A polynomial p(x) has a remainder of 4 when divided by (x+1) and a remainder of 7 when divided by (x-2) what will be the remainder when divided by (x+1)(x-2)

Answers

Answer 1

hello :
p(x) = (x+1)g(x)+4.......(1)
p(x) = (x-2)h(x)+7........(2)
find : R.... p(x) =(x+1)(x-2)L(x)+R ( R: remainder)
multiply (1) by : (x-2) and (2) by :(x+1)
(x-2)p(x) = (x-2)(x+1)g(x) +4(x-2).....(a)
(x+1)p(x) = (x-2)(x+1)h(x)+7(x+1)........(b)
(b) -(a) :
(x+1)p(x) - (x-2)p(x) = (x-2)(x+1)h(x) - (x-2)(x+1)g(x) + 7(x+1) - 4(x-2)
((x+1)-(x-2))p(x) = (x-2)(x+1)(h(x)-g(x)) +3x+15
3p(x) = (x-2)(x+1)(h(x)-g(x)) +3(x+5)
p(x) = (x-2)(x+1)((h(x)-g(x))/3) +(x+5)
so : L(x) = ((h(x)-g(x))/3)
and : R = x+5 is the remainder when divided p(x) by (x+1)(x-2).

Related Questions

PLEASE HELP!!!
How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?

3y − x = −6
4y − x = 44

3y + x = −6
4y + x = 44

3y − 3x = −6
4y − 4x = 44

3y + 3x = −6
4y + 4x = 44

Answers

y=1/3x-2
3y=x-6
3y-x=-6
y=1/4x+11
4y=x+44
4y-x=44

Answer: Hello!

we have that:

one third x − 2 = one fourth x + 11

this means:

(1/3)x - 2 = (1/4)x + 11

if this are equal numbers, we can write it as:

(1/3)x - 2 = y = (1/4)x + 11

now we have the system of equations:

(1/3)x - 2 = y

(1/4)x + 11 = y

if we "simplify" the rational therm in each equation, we get:

3*(1/3)x - 3*2 = 3y

x - 6 = 3y

and

4*(1/4)x + 4*11 = 4y

x + 44 = 4y

Then our system of equations is:

x - 6 = 3y

x + 44 = 4y

Now we can subtract x in each side of both equations:

-6 = 3y - x

44 = 4y - x

Then the right option is the first one.

3y - x = -6

4y - x = 44

For the polynomial below, what is the coefficient of the term with the power of 3?

x^3+1/3x^4+6x+5

A. 6
B. 5
C. 0
D. 1

Answers

the answer is
D.1

because even though there is not a number in front of X, we are to assume it is 1.

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

[tex]x^3+\frac{1}{3}x^4+6x+5[/tex]

Coefficient of the terms are as follows:

Coefficient of x³ is 1

Coefficient of x⁴ is [tex]\frac{1}{3}[/tex]

Coefficient of x is 6

Constant term is 5

Hence, coefficient of the term with the power of 3 is 1.

Therefore, Option 'D' is correct.

What is the solution set of the following equation? 3x2 - 6x = 0

Answers

The solutions are x=0 and x=2 because you have to find the gcf first and factor it. The gcf is 3x so, the factor is 3x(x-2)=0. When you solve that you get x=0 and x=2 for the solutions. 3x=0 divide both sides by 3 and you get x=0 and x-2=0 add 2 on both sides and you get x=2. Thanks for letting me help you.

Emily is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 14 km/h. After nine hours, the velocity of the cyclist is 4 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 10 hours? (5 points)

Answers

Assume that Emily starts from rest so that the velocity is zero at 0 hours.

Define the function v(t) for velocity in km/h, and t in hours.

Part A
From t=0 to t=4, v changes from 0 to 14.
Let v(t) = mt + b
The slope is
m = 14/4 = 3.5, and the y-intercept is
b = 0.
Therefore
v(t) = 3.5t, for 0 ≤ t ≤ 4

Fromt=4 to t=9, changes from 14 to 4.
Let v(t) = mt + b
The slope is
m = (4 - 14)/(9 - 4) = -2
Therefore
v = -2t + b
When t=4, v=14, therefore
14 = -2*4 + b = -8 + b
22 = b
v(t) = -2t + 22, for 4 < t ≤ 9.

