Answers
Answer:
[tex]\huge\color{Black}\boxed{\colorbox{pink}{Answer♡}}[/tex]
Given ,[tex]p(x) = ax {}^{3} + 8x {}^{2} + bx + 5 ...(1)[/tex]
Also According to Question ,on dividing polynomial p(x) by ( x + 2 ) , we obtain ( -25 ) as a remainder.
Therefore , putting the value of x as ( x = -2 )
[tex]p( - 2) = a( - 2) {}^{3} + 8( - 2)^{2} + b( -2) + 5[/tex]
[tex]p( - 2) = - 8a + 32 - 2b + 5 = - 25 \\ = > - 8a - 2b + 37 = - 25 \\ = > - (8a + 2b) = - (25 + 37) \\ cancelling \: negative \: sign \: at \: both \: sides \\ 8a + 2b = 52 \\ dividing \:both \: sides \: by \: 2 \\ 4a + b = 26...(2)[/tex]
also given that..
when the polynomial p(x) is divided by 2x-1 , it gives 0 as the remainder , i.e. , 2x-1 is a root of p(x)
putting value of x = 1/2 in equation (1)
[tex]p( \frac{1}{2} ) = a( \frac{1}{2}) {}^{3} + 8( \frac{1}{2} ) {}^{2} + b( \frac{1}{2} ) + 5 = 0 \\ = > \frac{a}{8} + \frac{8}{4} + \frac{b}{2} + 5 = 0 \\ = >taking \: LCM \\ = > \frac{a + 16 + 4b + 40}{8} = 0 \\ = > \frac{a + 4b + 56}{8} = 0 \\ = > a + 4b = - 56...(3)[/tex]
Now , we have equations (2) and (3) as...4a + b = 26... (2)
a + 4b = -56... (3)
multiply equation (2) by 4..16a + 4b = 104...(4)
Solving equations (3) and (4)a + 4b = -56
16a + 4b = 104
- - - ( bc signs are same )solving these equations we get,
-15a = -160
a = -160/-15
a = 32/3
putting value of a in (2) , we get...[tex]4a + b = 23 \\ 4( \frac{32}{3} ) + b = 23 \\ \frac{128}{3} + b = 23 \\ b = 23 - \frac{128}{3} \\ taking \: LCM \\ b = \frac{69 - 128}{3} \\ = > b = \frac{ -59}{3}[/tex]
hope helpful~
Related Questions
Select the correct answer.
Simplify the following expression.
Answers
In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 2x + 5 and g (x) = x-5/2 to determine if f(x) and g(x) are inverse of each other.
Answers
Answer:
In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 2x + 5 and to determine if f(x) and g(x) are inverses of each other?
It is very difficult to know because you did not include the function g(x), you only gave us f(x).
Given two lists of ordered pairs [x,f(x)] and [x,g(x)]. If for every ordered pair on the f(x) list the reverse is on the g(x) list the functions are inverses.
f(0) = 5 so for (0,5) on the f(x) list then (5,0) must be on the g(x) list
f(1) = 7 so for (1,7) on the f(x) list then (7,1) must be on the g(x) list
f(2) = 9 so for (2,9) on the f(x) list then (9,2) must be on the g(x) list
So even though you didn’t list g(x), g(x) = (x/2) - 5/2
A cylinder has a height of 7 centimeters and a diameter of 4 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
Answer:
V = 87.92 cubic cm
Step-by-step explanation:
V(cyl) = πr²h
V = 3.14(2²)(7)
V = 87.92
Your bank account starts with $1550 and every month $50 is automatically deducted for the cable bill. You want to know how long, x, it would take your account to drop below $0. How many months would it take for your account to drop BELOW $0?
Answers
Step-by-step explanation:
C(x) = 1550 - 50x
With C(x) the cash you have every month (x).
Now we solve:
1550 - 50x < 0
So it becomes:
50x > 1550
x > 31
The 32nd month you'll be broke.
Please help me with this
Answers
b= 2
y=3 into 2b- 4+ 6y
2x2 -4+6x3
Can i get some help :
Answers
Answer:
is not equal to sign is used
please help ASAP! What is the area of this figure?
Answers
Answer:
The answer is 75ft. Hope this helps.
A water cooler holds 1536 ounces of water each water bottle holds 16 ounces how many water bottles can be filled from the water cooler
Answers
Answer:
96 water bottles
Step-by-step explanation:
1536/16 = 96
The point (-1, 5) is reflected over the y-axis. Where is the location of the new image?
(-1, -5)
(5, 1)
(1, 5)
(1, -5)
Answers
The base of a triangular field is three times its height. If the cost of cultivating the feild at $36 per hectare is $486, find its base and height.
Please explain also
Answers
Answer:
Formula of the area of triangle = 1/2 × b × h (where 'b' is the base and 'h' is the height)
1 hectare = $36
$486 = 13.5 hectares
13.5 hectares = 1/2 × b × h
To get b × h, you use the reverse of the formula. Hence:
13.5 = 1/2 × b × h
13.5 ÷ 1/2 = b × h
= 27
27 is b × h.
The question states that the base is three times the height. Hence:
b = 3u
h = 1u
b × h = 27
= 3u × 1u
Thus, we need to find one value which is three times the other, in order to get a product of 27.
Factors of 27:
1 × 27
3 × 9
9 is three times of 3. Thus, the base is 9, while the height is 3.
what is the solution to this equation 4x -6 + 2x =18
Answers
Answer:
x=12
Step-by-step explanation:
4x-6+2x=18
2x-6=18
2x=24
x=12
A= (4,-1)
B= (0,-5)
which one is right ,two answer choices.
