Given:
The expression is:
[tex]2x^3+mx^2+nx+c[/tex]
It leaves the same remainder when divided by x -2 or by x+1.
To prove:
[tex]m+n=-6[/tex]
Solution:
Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).
Let the given polynomial is:
[tex]P(x)=2x^3+mx^2+nx+c[/tex]
It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that
[tex]P(2)=P(-1)[/tex] ...(i)
Substituting [tex]x=-1[/tex] in the given polynomial.
[tex]P(-1)=2(-1)^3+m(-1)^2+n(-1)+c[/tex]
[tex]P(-1)=-2+m-n+c[/tex]
Substituting [tex]x=2[/tex] in the given polynomial.
[tex]P(2)=2(2)^3+m(2)^2+n(2)+c[/tex]
[tex]P(2)=2(8)+m(4)+2n+c[/tex]
[tex]P(2)=16+4m+2n+c[/tex]
Now, substitute the values of P(2) and P(-1) in (i), we get
[tex]16+4m+2n+c=-2+m-n+c[/tex]
[tex]16+4m+2n+c+2-m+n-c=0[/tex]
[tex]18+3m+3n=0[/tex]
[tex]3m+3n=-18[/tex]
Divide both sides by 3.
[tex]\dfrac{3m+3n}{3}=\dfrac{-18}{3}[/tex]
[tex]m+n=-6[/tex]
Hence proved.
Can someone please help me. If you do thanks
Answer:
(B)
Step-by-step explanation:
Can't explain lol, but that's the answer
Darryl is finding the product of -5y(-4y^3+6y^2-5) Is he correct? If not, what changes should be made?
What is the first step in solving the equation x2 - 25 = 0?
What is the second step in solving the equation?
Answer:
first step - make x² the subject of the formula
x² = 25
second step :
find the square root of both sides
√x² = √25
x = 5
Step-by-step explanation:
Find the value of x that will make A||B.
Please help!
Answer:
x=30
Step-by-step explanation:
Hi there!
For A to be parallel to B, 5x would be equal to 3x+60. (If they were parallel, these two angles would be alternate exterior angles, which are equal.)
[tex]5x=3x+60[/tex]
Subtract 3x from both sides
[tex]5x-3x=3x+60-3x\\2x=60[/tex]
Divide both sides by 2
[tex]x=30[/tex]
I hope this helps!
Find all solutions to the equation
in the interval [0, 21). Enter the
solutions in increasing order.
sin 2x = 2 sin x
x = [?],[1]
TT
Remember: sin 20 = 2 sin 0 cos 0
Answer:
[tex]x=0, \\x=\pi[/tex]
Step-by-step explanation:
Recall the trigonometric identity [tex]\sin 2x=2\sin x\cos x[/tex].
Therefore, given [tex]\sin 2x=2\sin x[/tex], rewrite the left side of the equation:
[tex]2\sin x\cos x=2\sin x[/tex]
Subtract [tex]\sin x[/tex] from both sides:
[tex]2\sin x\cos x-2\sin x=0[/tex]
Factor out [tex]2\sin x[/tex] from both terms on the left:
[tex]2\sin x(\cos x-1)=0[/tex]
We now have two cases:
[tex]\begin{cases}2\sin x=0, x=k\pi\text{ for }k\in \mathbb{Z}\\\cos x-1=0,x=k2\pi\text{ for }k\in \mathbb{Z}\end{cases}[/tex]
Since the problem stipulates that [tex]x[/tex] is in the interval [tex][0, 2\pi)[/tex], we have:
[tex]\text{For }x\in [0, 2\pi):\\\sin x=0\rightarrow \boxed{x=0, x=\pi}\\\cos x-1=0\rightarrow \boxed{x=0}[/tex]
Recall that square brackets mean inclusive and parentheses mean exclusive. Therefore, [tex]2\pi \notin [0, 2\pi)[/tex].
Z Is An Even Integar Greater Than 30 And Less Than Or Equal To 34.
