show that P(x)=x³-6x²+11x-6 is divisible by x-1.
Answers
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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.
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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
In a school annual Day 60 students involved is Science Exhibition, 75 involved in Mathematics Exhibition, 20 involved in both Exhibitions, and the rest of 285 students are not involved in any exhibition. Illustrate the above information in a Venn- diagrom. How many students took part in Schools Annual Day? How many of them involved in only one exhibition ?
Answers
Answer:
440 man its so easy just add up all the numbers
Step-by-step explanation:
440
Answer:
1) See the explanation
2) 400 Students
3) 95 Students
Step-by-step explanation:
1) As can be known from the question
Then, draw the venn diagram according to the known conditions.
2) 60 + 75 - 20 = 115 { Draw a venn diagram to calculate }
115 + 285 = 400
3) 60 - 20 + 75 - 20 = 95 ( Draw a venn diagram to calculate }
plsss help me with this:(((
Answers
Answer:
First we need our slope equation
Y₂-Y₁/X₂-X₁
So we have our equation now lets plug it in
-9+2/-4-3 (we make it a plus for -9+2 because the two minuses cancel out).
So now we have -7/-7 which is 1 because -7 divided by itself is one. Thereby your answer is A. 1
Same thing for question 12
1-5/2-4
-4/-2 which is 2 because -2 goes into -4 two times so your answer is A. 2
in the the picture below, EG has a length of (4x-8) and AB has a length of 24
A 5
B 2
C 12
D 8
Answers
Answer:
C
Step-by-step explanation:
1. Add 4x +8
the awswer would be 12x
2. subtract the 12x from the lenght which is 24
then your and will be 12
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line 4x + 3y = 12? Drag and drop each choice into the boxes to correctly complete the table. Parallel Perpendicular Neither
Answers
Step-by-step explanation:
The line given:
4x + 3y = 12, its slope is m = - 4/3Other lines to compare:
-3x + 4y = 8, the slope is m = 3/4, it is perpendicular line as the product of the slopes is - 1;4x + 3y = 31, the slope is m = -4/3, same slope but different y- intercept, it is parallel line;3x + 4y = 12, the slope is m = -3/4, it is neither parallel nor perpendicular;-4x + 3y = - 1, the slope is m = 4/3, it is neither parallel nor perpendicularSlope=m=+4/3
#1
-3x+4y=8m=3/4
Perpendicular#2
4x-3y=31m=-4/3
Parallel#3
3x+4y=12m=-3/4
neither#4
-4x+3y=-1m=4/3
NeitherYour 2 year investment of $5,300 earns 2.9% and is compounded annually. What will your total return be?
Answers
The total return will be $5611.8
How to calculate the total return?A 2 year investment of $5,300 earns 2.9%
The investment is compounded annually
The total return can be calculated as follows
= 5300 (2.9/100 + 1)
= 5300 (0.029 + 1)
= 5300(1.029)²
= 5300(1.0588)
= $5611.8
Hence the total return is $5611.8
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Sixty tickets at $70 each cost
Answers
Answer:
60x$70=$4100
Step-by-step explanation:
ekdjnsjs
Answer:
60 x 70= 4200$
Step-by-step explanation:
60
70 x
_____
(jk no need to do this just multiply them this way,because there are zeros just multiply 6 and 7 which equals 42 then add the zeros which are equal to= 4200$
A train decreased its speed by 72 miles hour in 12 minutes. Find the average change in speed per minute.
Answers
Answer:
6 mph
Step-by-step explanation:
The average rate of change of the speed of the train will be 6 miles per hour.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that a train decreased its speed by 72 miles per hour in 12 minutes.
As the train is reducing its speed by 72 miles per hour in 12 minutes the average rate of change of the speed will be calculated by dividing the change by the time.
Rate of change = 72 / 12
Rate of change = 6 miles per hour
Therefore, the average rate of change in the speed of the train will be 6 miles per hour.
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the ratio of x and 5 minus 12
(turn this into a problem)
Answers
then is it.........!!!?
5x-12
predict the next number 5,3,2,1,-1
Answers
Answer:
impossible?
Step-by-step explanation:
Please help (view screenshot)
Answers
Answer:
h(2)=8
Step-by-step explanation:
The problem basically asks you to substitute 2 in, hence h(2).
Here is your base equation.
h(x)=-x^2+6x
Plug in 2.
h(2)=-2^2+6(2)
Simplify, using PEMDAS.
h(2)=-4+12
h(2)=8
There's your answer!
Hope this helped :)
How many people have to buy tickets for the two companies to have the same price?
y=22x+10
y=25x+4
Answers
katie can mow at a constant speed rate of 4/5 lawns per hour
Answers
Answer:
y=4/5x+B
what is the whole question?
10-24
Which graph represents the solution to this system of inequalities?
-
3х — 5у < 15
y> - x +1
Answers
Answer:
Like this...
Step-by-step explanation:
The best represented graph should look something like this :)
(program used is Desmos)
Please answer these and find the slope intercept form for each one.