Answer:
The equation for the velocity is
v(t) = 3.5t, 0 ≤ t ≤ 4
= -2t + 22, 4 < t ≤ 9

Part B
The equation for velocity is a piecewise function that is graphed as shown below. If we assume that the second part of the equation is valid at t=10, then
v(10) = -2*10 + 22 = 2 km/h

HELP
If f(x)=-6x+12, then f^-1(x)=?

Answers

The inverse is (x-12)/-6

200 gallon tank fills at 3 gallons/minute and loses 2 gallons/minute how long does it take to fill up

Answers

it fills at 3 gallons per minute, but loses 2 gallons per minute

3-2 =1, so it fills at 1 gallon per minute

200 gallons at 1 gallon per minute = 200 minutes,

200/60 = 3 hours and 20 minutes

The sum of three interior angles of a convex Pentagon is 420°.if the remaining angles are equal how much does each angle measure?

Answers

The sum of interior angles of any polygone is:

Sum of angles = (n-1)x180°, where n is the number of sides. For the pentagone n = 5, then Sum of angles of a PENTAGONE = (5-1)x180° = 720°.
Already the sum of 3 angles is 420°, the measure of the 2 remaining one is
720° - 420° = 300°. Since the remaining angles are equal, hence each one will have a measure of 300°/2 = 150°

Each one of the remaining angles measures 60°.

How much does each angle measure?

We know that the sum of the interior angles of a closed figure of n sides is given by:

(n - 2)*180°.

A pentagon has 5 sides, so we use n = 5 and we get:

(5 - 2)*180° = 540°

Now we know that 3 angles add up to 420°.

Then the other two angles must add up to:

540° - 420° = 120°

And those two angles are equal, then each one measures:

120°/2 = 60°.

If you want to learn more about angles, you can read:

https://brainly.com/question/17972372

You roll a six sided die and toss a coin. What is the probability of rolling an odd number and then getting heads?

Answers

P(O,T)=(3/6)(1/2)

P(O,T)=1/4

Hello there! Thank you for asking your question here at Brainly! I will be assisting you with answering your question, and will teach you how to tackle it on your own in the future.

So, let's take a look at our question.
"You roll a six sided die and toss a coin. What is the probability of rolling an odd number and then getting heads?"

First, we need to understand what we're dealing with, and how to handle it.
Let's tackle these individually, rather than doing it all at once and getting confused/stuck.
We roll a six sided die, which is numbered from 1 to 6. "What is the probability of rolling an odd number?"
Well, let's count how many odd numbers there are from 1 to 6.
1, 3, 5; We have three odd numbers on our six sided die.
Let's set that up as a fraction, [tex] \frac{3}{6} [/tex]
However, we can simplify it into simpler terms - divide both numbers by 3.
3/3 = 1
6/3 = 2
We now have our simplified fraction, [tex] \frac{1}{2} [/tex]

Now, let's focus on the other half of the problem.
"You flip a coin. What's the probability of landing on heads?"
Well, a coin only has two sides - heads and tails - which means we have 1/2 chances of landing on heads or tails generally.

Since the question asks for the probability of an odd number and landing on heads, we need to multiply our fractions.

We have these two fractions:
[tex] \frac{1}{2} [/tex] * [tex] \frac{1}{2} [/tex]
Multiply them.
[tex] \frac{1}{2} [/tex] * [tex] \frac{1}{2} [/tex] = [tex] \frac{1}{4} [/tex]

Your answer is [tex] \frac{1}{4} [/tex]

I hope this helps!

How tall would a stack of 1000 pennies be in centimeters?

Answers

US Penny dimensions are:
Diameter: 19 mm
Thickness: 1.52 mm ( according to the US mint )
1000 * 1.52 = 1,520 mm = 1.52 m = 1 m 52 cm
Answer:
A stack of 1000 pennies would be 1 m 52 cm tall.

Final answer:

To calculate the height of a stack of 1000 pennies, multiply the thickness of one penny (0.1524 cm) by 1000. The total height would be 152.4 cm.

Explanation:

Calculating the Height of a Stack of 1000 Pennies

To calculate the height of a stack of 1000 pennies, we first need to know the thickness of one penny. Unfortunately, the data provided talks about the volume of a stack of 100 bills, which is not directly relevant to our problem. However, by using the correct information, we find that a US penny is approximately 0.0598 inches (or 0.1524 cm) in thickness. So the calculation for the height of 1000 pennies stacked would be as follows:

Thickness of one penny = 0.1524 cmTotal height = 0.1524 cm/penny × 1000 penniesTotal height = 152.4 cm

Thus, the height of a stack of 1000 pennies would be 152.4 centimeters.