Answer:
32, 34
Step-by-step explanation:
The answer must be grater than 30 so 30 is not an option the integers in the range are 31, 32, 33, and 34 the only even integers in this set are 32, and 34. Hope this helps. :)
At maximum speed, an airplane travels
1680 miles against the wind in 5 hours.
Flying with the wind. the plane can
travel the same distance in 4 hours.
What is the speed of the plane with no wind?
Answer:
The speed of the plane with no wind is 378 miles per hour.
Step-by-step explanation:
Since at maximum speed, an airplane travels 1680 miles against the wind in 5 hours, and flying with the wind. the plane can travel the same distance in 4 hours, to determine what is the speed of the plane with no wind, the following calculation must be performed:
Against the wind = 1680/5 = 336
With the wind = 1680/4 = 420
420 - ((420 - 336) / 2) = X
420 - 42 = X
378 = X
Therefore, the speed of the plane with no wind is 378 miles per hour.
7 of 8
Write the number three million and eighty-two thousand in figures
Answer:
3,082,000
Step-by-step explanation:
THE ANSWER IS 3,082,000 HOPE IT HELPS
hamood spelled backwards is hamood also let me know if u want my account by 12 AM PDT 6/2/21
Answer:
yo congratulations on finishing 10th grade (congratulate me on finishing 8th)
hamood spelled backwards is doomah so...um...
also do u mean 7/2/21..bc 6/2/21 is like in June and we're in July
Arturo is building a flower bed in the shape of a right triangle. The hypotenuse of the right triangle is 13 feet. One of the legs needs to be 7 feet longer than the other leg.
Which equation can be used to find x, the length of the shorter leg?
x(x + 7) = 13
x(x + 7) = 169
x2 + (x + 7)2 = 13
x2 + (x + 7)2 = 169
Answer:
x(x + 7) = 169
Step-by-step explanation:
We are given that
Let length of shorter leg of right triangle = x ft
Length of other leg = x+7 ft
Hypotenuse of right triangle = 13 ft
We have to find the equation which can be used to find x, the length of shorter leg.
By pythagorous theorem
(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2
Substitute the values then, we get
(13)^2=x^2+(x+7)^2
x^2+(x+7)^2=169
This is required equation which can used to find x.
Answer:
d. x2 + (x + 7)2 = 169
Step-by-step explanation:
use Pythagorean theorem, substitute in the given values, and you get this
Pls answer 13 b ill mark u brainlist
Answer:
7 students
Step-by-step explanation:
1+2+4=7students
What is the standard form equation of the line shown below? Graph of a line going through negative 1, 5 and 2, 4
Answer:
y = -1/3x + 14/3
Step-by-step explanation:
We have the standard equation as;
y = mx + b
where m is the slope and b is the y-intercept
the given points are;
(-1,5) and (2,4)
So we plug x and y for each of the points
then we create two linear equations which we can solve simultaneously to get the values of m and b
From the points;
5 = -m + b•••••••(i)
4 = 2m + b
from i;
b = 5 + m
substitute this into equation ii
4 = 2m + 5 + m
4 = 3m + 5
4-5 = 3m
3m = -1
m = -1/3
Recall;
b = 5 + m
b = 5-1/3
b = 14/3
so we have the equation as;
y = -1/3x + 14/3
Multiply through by 3
3y = -x + 14
Convert the following 4.5 hours Into Second- ( Soin 24
Answer: 16,200 Seconds
Step-by-step explanation:
Data: 4.5 hours(h)=x seconds(s)
Step One, Convert Hours Into Minutes
4.5h=4h and 30 minutes(m)
1h=60mx4=240m+30=270m
Reason: Since to convert to seconds, minutes are needed, you have to convert everything to minutes. And with 60 minutes in an hour you have to multiply 60 by 4 to get 240 and add 30 minutes to it(since it's 4.5 hours) to find ourselves at 270 minutes.