Best answer gets brainliest
Answers
12) y=-2x+8
please help MARKING BRAINLIST
Answers
Answer:
I don't know ask your parents
Step-by-step explanation:
One-fourth of a number is five-eights. Find the number. Simplify your answer
Answers
Answer:
2.50 or 2.5
Step-by-step explanation:
1/4=.25 so 25% of a number=5/8=0.625
So we multiply .625*4 to get the number. Since it's 25% and we want 100% to get it back to the original number
.625*4=2.50 or 2.5
x- intercept? explanation please
Answers
Answer:
x-intercept = 2
Step-by-step explanation:
Sum = 3
Product = -10
Factors = 5 , (-2) {5*(-2) = -10 & 5 +(-2) = 3)
Rewrite the middle term using the factors: 3x = 5x - 2x
x² + 3x - 10 = x² + 5x - 2x - 10
=x(x + 5) - 2(x + 5)
= (x +5)(x - 2)
x² + 8x +15 = x² + 3x + 5x + 15
= x(x + 3) + 5(x + 3)
= (x + 3)(x + 5)
[tex]f(x) =\dfrac{x^{2}+3x -10}{x^{2}+8x + 15}\\\\=\dfrac{(x+5)(x -2)}{(x+5)(x+3)}\\\\=\dfrac{x-2}{x+3)}[/tex]
At x-intercept, y = o
[tex]\dfrac{x -2}{x + 3}=0\\[/tex]
x - 2 = 0
x = 2
Can someone please? I don’t really understand how to do this with different variables
Answers
Answer:
Step-by-step explanation:
∠1 = ∠2 = 70 {Corresponding angles}
2x +2 y = ∠1
2x + 2y = 70 --------------(I)
2x + y = ∠2
2x +y = 70 --------------(II)
Subtract equation (II) from (I)
(I) 2x + 2y = 70
(II) 2x + y = 70
- - - {subtract}
y = 0
Plugin y= 0 in equation(I)
2x + 0 = 70
2x = 70
x = 70/2
x = 35
x = 35 ; y = 0
pls help!!!!! i will give brainliest!!!!!
Answers
Answer:
I believe it to be the first answer. Since, similar triangles always have the same slope.
Step-by-step explanation:
Select all of the number of ways in which a line
and a circle can intersect.
Answers
Answer:
0, 1, 2
Step-by-step explanation:
Hi there!
0
It is possible for a line and a circle to not intersect at all.
1
It is also possible for a line and a circle to meet at one point only. They would be tangent to each other and touch.
2
Finally, it is possible for a line to intersect the circle. They would appear overlapping. In any of these cases where a line intersects a circle, they would have crossed the circle at two points.
3
A line and a circle can only have a total number of 2 intersection points.
I hope this helps!
Graph the inequality
4x-12y<24
Show all your work!
Answers
Answer:
Slope = 0.667/2.000 = 0.333
x-intercept = 6/1 = 6.00000
y-intercept = 6/-3 = 2/-1 = -2.00000
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*x-12*y-(24)=0
Step 1: Pulling out like terms
Pull out like factors :
4x - 12y - 24 = 4 • (x - 3y - 6)
Equation at the end of step 1:
Step 2:
Equations which are never true:
Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
Solve x-3y-6 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line x-3y-6 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 2/-1 so this line "cuts" the y axis at y=-2.00000
y-intercept = 6/-3 = 2/-1 = -2.00000
Calculate the X-Intercept :
When y = 0 the value of x is 6/1 Our line therefore "cuts" the x axis at x= 6.00000
x-intercept = 6/1 = 6.00000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.000 and for x=2.000, the value of y is -1.333. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.333 - (-2.000) = 0.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 0.667/2.000 = 0.333
Geometric figure: Straight Line
Slope = 0.667/2.000 = 0.333
x-intercept = 6/1 = 6.00000
y-intercept = 6/-3 = 2/-1 = -2.00000
What is the function form of:
8x + 2y = -2
y = ?
Answers
Answer:
-4x-1
Step-by-step explanation:
-4x-1
Rise over run ???please
Answers
Answer:
1/4 slope
Step-by-step explanation:
From (-8,0) to (-7,4) it goes 1 up and 4 to the right
1. There is 1 /2cupcake left from Henry's birthday party. Henry and his friend want to share it equally. What fraction of a cupcake will each boy get?
Answers
Answer:
1/4
Step-by-step explanation:
what is the percent of games won if a team won 92 games and lost 58 games?
Answers
Answer:
I think this is it 61.33
Have a blessed day <333
Step-by-step explanation:
Melinda put 64 pieces of cake on a table. She placed them in 8 rows with the same number in each row. Each row had an equal number of two flavors of cake. How many pieces of each flavor were in one row?
( ugh math)
Answers
Answer:
There were 4 pieces
Step-by-step explanation:
write the equation of the line parallel to the given line 4x - 2y = 7
Answers
Answer:
2x+y = 3
Step-by-step explanation:
Let's take y=-2x+b through the point (1,1), so we get b is equal to 3. So this is y=-2x+3, so 2x+y=3
Complete the equation of the line through (4,-8)(4,−8)
Use exact numbers.
Y=____+_____
Answers
Answer: y = 4x-8
Step-by-step explanation:
(4,-8)
(x,y)
Solve for x, y and z ( help ♡ )
Answers
Ans of your question . in which class do u read?
Zach bought his parents anniversary gifts. His dad's present cost $25. He bought his mom 3 presents (p) that all cost the same amount. If he paid a total of $40, how much did each of his mom's gifts cost?
What is the value of p in the equation?
25 + 3p = 40
Answers
2) 15/3=5
3) each gift costs $5
Then to check:
1) 5x3=15
2) 25+15=40
Therefore p=5
Answer:
5
Step-by-step explanation: