Answers
Answer:
[tex](x-1)^2(x+3)[/tex]
Step-by-step explanation:
For factorization the given expression you can use the Ruffini's rule.
First find the divisors of the independent term (these are the possible rational roots), in the given polynomial the independent term is [tex]3[/tex].
[tex]3 = \{\pm1,\pm3\}[/tex]
Now replace each number in the polynomial
[tex]P(1) = 1^3 + 1^2 - 5(1) + 3 = 0[/tex]
If the result is equal to 0 that's meaning that is a possible root of the polynomial. Then for know if is a root you have to divide the polynomial by [tex](x - \text{possible root})[/tex].
[tex](x^3 + x^2 -5x+3 )/ (x-1)[/tex]
In the first row are the coefficients of the given polynomial.
In the second row are the product between the coefficients and the independent term of the [tex]x-1[/tex].
The third row are the coefficients of the quotient polynomial (except the last that is the remainder).
[tex]\qquad 1\qquad 1\qquad-5\qquad \quad3\\1\qquad\qquad1\qquad \quad 2\qquad-3\\-------------\\ 0 \ \ \quad1 \qquad 2 \qquad -3 \qquad \quad 0[/tex]
Because the last term is the remainder and it's 0 you can factorizate [tex](x-1)[/tex] and the quotient polynomial is equal to
[tex]x^2 + 2x -3[/tex]
So our current expression is [tex](x-1)(x^2 + 2x -3)[/tex], however you can factorizate the quotient polynomial in:
[tex]x^2 +sx +rx +rs = x^2 + 3x -x + 3(-1) = (x + 3)(x -1)[/tex]
So the last expression is:
[tex](x-1)(x+3)(x-1) = (x-1)^2(x+3)[/tex]
Related Questions
¿Qué fuerza media se requiere para que un objeto de 2 Kg aumente su velocidad de 5 m/s a 12 m/s en una distancia de 8 m?
Answers
Answer:
14.87
Step-by-step explanation:
Para conocer cual es la fuerza que necesita el cuerpo para aumentar su velocidad de 5 m/s a 12 m/s en 8 m
Necesitamos conocer la aceleración y para conocer la aceleración debemos saber cuanto tiempo tarda en recorrer los 8m
Vf = Vo +a(t)
12 = 5 +a(t) -------> Vamos a despejar el tiempo.
t = 7/a
X= Vo(t) +1/2a(t²)
X= 5(7/a)+1/2a( 7/a )²
8 = 35/a+49/2a
a = 7.43 m/s²
Ahora que conocemos la aceleración podemos calcular la fuerza como:
F = m*a
F = 7.43 * 2 kg.
F = 14.87
The American customer satisfaction index scores of McDonalds restaurants grew from 61 in 2002 to 71 in the year 2014. Find the average rate of change for the data. Show work.
Answers
Answer:
[tex]\large\sf{average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}[/tex]
Step-by-step explanation:
Given the American customer satisfaction index scores that increased from 61 in 2002, to 71 in 2014:
In order to solve for the average rate of change, we could simply use the average rate of change formula:
Average rate of change = Change in output/Change in input
[tex]\huge\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}}[/tex]
Let (x₁, y₁) = (61, 2002)
(x₂, y₂) = (71, 2014)
Substitute these values into the average rate of change formula:
[tex]\BIGG\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}\:=\frac{2014\:-\:2002}{71\:-\:61}\:=\:\frac{12}{10}\:=\:\frac{6}{5}}[/tex]
[tex]\large\bf\sf{Therefore,\:the\:average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}[/tex].
A family buys a studio apartment for $180,000. They pay a down payment of $27,000.
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $9,000 down payment be
Answers
Answer:
down is $153000 while purchase price is $144000
help plz
find the size of unknown angle in the flowing figures
Answers
Answer:
it is 95 degrees because it is a vertically opposite angle
a scale diagram, 0.125 inch represe
5 feet. How many inches represent
pot?
0.001
0.01
0.1
0.12
Math
Answers
Answer:
the scale diagram is 9.12
What is 20% of $1575.00
Answers
step:
20% = 20/100
of = ×
20/100 × $1575.00
answer : $315
Step:
20% = 20/100
of = ×
20/100 × $1575.00
Answer : $315
Match the equation to the type of solution.
3=3 A. One solution
x=0. B. No solution
4=-2. C. Infinite many solutions
Answers
X=0 - B. No solution
4=-2 - A. One solution
hope this helps .
Dependent Task:
Directions: Write the place value and the value of the underlined digit.
Number PLACE OF VALUE VALUE
1. 0.345 _____________ _____
2. 0.3469 _____________ _____
3. 0.6ó54 _____________ ______
(UNDERLINED DIGIT)
1. 5
2.3
3.4
please
Answers
Answer
Use your mind
Nobody wants to help you, especially since you are no help to others.
The hypotenuse of a 30°-60°-90º triangle is 8 units and one leg is 4 units. What is the length of the other leg?
Answers
Answer:
The length of the other leg is [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
There are 2 ways to solve this.