Step two, Convert Minutes Into Seconds
1m=60s
270mx60=16,200s
Reason: Since we are ultimately trying to get 4.5 hours into seconds, we have to convert the minutes we have into seconds by multiplying 270 minutes by 60(since 60 seconds are in a minute) to get our final answer of 16,200 seconds.
I hope this helps!
write a function rule for the following data
What should the follow equations is equivalent to 6.87p+9.2=-7.056
Answer:
P=-2.3662299854
Step-by-step explanation:
6.87p = - 7.056 -9.2
So 6.87p= - 16.256
P=-2.3662299854
Find the missing angle measures.
Answer:
<ABD = 42 degrees
<ABC = 84 degrees
Step-by-step explanation:
<ABC = 42 + 42 = 84
Helppp and explain !!!!
Answer:
try 4
Step-by-step explanation:
basically need to find number that when multiplied 3 times equals 64 so 4*4*4=64
What is the vertex of the graph of the function f(x) = (x + 2)^2 − 3?
A circular sheet covers 425cm on the table,find the area of the sheet.
solve this question plz.
Answer:
sorry i cannot help you
The owner of a coffee shop compared the amount of hot coffee per day, in fluid ounces, sold and the daily high temp. In degrees f per day, 5.9x+850=
The question is not complete as the scatter plot is missing.
Thus, I have attached the complete question showing the scatter plot.
Answer:
D: On a day with a high temperature of 0°C, the shop can expect to sell about 850 fluid ounces of hot coffee
Step-by-step explanation:
From the attached image showing the question and scatter plot, we can see that the scatter plot is modeled by the line; y = -5.9x + 850
Where;
x is the high temperature in °F
y is the amount of fluid ounces sold
Let's try x = 0°F
Thus;
y = 0 + 850
y = 850 fluid ounces
Let's try x = 10°F
Thus;
y = -5.9(10) + 850
y = 850 - 59
y = 791
This means for every increase in temperature of 10°F, the amount sold is approximately 60 fluid ounces lesser.
Looking at the options in the attached file, the only correct one that corresponds to our answer is option D where it says;. On a day with a high temperature of 0°C, the shop can expect to sell about 850 fluid ounces of hot coffee
solve the problems. write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it
Answer:
[tex]m \angle A = m \angle C[/tex] by reason [tex]\overline{AB} \cong \overline{BC}[/tex] and [tex]m \angle B = m \angle M = m \angle P[/tex].
[tex]\triangle AMO \cong \triangle CPO[/tex] SAS Theorem
Step-by-step explanation:
We proceed to demonstrate the statement by Geometric means:
1) [tex]\overline{AB} \cong \overline{BC}[/tex], [tex]\overline {AM} \cong \overline {PC}[/tex], [tex]m\angle AMO = m\angle CPO[/tex] Given.
2) [tex]\frac{AM}{AB} = \frac{PC}{BC}[/tex] Proportionality.
3) [tex]\frac{AM}{AM + MB} = \frac{PC}{BP + PC}[/tex] Definition of line segments.
4) [tex]\frac{1}{1+\frac{MB}{AM} } = \frac{1}{\frac{BP}{PC}+1}[/tex] Algebra.
5) [tex]\frac{BP}{PC} + 1 = 1 +\frac{MB}{AM}[/tex] Algebra.
6) [tex]\frac{BP}{PC} = \frac{MB}{AM}[/tex] Algebra.
7) [tex]BP = BM[/tex] By 1)
8) [tex]m \angle B = m \angle M = m \angle P[/tex] By 1), 7)
9) [tex]\triangle AMO \sim \triangle ABC[/tex], [tex]\triangle CPO \sim \triangle ABC[/tex] By 1), 7), 8). Defintion of simmilarity.
10) [tex]\frac{AM}{MO} = \frac{AB}{BC}[/tex], [tex]\frac{PO}{PC} = \frac{AB}{BC}[/tex] Definition of proportionality.