Learn more about Stack of 1000 Pennies Height here:

https://brainly.com/question/4558969

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A brick patio measures 18 ft by 16 ft by 6 in. find the volume of the bricks. if the density of the bricks is 130 pounds per cubic foot, what is the weight of the patio in pounds?

Answers

18 x 16 = 288

6 inches = 0.5 ft

288*0.5 = 144

patio = 144 cubic feet

144*130 = 18,720 total pounds

Use the information in the figure. If m∠F = 76°, find m∠E

Answers

52 because the whole triangle is 180 if you subtract that by 76 you get 102 since both sides equal each other the angles equal each other so you devide that by 2 you get 52

Answer:

m∠E=52°.

Step-by-step explanation:

The given triangle has two sides equal. In isosceles triangle two sides are equal and base angles are equal.m∠E=m∠D.

Let m∠D=m∠E= x

The sum of angles in any triangle is 180°.

Or,

x+x+76= 180

Addling like terms :

2x+76=180

Subtracting 76 both sides,

2x=104.

Dividing by 2:

x=52.

m∠E= 52°.

Describe how the graph of y=|x|-12 is like the graph of y=|x| and how it is different?

Answers

The graph of y = |x| - 12 can be transformed from y = |x| by:

Shift it downward by 12 units.

The whole shape of the two graphs will be the same.

Answer:

Both functions are similar, because basically they have the same behaviour, but the difference is that they start from a different vertex. The reason of this is because [tex]y=|x|-12[/tex] is a translation of [tex]y=|x|[/tex].

Basically, the first function is similar to the second one, but translated downwards 12 units.

So, they are similar in behaviour, we could say parallel, but different on the position of the vertex, the first is at y=-12, and the second one at y=0.

The graph of each function is attached, there you can observe the similarity and different we mentioned before.

Simplify the sum. (8u3 + 8u2 + 6) + (4u3 – 6u + 3)

Answers

-Hai There! :3

-Your answer and work for the question above should look like this:

8u3+8u2+6+4u3−6u+3
=8u3+8u2+6+4u3+−6u+3
=8u3+8u2+6+4u3+−6u+3
=(8u3+4u3)+(8u2)+(−6u)+(6+3)
=12u3+8u2+−6u+9

-Remember to mark this answer as Brainliest! Glad I could help!

A҉z҉u҉i҉e҉x҉

Answer:

[tex]12u^{3}+8u^{2}-6u+9[/tex]

Step-by-step explanation:

we have

[tex](8u^{3}+8u^{2} +6)+(4u^{3}-6u+3)[/tex]

Group terms that contain the same variable

[tex](8u^{3}+4u^{3})+8u^{2}-6u+(6+3)[/tex]

Combine like terms

[tex](12u^{3})+8u^{2}-6u+(9)[/tex]

[tex]12u^{3}+8u^{2}-6u+9[/tex]

Practice writing linear equations in different forms. Line AB goes through the points A (0, –4) and B (6, 2). Which equation represents line AB? y – 4 = 3x y – 2 = 3(x – 6) y + 4 = x y + 6 = x - 2

Answers

(0,-4)(6,2)
slope = (2 - (-4) / (6 - 0) = 6/6 = 1

y = mx + b
slope(m) = 1
(0,-4)..x = 0 and y = 4
sub and find b
4 = 1(0) + b
4 = b

equation is : y = x + 4...or x - y = -4
or y + 4 = 6(x - 0) ...or y - 2 = 6(x - 6)

the answer is c . y + 4 = x

Statistical Literacy For a binomial experiment with rr successes out of nn trials, what value do we use as a point estimate for the probability of success pp on a single trial? Select one: a. p hat = n-r b. p hat = n+r c. p hat = n/r d. p hat = r/n

Answers

For a binomial experiment with r successes out of n trials, the value we use as a point estimate for the probability of success p on a single trial is given by
[tex]\hat{p}= \frac{r}{n} [/tex]

What is the point slope equation of the line with slope -12 that goes through the points (5, 3)?

Answers

The point-slope form of ay line is:

y-y1=m(x-x1), where m=slope and (x1,y1) is any point on the line.

