
The parabola y = a(x-h)²+2k is the same shape as the first equation, but it is shifted vertically by k units.
Since (2,4) is a point on the first parabola, (2,4+k) is a point on the second parabola.
Nancy has 1 box of carrots. Each day, she picks another 1/2 box .How many boxes of carrots will Nancy have in 6 days? Write an equation, complete the table, and then graph to sove the problem. Let x = the number of days and let y = the number of boxes
Given :
Nancy has 1 box of carrots.
Each day, she picks another 1/2 box
So, the number of boxes will every day will increase by 1/2 box
this can be represented by following sequence:
1 , 1 1/2 , 2 , 2 1/2 , ......
The first term is : a = 1
And the common difference : d = 1/2
So, if the number of days = x
And the number of boxes = y
so,
\(\begin{gathered} y=d\cdot x+a \\ \\ y=\frac{1}{2}x+1 \end{gathered}\)The graph and the table of the equation will be as shown in the following image :
How many boxes of carrots will Nancy have in 6 days ?
When x = 6
The number of boxes = 1/2 * 6 + 1 = 3 + 1 = 4 boxes
What function is being described Justify each part of your function, explaining how you determined it.
My function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2. It has end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity. The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.
What is the end behavior of a polynomial function?The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.
Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.
The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.
The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.
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(02.09 mc) module two practice test
Answer:
no
Step-by-step explanation:
Answer:
what is this supposed to be?
Step-by-step explanation:
Each small square in the graph paper represents 1 square unit.
Find the area of the given figure in square units.
Do not include units (square units) in your answer.
Pls help in a pre-test thank you!
Express the answers in simplest form. A list contains the names of six anthropology students, two sociology students, and four psychology professor's new study, find the probability that the chosen student (a) A psychology student (c) A psychology student or an anthropology (d) Not a sociology student.
a) P(psychology student) = 1/3. b) P(psychology or anthropology student) = 5/6. c) P(not sociology student)= 5/6
How to find the probability that the chosen student(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:
P(psychology student) = 4/(6+2+4) = 4/12 = 1/3
(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:
P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6
(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:
P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6
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2x + 3x/4 = 11
Please solve I am doing it for homework :)
Answer:
x = 4
Step-by-step explanation:
Bob's Bagels sells 10 bagels for $11.00, and Donny's Bagels sells 4 bagels for $3.00. Which is the better deal? Answer the questions to find out.
What fractions do you compare to find the better deal
Answer:
11/10 and 3/4
Step-by-step explanation:
To find the better cost, you need to determine which options has a lower cost per bagel.
Kim has worked at the front desk of a hotel for 3 years. She earns $14.50 an hour and works 40 hours a week for 48 weeks a year. She gets an annual bonus of 5% of her yearly earning, how much has Kim earned over 3 years? PLEASE HELP :)
Answer:
$87,696
Step-by-step explanation:
First lets multiple how much she makes a week. So do 14.5 times 40 =580. So Kim makes $580 a week. Now multiply this $580 times the 48 weeks = $27,840. Now we need to find her bonus. So we will multiply .05 times 27,840 = 1392. Now we need to add that back to her total. So 27,840 plus 1392 = 29,232. Now since she has worked there for 3 years, we will multiply her yearly salary (29,232) by the 3 years she has worked there. So we do 29,232 times 3 = 87,696. And that's your answer.
The length of a rectangle is 2 less than two times the width. Perimeter is 42. Find the length and the width.
Answer:
Hi there
Your answer is
width= 5.75
length= 9.5
Step-by-step explanation:
L=2w-2
P=42
Perimeter formula
L+L+W+W=P
(2w-2)+(2w-2)+w+w=42
8w-4=42
+4
8w=46
/8
w= 5.75
Plug in width in length formula!
L=2w-2
L=2(5.75)-2
L=9.5
A salesman receives a salary of RM 2000 per month. He wis receive a commission of RM 800 for each car he sells. If he sells n cars in a particular month,
a. Find his monthly salary when n = 18.
b. Express his salary in terms of n.
Answer:
a) month salary = RM(18×800+2000)
= RM 16400
b) his salary = RM(800n+2000)
Hope it helps
What is the common ratio of the geometric sequence below?
-2, 4, 8, 16, -32, ...
-4/2
-2/4
2/4
4/2
Answer:
-4/2
Step-by-step explanation:
just take 4 and divide it by -2 and youll get the common ratio as-2
Hope it helps
7x4 is 8 more than blank x 4
Answer:
7 × 4 = _5__ × 4 + 8
Step-by-step explanation:
7 × 4 = ___ × 4 + 8
28 = ___ × 4 + 8
20 = ___ × 4
___ = 20/4
___ = 5
7 × 4 = _5__ × 4 + 8
54 ÷ 6 x (12-4) + 2 =
Answer:
3
Step-by-step explanation:
1. 54÷6 =9
2. (12-4)=8
3. 9-8 = 1
4. 1+2 = 3
5. I hope this helps it's pretty simple oh and 3 is your anansw.Also you can you your calculator
Answer:
a=72\(\frac{2}{3}\)
Step-by-step explanation:
56/6*(12-4)+2=n
56/6*8+2-2=n-2
56/6*8/8=(n-2)/8
x=9\(\frac{1}{3}\)
x=(n-2)/8
y=74\(\frac{2}{3}\)
y=n-2=a
a=72\(\frac{2}{3}\)
solve for me please
(5xy+3x-7)+(3xy-xy+3y+4)
Answer:
Step-by-step explanation:
7xy+3x+3y−3
50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!
ΔABC is rotated 90° clockwise about the origin.
Answer:
(4,5)
Step-by-step explanation:
What is the value of s?
Answer:
S=4
Step-by-step explanation:
All the sides of an equilateral triangle are equal, so if one side is equal to 4, every side is equal to 4.
I literally used a protractor to check.
PLEASE MARK BRAINLIESTThe conditional statement below is true. If possible, write the biconditional statement.
If 2x = 18, then x = 9.
The biconditional statement for the given conditional statement would be:
2x = 18 if and only if x = 9.
The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".
To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.
If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.
Based on this, we can write the biconditional statement:
2x = 18 if and only if x = 9.
The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.
In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.
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