11) [tex]\frac{AM}{MO} = \frac{PO}{PC}[/tex] Algebra.
12) [tex]AM^{2} = PO\cdot MO[/tex] Algebra.
13) [tex]PO = MO[/tex] By 12) and Algebra.
14) [tex]\overline{PO} \cong \overline{MO}[/tex] By 13).
15) [tex]\triangle AMO \cong \triangle CPO[/tex] SAS Theorem/Result.
hello! I'm having a bit of trouble trying to solve this, could anyone help explain it to me?
[tex]\displaystyle\ 60^2 =36(36+x)\\\\1296+36x=3600\\\\36x=2304\\\\\boxed{x=64}[/tex]
Step By Step Explanation:
[tex] {60}^{2} = 36(36 + x)[/tex]Step 1Calculate 60 to the power of 2 and get 3600.
[tex]3600 = 36(36 + x)[/tex]Step 2Use the distributive property to multiply 36 by 36 + ×.
[tex]3600 = 1296 + 36 \times [/tex]Step 3Swap sides so the all variable terms are on the left hand side.
[tex]1296 + 36 \times = 3600[/tex]Step 4Subtract 1296 from both sides.
[tex]36 \times = 3600 - 1296[/tex]Step 5Subtract 1296 from 3600 to get 2304.
[tex]36 x = 2304[/tex]Step 6Divide both side by 36.
[tex] \times = \frac{2304}{36} [/tex]Step 7Divide 2304 by 36 to get 64
My Answer is
[tex]\color{GREEN} \times = 64[/tex]Beth wants to build a thin wire frame for a photo that is $$15 cm long and $$6 cm wide. What length of wire will she need to go around the entire photo?
Answer:
42
Step-by-step explanation:
1. PerimeterPerimeter is [tex]2l+2w[/tex]
2. Solving[tex]2(15)+2(6)=30+12=42[/tex]Answer: 42
Hope this helped! Please mark brainliest :)
what is the sum of all the exterior angle of a polygon
Answer:
From what I learn it is 360 degrees
the lines given by the equations y=6x and y=6x+2 are ____
They are parallel, as shown by the graph.
question 3 help pls in algebra
Answer:
50
Step-by-step explanation:
simplify the radical by breaking the redicand up into a product of known factors, assuming positive real numbers.
-5(x+4) + -3x + -9x+-7
Answer:
x - 27
Step-by-step explanation:
Our goal here is to solve for x.
Start by performing the indicated multiplication:
-5(x+4) + -3x + -9x+-7 => -5x - 20 - 3x + 9x - 7
Combine like terms: x - 27
Answer:
[tex]-5(x+4) + -3x + -9x+-7[/tex]
[tex]\longmapsto -5\left(x+4\right)+\left(-3\right)x+\left(-9\right)x+\left(-7\right)[/tex]
[tex]\longmapsto -5\left(x+4\right)-3x-9x-7[/tex]
[tex]\longmapsto -5(x+4)=-5x-20[/tex]
[tex]\longmapsto -5x-20-3x-9x-7[/tex]
[tex]\longmapsto =-17x-27[/tex]
[tex]ANSWER:=-17x-27[/tex]
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hope it helps....
have a great day!!
The area (A) of a circle is a function of its radius (r) and is given by the function A=f(r)=pie r^2. What is the domain of this function
A. All positive real numbers
B. All real numbers
C. All positive real numbers including 0
D. All real numbers excluding fraction
given the figure below, what is the value of x?
Answer:
x = 6
Step-by-step explanation:
6 is x so this is the answer
1. If f(x) = 6x + 13x + 2x - 5 and f(-1) = 0, find the
factors of f(x)
Answer:
-26
Step-by-step explanation:
Insert the f(-1) into the equation.It'll be f(-1) = 6(-1) + 13(-1) + 2(-1) - 5After you times all of it. You'll get 7-13-2-5Solve it and you'll get -26