show that P(x)=x³-6x²+11x-6 is divisible by x-1.
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[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
Show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
[tex] \huge \boxed{\mathfrak{Explanation} \downarrow}[/tex]
To show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1, we must divide the polynomial by x - 1. If we get the remainder as 0, then we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
So, let's do the division (steps in the attached picture).
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We got the remainder as 0. So, yes p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
__________________
More steps :-x² - 5x + 6
= (x - 3) (x - 2) [use the splitting the middle term method].
So, the zeroes are,
(x - 3)
x - 3 = 0
x = 3 ⇨ 1st zero.
(x - 2)
x - 2 = 0
x = 2 ⇨ 2nd zero.
Now, use the values of x on the equation. If we get 0 as the solution of the equation then we can prove that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
p(x) = x³ - 6x² + 11x - 6
p(3) = 3³ - 6(3)² + 11 (3) - 6
p(3) = 27 - 54 + 33 - 6
p(3) = 0.
p(x) = x³ - 6x² + 11x - 6
p(2) = 2³ - 6(2)² + 11 (2) - 6
p(2) = 8 - 24 + 22 - 6
p(2) = 0
Since we got the solutions as 0 we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.
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Related Questions
Evaluate the function when x= -3,0 and 1. Show work H(x) = 2.5x + 7
Answers
Answer:
H(-3)= -0.5
H(0)= 7
H(1)= 9.5
Step-by-step explanation:
For H(-3)
Substitute all of the x into -3
H(-3)=2.5(-3)+7
2.5 times -3 is -7.5
-7.5+7 is -0.5
So the answer for H(-3) is -0.3
For H(0)
Substitute all of the x into 0
H(0)=2.5(0)+7
2.5 times 0 is 0
0+7 is 7
So the answer for H(0) is 7
For H(1)
Substitute all of the x into 1
2.5(1)+7
2.5 times 1 is 2.5
2.5+7 is 9.5
So the answer for H(1) is 9.5
Hope this helps!
Can someone tell me the answer to this please???
Answers
Answer:
36
Step-by-step explanation:
Answer:
It's 36 ya know
Step-by-step explanation:
60 and 60 so 36 and 36
:)
)
2 ft
2 ft
Perimeter:
Area:
Answers
Answer:
perimeter = 8 ftarea = 4 ftSolution:
perimeter- 2 + 2 + 2 + 2 = 8
area of square- (length × width) 2 × 2 = 4
can someone help me with this i am so confused
Answers
Answer:
HGI = 30
b/ce they are Vertically opposite angles
JGH = FGI
Answer:
1: Angle HGI is 30 degrees, Angle FGI is the same as JGH
Hope that helps. Brainliest is appreciated if it did!
find the domain and range of the following functions
Answers
Answer:
Step-by-step explanation:
X values are the domain and y values are range.
Domain = {-1,8,1,-2 }
Range = {3,2,5}
I need this bonus question
Answers
Answer:
52 units^2
Step-by-step explanation:
The area of the dresser is simple. It is just a rectangle that is 4 units by 3 units.
A_dresser = LW = 4(3) = 12 units^2
The area of the bed is a little more complicated, but you can get by using just areas of rectangles.
See the picture below.
Notice that the entire bed fits within a square (shown in blue) that is 9 units by 9 units.
The area of the square is 81 units^2.
We need to subtract the areas of the 4 triangles at the corners.
There are two triangles, top left and bottom right (shown in green), that have a base of 5 and a height of 5. They combine to for a square that is 5 units by 5 units. The area of this square is 25 units^2.
There are two triangles, top right and bottom left (shown in red), that have a base of 4 and a height of 4. They combine to for a square that is 4 units by 4 units. The area of this square is 16 units^2.
Now subtract 25 and 16 from 81 to get the area of the bed.
81 - 25 - 16 = 40
A_bed = 40 units^2
Combined area of bed and dresser:
A = 40 units^2 + 12 units^2 = 52 units^2
Answer: 52 units^2
Here's another way of finding the area of the bed:
Count the number of full squares inside the bed (there are 31). Each full square is 1 unit^2. Then count the number of half-squares inside the bed (there are 18). Each half-square is 1/2 units^2. Add them all up:
31 + 1/2 * 18 = 31 + 9 = 40
You get 40 units^2
USE THE CLUES TO CRACK THE CODE
The digits of the code are 4,4, 0, and 2.