In this case we are given that m=-12 and (x1,y1) is (5,3) so

y-3=-12(x-5)

Answer:

y = -12x + 63

Step-by-step explanation:

- The equation of a line in a cartesian coordinate system is given by the following linear relationship:

y = mx + c

- The constants m and c are to be determined.

- The constant m denotes the slope of the line which is given as -12.

- To evaluate constant c we will plug the slope m = -12 and use the given point ( 5 , 3 ) as the lines passes through it. Hence, we have:

y = -12x + c

3 = -12(5) + c

3 = - 60 + c

c = 63

- Then the equation of the line can be expressed by plugging in the constants m and c as follows:

y = -12x + 63

Question 25. How do you do it?

Answers

All the prices listed are for each person, so the "three friends" and 2 club renters don't matter.

One person rents for $6 plus the green fee for one person. Let g = the green fee for a person. The total cost, club rental plus green fee, was $76.

6 + g = 76
g = 70

The perimeter of a rectangle is 42 m. the length of the rectangle is 3 m more than twice the width. find the dimensions of the rectangle.

Answers

42/2 = 21

21 = w +2w+3

21 = 3w +3

18 =3w

w = 18/3 = 6

width is 6

length = 6x2=12+3 = 15

6+6+15+15 = 42

width = 6 m

length = 15 m

In a 45-45-90 triangle, the length if the hypotenuse is 11. Find the length of one of the legs

Answers

the answer is B, picture shows how to solve it although the answer is written slightly different

Answer:

[tex] \frac{11\sqrt{2}}{2}[/tex]

Step-by-step explanation:

In a 45-45-90 triangle, the length if the hypotenuse is 11

WE use the common ratio of 45-45-90 degree triangle

common ration is x: x: x sqrt(2)

x sqrt(2) is the length of the hypotenuse

[tex]x\sqrt{2} = 11[/tex]

Divide by sqrt(2) on both sides

[tex]x= \frac{11}{\sqrt{2}}[/tex]

To rationalize the denominator, multiply by sqrt(2) at the top and bottom

sqrt(2) * sqrt(2) = 2

[tex]x= \frac{11\sqrt{2}}{2}[/tex]

How many values of θ will satisfy tan-1 0 = θ when 0º<θ<90º?

Answers

We want to satisfy
tan⁻¹ 0 = θ when 0° < θ < 90°.

The restriction on θ places the angle in the 1st quadrant.
When tan θ = 0, θ = 0°, 180°, 360°, ...
If θ >= 0, then a solution exists in the 1st quadrant.
Because of the requirement θ>0, no answer satisfies the given equation.

Answer: None

PLEASE HELP I WILL RATE YOU BRAINLIEST!!

Write -5.8 as a mixed number in simplest form. Show your work

Answers

[tex]-5.8 = -5 \frac{8}{10} = -5 \frac{4}{5} [/tex]

lady runs 20 miles in 4 hours. write an equation representing the direct relationship between distance and time

Answers

d=rt
20=40t
divide by 20
t=2
d=10

Ac=3x+6 and CD=2x+14 what is the value of x

Answers

AC = CD

And since the problem gave us two equations to use we will substitute them into the previous statement.

3x + 6 = 2x + 14
We now simplify with algebra and I will show every step.

3x + 6 = 2x + 14
-2x = -2x

x + 6 = +14
-6 = -6

x = 8

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

We have been given that [tex]AC=3x+6[/tex] and [tex]CD=2x+14[/tex].

To solve for x, we are assuming that C is the midpoint of segment AD and we will equate both expressions as:

[tex]3x+6=2x+14[/tex]

[tex]3x-2x+6=2x-2x+14[/tex]

[tex]x+6=14[/tex]

[tex]x+6-6=14-6[/tex]

[tex]x=8[/tex]

Therefore, the value of x is 8.

The sum of the exterior angles of a convex polygon, one angle at each vertex, is equal to how many degrees?

Answers

Answer: 360°

Step-by-step explanation:

Please HELP
1-) Solve the equation using the Properties of Equality.

11 − c = −17
2-)Solve the equation using the Properties of Equality.
1/2y + 1/5=1/2

Answers

Problem 1:
11-c = -17
First, we need to isolate the term with the variable. We can simply do that by subtracting 11 from both sides as follows:
11-11-c = -17-11
-c = -28
Then, we will multiply both sides by -1 to get the positive value of c as follows:
-c x -1 = -28 x -1
c = 28

Problem 2:
1/2 y + 1/5 = 1/2
First, we need to isolate the term with the variable by subtracting 1/5 from both sides as follows:
1/2 y = 1/2 - 1/5 = 3/10
Then, we will get rid of the coefficient in the term with variable by dividong both sides with 1/2, this will give the following output:
y = 3/5

what would be the measure of angle DGF, if segment DG is a bisector of angle G

30 degrees.60 degrees.90 degrees.None of the choices are correct.