1) Pythagorean theorem (the harder way)
A 30-60-90 triangle is a right triangle, and therefore you can use the pythagorean theorem to calculate the measure of 1 side given the 2 others.
[tex]a^2+b^2=c^2\\a^2+4^2=8^2\\a^2+16=64\\a^2=48\\a=\sqrt{48}\\a=6.9282...[/tex]
That's one solution, but its not a very nice number or the exact answer you probably want. Instead, you can simplify the root.
First, you need to factor 48:
[tex]2*24=48\\2*12=24\\2*6=12\\2*3=6[/tex]
The prime factors of 48 are:
[tex]2*2*2*2*3=48[/tex]
Then, you need to find perfect squares:
[tex](2*2)*(2*2)*3=48\\2^2*2^2*3=48[/tex]
And finally, you can remove those like this:
[tex]\sqrt{48} =\sqrt{2^2*2^2*3} \\\sqrt{48} =2\sqrt{2^2*3} \\\sqrt{48} =2*2\sqrt{3} \\\sqrt{48} =4\sqrt{3}[/tex]
The length of the other leg is [tex]4\sqrt{3}[/tex]
2) 30-60-90 triangle relationships (the easier way)
There are 4 simple rules here:
Short leg × 2 = hypotenuseShort leg × √3 = long legLong leg ÷ √3 = short legHypotenuse ÷ 2 = short legThey're actually pretty easy to remember. You can multiply the short leg by 2 or √3, and 2 is greater than √3 (check a calculator). The hypotenuse of course is also longer than the long leg, so you have to multiply by 2 to get it. Then for the long leg, the only option is to multiply by √3. The same works in reverse for both of those.
Here, we have the short leg. You can check that with the pythagorean theorem again to be sure:
[tex]a^2+4^2=8^2\\a^2+16=64[/tex]
Because 16 is less than half of 64, a has to be the longer leg. Using the rules above, multiply the short leg by √3 to get the answer:
[tex]4 * \sqrt{3} \\4\sqrt{3}[/tex]
Same answer as the previous method.
A local hamburger shop sold a combined total of 637 hamburgers and cheeseburgers on Wednesday. There were 63 fewer cheeseburger sold than burgers. How many hamburgers were sold on Wednesday?
Answers
2x=700
X=350
Burgers=350
Cheeseburgers=350-63
Cheeseburger=287
If each rabbit consumes 10 pounds of rabbit food each year, then how much rabbit food is consumed in 10 years
Answers
Answer:
100 pounds in 10 years
Step-by-step explanation:
10 pounds per year for 10 years
We simply multiply 10 pounds to 10 years to get 100 pounds
-Chetan K
Mr. Haynes wants to expand his rectangular living room to make room for an indoor theater system. He asks the contractor to make the width of the room 5 feet longer and he wants the length of the room to be 5 feet longer than twice the width. When finished the new room will have a perimeter of 140ft around. The new dimensions of the room will be
Answers
Step-by-step explanation:
check the image for detailed solution
A campus survey states that 40% of students ride the bus if there are 300 students how many ride the bus?
Answers
Answer: 180 students
Step-by-step explanation:
10%=30
30x4=120
5. The coordinate increments from (4, 3) to (9, 7) are :
6. The coordinate increments from (- 6, - 4) to (12, - 9) are:
7. The coordinate increments from (10, - 7) to (14, - 9) are: are:
8. The coordinate increments from (- 47, - 10) to ( 17 , 8) are:
Answers
Answer:
the correct answer is 8
Step-by-step explanation:
Answer:
5. Is "+" 6. is "-" 7. is "+" 8. is "-"
Step-by-step explanation:
Food A 150 calories in 3/4 of a serving. Food B 250 calories in 2/3 of a serving. Find each unit rate. Which food has fewer calories per serving?
Answers
Food B 166.50
Food A has less calories
How many solutions does this equation have
-4(5-3x)=12x+20
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answers
Answer:
A) no solution
Step-by-step explanation:
It’s A Contradiction
Answer:
its one solution
Step-by-step explanation:
-20+12
A shirt cost $24.92 with 10% discount if the sales tax is 6.35% how much will the shirt cost?
Answers
= 2.492
Sale tax 6.35+2.492
The total Cost of shirt is = 8.732
A square field has a side length of 6x10 meters. Which of the following is its area in square meters?
Answers
Answer:
60 square meters
Step-by-step explanation:
area is just its length times its width and both numbers are provided here
6 * 10 is 60
The mean of 11 numbers is 49. Removing one of the numbers causes the mean to decrease to 45. What number was removed?
Answers
Answer:
89Step-by-step explanation:
The mean:
[tex]\overline{x}=\dfrac{a_1+a_2+a_3+...+a_n}{n}[/tex]
We have:
[tex]\overline{x}=49;\ n=11[/tex]
Then we have
[tex]\dfrac{11\cdot49}{11}=49[/tex]
[tex]n[/tex] - the number
new mean is equal 45.
Therefore we have the equation:
[tex]\dfrac{11\cdot49-n}{11-1}=45\\\\\dfrac{539-n}{10}=45\qquad|\text{multiply both sides by 10}\\\\539-n=450\qquad|\text{subtact 539 from both sides}\\\\-n=-89\qquad|\text{change the signs}\\\\n=89[/tex]
Step-by-step explanation:
(x1 + x2 + ... + x11)/11 = 49
x1 + x2 + ... + x11= 49×11 = 539
(x1 + x2 + ... + x10)/10 = 45
x1 + x2 + ... + x10 = 45×10 = 450
so, the difference in both sums is
539 - 450 = 89
89 was the removed number.
The graph below represents the function f(x) and the translated function g(x).
AVA
2x
/g(x)
a
If f(x) = x, which of the following functions could be an algebraic representation of g(x)?
Answers
Answer:
letter A.g(x)=x2+b that's the answer cause g(x) is in the positive
Please help me out with this Math sheet. Thanks
Answers
Answer:
1. acute
2. obtuse
3. right
4. acute
5. straight
6. obtuse
7. acute
8. obtuse
9. straight
10. ∠ EAD , ∠ CED , ∠ BCE , ∠ BEA , ∠EBC
11. ∠CDA , BCD
12. ∠AED ,∠BEC
13. ∠ AEC, ∠ BED
14. ∠ EAU , ∠EUI , ∠IUO , ∠OAE
15. ∠ EUO , ∠IUA
16. ∠AUO , ∠EIO
Please help pleasee right now
Ms. Mary spent $192 less than Ms.Mona on supplies for their class. Together they spent a total of $988. How much did each person spend?
Answers
Answer:
Mary:604
Mona:796
Step-by-step explanation:
Answer:
Ms. Mary spend $302
Ms. Mona spend $ 686
Step-by-step explanation: We know that Ms. Mary spend $192 less than Ms. Mona.
So we are to divide $988 by 2 which is 494
now both have $494 each but Ms. Mona spend 192 so we are to add 192 + 494 to get the right sum of how much money Ms. Mona have and take away 494-192 to get the right sum of how much money Ms. Mary spend.
192 + 494 = 686
494 - 192 = 302
720 is what percent of $800?
Answers
the answer is 90 hope this help.
What is the base of 4×4×4×4×4?
Answers
Answer:
Step-by-step explanation:
Your base would be the 4
Answer:
4
Step-by-step explanation:
When you have a something raise up to a number this can be represented as:
[tex]b^a = b_1 \cdot b_2 \cdot \cdot \cdot b_a[/tex]
Where [tex]b[/tex] is the base and [tex]a[/tex] the exponent. In this case you have five times four, then you can re-write the expression as:
[tex]4 \times 4 \times 4 \times 4 \times 4 = 4^5[/tex]
Where the [tex]b[/tex] is equal to 4 and [tex]a[/tex] equal to 5
Simple Arcs and Sectors question attached. First person to answer correctly gets 50 points. ONLY ANSWER 1ST QUESTION Good Luck!! Spam comments will be blocked and accounts reported.
Answers
Answer:
θ = 60º
Step-by-step explanation:
s = (θ/180)πr
Solving for θ yields
θ = (180s) / (πr)
--------------------------------
For the 1st one
θ = (180 * 12.56) / (π * 12)
θ = 60º
Two functions f and g are defined on the set R, of real numbers by f : x 2x 3 and
x g : x 1 3x . Find the inverse of the function f and the domain of gof.
Answers
Answer:8
Step-by-step explanation:
Rick’s Rentals is a car rental company that uses the function f(x)=22+0.10x to determine the to
tal cost of a rental as a function of how many miles a person drives. Penny’s Pencils is another company that uses a similar function g(x)=22+0.10x to determine the total cost of an order of personalized pencils as a function of the number of pencils ordered. Determine the domain and range of the company whose function is continuous and justify your answer.
Answers
Answer:
Step-by-step explanation:
The number of miles driven is sometimes written as a mixed number, and thus is a continuous variable (whereas the number of pencils purchased is not continuous (it's a whole number).
The domain of the continuous function are [0, n), where n represents the number of miles driven and is rarely over about 500 miles per day; the range is [$22, r), where r is ($0.10/mile)(number of miles driven), or approximately $50. If the renter drove 600 miles the upper end of the range would be $60. And so on.
A single card is drawn at random from a standard 52 card deck. Work out the following probabilities in their simplest form: P(4)= P(not 4)=
Answers
Answer:
Step-by-step explanation:
Total Number of possible outcomes = 52
Getting a jack from a deck of 52 cards for a certain event (A) = 4
The Probability (A) = 4/ 52
= 1 / 13 = 0.07
Hope you like it please mark as brainliest.
I need help as soon as possible please!!!!
Answers
Answer:
Which grade math is this? I haven't learned it
In a group of 84 kids, three-sevenths bought their lunches.Of those who bought their lunches got a slice of pizza? Write your fraction in simplest form
Answers
Answer:
There's not enough information to answer the question.
Step-by-step explanation:
The question says that out of 84 kids, 3/7 bought their lunches. Then it asks how many of the 3/7 got pizza without providing a number of those who bought a different food. And so, there's not enough information to solve this question.