The number is less than 1.
The value of the thousandths digit is
value of the hundredths digit.
the
10
Answers
Answer:
Is the answer 0.244? Not sure whether you are asking for help or asking for others to do.
Jones needs to travel from Town A to Town B in 2 hours. If the distance between between two towns is 320km. At what speed will Jones need to drive?
Answers
Answer:jone cần lái xe với tốc độlà:
Step-by-step explanation: 320/2=160(km/h)
a 450-square-foot apartment in new york city costs $540,00 what is the price per square foot?
Answers
Answer:
$1200
Step-by-step explanation:
Let cost of 1 square foot be x
So, Cost of 450 square feet = 450x
We are given that A 450-square-foot apartment in New York City cost $540,000.
So, 450x = 540000
x= [tex]\frac{540000}{450}[/tex]
x= 1200
Cost of 1 square foot = $1200
Hence the price per square foot is $1200
3x(5+4)=7
what dose that =
Answers
Help plsssssssssssssssssssssssssssssssssssssssssss
Hehe it’s a test for y’all the best will get full marks and 100 points with brainly
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Make me as brain liest
Jorge has a standard deck of 52 cards and a six-sided number cube. What is the probability that he will draw a diamond from the deck of cards and roll a number greater than two? Write your answer as a simplified
Answers
The probability that Jorge draw a diamond from the deck of cards and roll a number greater than two is 2/39
Probability is the like likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome
If Jorge has a standard deck of 52 cards, the total outcome is 6
If Jorge draw a diamond card, the probability that he will draw a diamond card is 4/52 = 1/13
For a six-sided cube, the total outcome is 6. If he rolls a number greater than two, the expected outcome will be 4
The probability that he rolls a number greater than 2 is 4/6 = 2/3
The probability that Jorge draw a diamond from the deck of cards and roll a number greater than two is 1/13 * 2/3 = 2/39
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How do you solve this
Answers
Answer:
x = 8
Step-by-step explanation:
1. First, we should realize that the angle with 16x + 7 and the angle with 5x + 5 are same-side interior angles, meaning they add up to 180 degrees. This means that 16x + 7 + 5x + 5 = 180.
2. (Solving)
Step 1: Simplify both sides of the equation.
[tex](16x+5x)+(7+5)=180[/tex] [tex]21x + 12 = 180[/tex]Step 2: Subtract 12 from both sides.
[tex]21x + 12 - 12 = 180 - 12[/tex] [tex]21x = 168[/tex]Step 3: Divide both sides by 21.
[tex]\frac{21x}{21}=\frac{168}{21}[/tex] [tex]x = 8[/tex]Step 4: Check if solution is correct.
[tex]16(8)+7+5(8)+5=180[/tex] [tex]128 + 7 + 40 + 5 = 180[/tex] [tex]135 + 40 + 5 = 180[/tex] [tex]175 + 5 = 180[/tex] [tex]80= 80[/tex]Therefore, x = 8.
please help me thank you
Answers
Answer:
Step-by-step explanation:
1.x +y = 1 Yes
2. Power of variable e is 3. So, it is not a linear equation
No.
3) Great than symbol is there. No, it is not a linear equation.
4. 2x -y = 2x + 5
2x - y - 2x = 5
-y = 5 is not a linear equation with two variable.
No.
5. No.
1) (5,14) ; (19,7)
[tex]Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{7-14}{19-5}\\\\=\dfrac{-7}{14}\\\\=\dfrac{-1}{2}[/tex]
2) (-10 , 1) ; (-10 ,4)
x- coordinate is same for both the points. So, the line is parallel to y-axis
Slope = undefined
[tex]3) (-3,-3) ; (15,13)\\\\slope=\dfrac{13-[-3]}{15-[-3]}\\\\=\dfrac{13+3}{15+3}\\\\=\dfrac{16}{18}\\\\=\dfrac{8}{9}[/tex]
[tex]4)(\dfrac{-1}{2},\dfrac{1}{7}) ; (\dfrac{-3}{2},\dfrac{2}{7})\\\\Slope=\dfrac{\dfrac{2}{7}-\dfrac{1}{7}}{\dfrac{-3}{2}+\dfrac{1}{2}}\\\\\\=\dfrac{\dfrac{1}{7}}{\dfrac{-2}{2}}\\\\\\=\dfrac{\dfrac{1}{7}}{-1}\\\\\\=\dfrac{-1}{7}[/tex]
Compare with y = mx + b ; here m is slope
1. y = -2x - 8
slope = -2
2. x = 3
Line is parallel to y-axis.