Answers

check the picture below.

a bisector, means, it "cuts in two equal halves".

Find 3 consecutive integers if the sum of the first and third is 128

Answers

x + x + 2 = 128
2x + 2 = 128
2x = 126
x = 63

numbers are: 63, 64, 65

Which of the following is an identity? A. sin2x sec2x + 1 = tan2x csc2x B. sin2x - cos2x = 1 C. (cscx + cotx)2 = 1 D. csc2x + cot2x = 1

Edit: no one answered but I figured out that the right answer is A

Answers

There are three 'Pythagorean' identities that we can look at and they are

sin²(x) + cos²(x) = 1
tan²(x) + 1 = sec²(x)
1 + cot²(x) = csc²(x)

We can start by checking each option to see which one would give us any of the 'Pythagorean' identities as its simplest form

Option A:

sin²(x) sec²(x) + 1 = tan²(x) csc²(x)

Rewriting sec²(x) as 1/cos²(x)
Rewriting tan²(x) as sin²(x)/cos²(x)
Rewriting csc²(x) as 1/sin²(x)

We have

[tex]sin^{2}(x)[ \frac{1}{ cos^{2}(x) }]+1=[ \frac{ sin^{2}( x)}{ cos^{2} (x)}][ \frac{1}{ sin^{2}(x) } ][/tex]
[tex] [\frac{ sin^{2}(x) }{ cos^{2}(x) } ]+1= \frac{1}{ cos^{2}(x) } [/tex]
[tex] tan^{2}(x)+1= sec^{2}(x) [/tex]

Option B:

sin²(x) - cos²(x) = 1

This expression is already in the simplest form, cannot be simplified further

Option C:

[ csc(x) + cot(x) ]² = 1

Rewriting csc(x) as 1/sin(x)
Rewriting cot(x) as cos(x)/sin(x)

We have

[tex][ \frac{1}{sin(x)}+ \frac{cos(x)}{sin(x)}] ^{2} =1[/tex]
[tex] \frac{1}{sin^2(x)}+2( \frac{1}{sin(x)})( \frac{cos(x)}{sin(x)})+ \frac{cos^2(x)}{sin^2(x)}=1 [/tex][tex]csc^2(x)+2csc^2(x)cos(x)+cot^2(x)=1[/tex]

Option D:

csc²(x) + cot²(x) = 1

Rewriting csc²(x) as 1/sin²(x) and cot²(x) as cos²(x)/sin²(x)

[tex] \frac{1}{sin^2(x)}+ \frac{cos^2(x)}{sin^2(x)}=1 [/tex]
[tex] \frac{1+cos^2(x)}{sin^2(x)} =1[/tex]
[tex]1+cos^2(x)=sin^2(x)[/tex]
[tex]1=sin^2(x)-cos^2(x)[/tex]

from our working out we can see that option A simplified into one of 'Pythagorean' identities, hence the correct answer

Answer: A is the correct answer.

Step-by-step explanation:

Just did the question, followed OP's advice since no one answered. Good luck.

uhhhh how do i make a line parallel to AB through point C

Answers

you draw it up on a diagonal to the right so basically draw line ab starting at point c

In one baseball season, Peter hit twice the difference of the number of homeruns Alice hit and 6. Altogether, they hit 18 homeruns. how many homeruns did each player hit that
season?

Answers

In order to solve this problem, the approach should be formulating equations such that they form a system of linear equations. Let's start by assigning variables. Let x be the number of homeruns made by Peter, and y be the number of homeruns made by Alice. Therefore,

x = 2(y - 6)

This is the equation for the relationship between Peter's and Alice's hits. The second equation would be the sum of their hits:

x + y = 18

These are the two independent equations in order to solve the two unknowns, x and y. Substituting the first equation into the second equation,

2(y - 6) + y = 18
2y - 12 + y = 18
3y = 18 + 12
3y = 30
y = 10

Using y=10 to the first equation:
x = 2(10 - 6)
x = 8

Therefore, Peter made 8 homeruns, while Alice made 10 homeruns for a total of 18.

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