So, slope = undefined
3.2x - y = 4
2x - 4 = y
y = 2x - 4
Slope = 2
4.) 2x + y - 5 = 0
y = -2x + 5
Slope = -2
Write an equation in slope-intercept form for the line described. Write the slope and y-intercept as fractions, if necessary. passes through (6, 2), parallel to y = -}x+1
Answers
The slope of your answer will be whatever number is supposed to be in front of the x (assuming you hit the close brace on accident the same time you hit the minus sign, I’m gonna assume you meant to put -x+1) making the slope of your answer -1.
So you have y=-x+b
To find b, plug in (6,2)
2 = -(6) + b
8 = b
So, your answer would be
y = -x + 8
Otherwise, whatever is suppose be in front of the x,
y = -mx + (2+6m)
i need serious help guys!!!!!!
Answers
Answer:
b.
Step-by-step explanation:
Eliot went to the store and bought 4 1/2 pounds of chicken for $12.00. What was the cost per pound of chicken? round you answer to the nearest cent is necessary.
I will give you brainly
Answers
Answer:
$2.67
Step-by-step explanation:
$12.00 divided by 4.5 (aka four and a half) = 2.6666 = amount per pound
Round to the nearest cent. 2.666, that last six makes the six in the hundredths place round up to 7.
en un restaurante se usan 70 gramos por cada porción de arroz por persona.Si un día se preparan 4760 gramos de arroz ¿cuántas porciones se obtendrán?
Answers
Queremos saber cuantas porciones de arroz se preparan dado que conocemos cuantos gramos de arroz se utilizan.
Se prepararon 68 porciones.
Lo que sabemos en principio es que, por cada porción de arroz, se necesitan 70 gramos de arroz.
Sabemos que en total se utilizan 4,760 gramos de arroz. Para saber cuantas porciones se prepararon, hay que tomar el cociente entre la cantidad total utilizada y lo que se usa para cada porción.
Esto nos da:
4,760g/70g = 68
Es decir, se prepararon 68 porciones.
Sí quieres aprender más, puedes leer
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If x + y = 10 and x - y = 4, find the value of x² - y²
Answers
Answer:
x²-y² = 40
Step-by-step explanation:
Factorising x²-y²:
x²-y² = (x+y)(x-y)
This is due to the property that states:
a²+b² = (a+b)(a-b)
Substituting the given values into the above equation:
x²-y² = (10)(4)
= 40
Hence, x²-y² = 40
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
Answer:
x² - y²=40 or 7²-3²=40
Step-by-step explanation:
if x=7 that would make y=3
7+3=10 and 7-3=4
7x7=49
3x3=9
49-9=40
What is the equivalent ratio to 14:10 ?
?:30
Answers
Answer:
42:30
Step-by-step explanation:
10 x 3 = 30
14 x 3 = 42
10 is 3 times to get to 30
So 3 times 14 gets to ?
14:10
42:30
Evaluate the expression when n=6
n² – 5n-2
Answers
Answer:
4
Step-by-step explanation:
(6^2) -5(6) -2 =4
that is the answer
Step-by-step explanation:
6^2 - 5×6 - 2
= 36 - 30 -2
= 4
*PLEASE HURRY WILL GIVE BRAINLY* A company's profits (in dollars) are modeled by the function p(x) = —x^2+ 1100x - 300000, where x is the number of units produced. To determine the minimum number
of units that must be produced in order to earn profits of $590, the company plots the parabola of y = —x^2 1100x -- 300000 and the line x = 590, finds the intersection
of the two, and concludes that 900 units must be produced. Is the company correct? Explain, rounding values to the nearest whole number if necessary.
Answers
A choir teacher is dividing 6 sopranos and 20 altos into singing groups. He wants each group to have the same combination of sopranos and altos, with no singers left over. What is the greatest number of groups he can make?
Answers
6: 1,2,3,6
20: 1,2,4,5,10,20
2 is the greatest number in both, therefore there can only be 2 groups of 3 sopranos, and 10 altos.
Solve the Expression
5-(2*8)+14=
Answers
Answer:
3
Step-by-step explanation:
5-(2*8)+14=
Parentheses first
5-16+14=
Then add and subtract from left to right
-11 +14
3
If there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a black sock as a fraction in simplest form?
Answers
Answer:
3/13
Step-by-step explanation:
three socks out of the 13 are black. therefore you have a 3/13 chance of picking black.
Simplify the following expressions by distributing. 4(-w +8)
Answers
Answer:
-4w+32
Step-by-step explanation:
distribute the 4 to everything in the ( )
Fatima conducted an experiment where she asked people to estimate the temperature of glasses of water. She recorded how far the estimates were from the actual temperatures, using positive values for guesses that were too high and negative values for guesses that were too low. Her results are in the table below.
Estimate -−minus actual temperature (\degree\text{C})(°C)left parenthesis, degree, start text, C, end text, right parenthesis
Person A Person B Person C
-3−3minus, 3 444 888
-1−1minus, 1 -4−4minus, 4 -2−2minus, 2
000 222 555
222 -3−3minus, 3 111
What is the mean value in Fatima's results?
Answers
The mean value is the sum of the temperature values divided by the total frequency. Hence, the mean value in Fatima's temperature result is -0.75°C
Given the data :
Person 1 :
-3, - 1, 0, 2, Sum = (-3 + (-1) + 0 + 2) = - 2Person 2 :
4, -4, 2, - 3 Sum = (4 + (-4) + 2 + (-3)) = - 1Person 3 :
8, - 2, 5, 1Sum = (8 + (-2) + 5 + 1) = 12Mean value = (Total sum ÷ Frequency)
Mean value = [(-2 + (-1) + 12) ÷ 12]
Mean value = - 9 ÷ 12 = - 0.75
Therefore, the mean value of the result is 0.75°C
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If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y = mx + b. To do so, substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. Using the above technique, find the equation of the line containing the points (-4,7) and (2,-2).
What is the equation of the line?
(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
Answers
Answer:
y=-3/2x+1
Step-by-step explanation:
NOTE: Doing graphs by hand is a lot easier, it saves a lot more time as well.
Step 1: plot your 2 known points.
Step 2: draw a line that goes between both points
Step 3: find the distance of the points in RISE/RUN format.
-9/6. The slope is negative because the line goes down to the right.
Step 4: find your y-intercept.
1.
Step 5: simplify your equation
-9/6 = -3/2
Evaluate 4.56 × 3.6/ 0.12 and leave you answer in standard form.
Answers
Answer:
136.8
Step-by-step explanation:
As per DMAS rule, we can divide first or multiply first. I would choose divide first. Then:
4.56 x 3.6/0.12
= 4.56 x 30.
Since I divided first, the next step is to multiply.
4.56 x 30
= 136.8
Since there is no addition or subtraction happening next, the process ends here and the answer is 136.8.
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The expression value [tex]4.56 \times \frac{ 3.6}{0.12}[/tex] in standard form is 136.8=1.368×10².
To evaluate the expression [tex]4.56 \times \frac{ 3.6}{0.12}.[/tex]
Find the multiplication of the numerator with 4.56 and then divide it by 0.12.
Perform the multiplication first:
4.56×3.6 = 16.416
Now we divide the result by 0.12:
[tex]\frac{16.416}{0.12} = 136.8[/tex]
To express the answer in standard form, we rewrite it as a number multiplied by a power of 10.
In this case, we move the decimal point two places to the right to obtain a whole number:
136.8=1.368×10²
Therefore, the answer to the expression [tex]4.56 \times \frac{ 3.6}{0.12}[/tex] in standard form is 136.8=1.368×10²
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Factor the following Polynomial a) 6x - 18