Answers
Answer:
A
Step-by-step explanation:
Please help! IXL math problem
Answers
Answer:
224, 755
Step-by-step explanation:
you first have to find the differnce between 177 and 47 which equals to 133.
so you have to do 94+133
and 885-133
what is the answer, i need help
Answers
Answer: C 1/2mL LMN= mL LMO
Step-by-step explanation: because 2/76 is 38 C is the right answer
Plz help fast I will mark Brainlyist
Answers
Answer:
-4 -2 1 the top are 2/6 -2/8
Step-by-step explanation:
I don't know if that's right but yea hope that helps
pls help me with math asap pls no links thx
Answers
Answer:
8
Step-by-step explanation:
Divide 192 by 24 and you'll get 8 classes per grade as the answer
Answer:
8 classes
Step-by-step explanation:
To find the minimum amount of classes, you divide 192 by 24 and you get 8 classes.
Help!! NO SPAM!!!! I will mark brainliest. A phone banking password consists of 2 letters followed by 4 digits. The letters B and X are not used, and the last digit cannot be 0. How many different passwords are possible?
Answers
In this exercise we have to use the combination knowledge to calculate the different possibilities, so we have to:
5184000 possible ways
in this way, when we deal with possibilities it is the same as talking about multiplication, so we have that:
[tex]24*24*10*10*10*9=5184000[/tex]
See more about possibilites at brainly.com/question/488013
PLEASE HELP
Solve for x
Answers
Answer:
you get 32
Step-by-step explanation:
The diameter of a circle is 3 miles what is the area
Answers
Answer:
[tex]2.25\pi[/tex] or [tex]7.07 mi^{2}[/tex]
Step-by-step explanation:
The formula for the area of a circle is:
[tex]\pi r^{2}=A[/tex]
Radius is half of the diameter of a circle so you will get this:
[tex]\pi (\frac{3}{2}) ^{2}\\\\\pi (1.5)^2\\\\2.25\pi \\\\7.07[/tex]
please help me with this as soon as possible
Answers
Answer:
the answer is i dont know XD
Step-by-step explanation:
So if we want to do the first one it will be
Y = 4 x (1) - 3
Y = 4 - 3
Y = 1
For the second one we got x = 6
So we do the same thing but with 6 and say
Y = 4 x (6) - 3
Y = 21
It seems confusing at first but I’m sure you’ll get the hang of it
Lila planted a tree in her backyard. She made a graph to show the tree growth over 5 years.
1) What does the slope mean in real life in the context of the problem?
2) What does the y-intercept mean in real life in the context of the problem?
Answer in complete sentences.
Answers
Answer:
1. Growth rate of tree 3 ft per year, 2. Beginning height of tree 5 feet, rise/run = 3/1 = 3
Step-by-step explanation:
The solution is
1) The slope of the graph m = 3 represents the growth of the tree per year
2) The y-intercept means the initial height of the tree , when x = 0
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P = P ( 3 , 14 )
Let the second point be Q = Q ( 1 , 8 )
Now , the slope of the two points on the line is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 14 - 8 ) / ( 3 - 1 )
Slope m = 6/2
Slope m = 3
Therefore , the slope is 3 feet per year
b)
The y intercept is calculated from the equation of line , when x = 0
So , the equation of line is given as
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 14 = 3 ( x - 3 )
On simplifying the equation , we get
y - 14 = 3x - 9
Adding 14 on both sides of the equation , we get
y = 3x + 5
Now , when x = 0
y = 3 ( 0 ) + 5
y = 5 feet
From the graph we can see that , at 0 years the initial height of the tree is also 5 feet
Therefore , the y intercept is 5 feet
Hence , The slope of the equation is 3 and y intercept is 5
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ2
A motorcycle can run 108km in 2h20mn Find the average speed
Answers
Answer:
do it got a picture
on the edge2020
Step-by-step explanation:
Officer Brimberry wrote 32 tickets for traffic violations last week, but only 12 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent. [The percent decrease is___%
Answers
Answer:
62.5 %
Step-by-step explanation:
you have to subtract 32-12, which equals 20
then divide 20 by the original amount (20/32)
20/32= .625, then you have to multiply to get the final answer...hope this helped!
PLs help me 15 points on total
Answers
Answer:
i think its C
Step-by-step explanation:
a diver is 19 meters below the surface of the water.use an interger to represent how far the diver will need to travel to reacg the surface'
Answers
Answer:
19 meters
Step-by-step explanation:
if he goes straight up at 90 degreed to the surface of water, it would be 19 metres
5m - 2 represents the statement two less than five times a number
Answers
Answer:
yes
Step-by-step explanation:
A set of 3 consecutive integers has a sum of 15. Which integers are they?
Answers
The answer is 4+5+6=15.Hope that helps. :)
Answer:
Step-by-step explanation:
Let the first number be x,
The second number (since it is consecutive) will be = x + 1
The third number (since it is right after the second) = (x+1) + 1 = x + 2
x + x + 1 + x + 2 = 15
3x + 3 = 15
3x = 15 - 3
3x = 12
x = 12/3 = 4
If the first number = 4,
Second number will be = 5 [(x+1) = 4+1]
Third number will be = 6 [(x+2) = 4 + 2]
in baseball the home plate is shaped like the one shown it has three right angles and two other congruent angles A and B find measurement of angle a and measurement of angle B
Answers
Answer:
135
Step-by-step explanation:
the triangle is 90-45-45
the square is 90-90-90-90
where the two meet just add 45 + 90
135
Pablo has $5,483 in a savings account. The interest rate is 5%, compounded annually.
To the nearest cent, how much will he have in 3 years?
(compound interest formu)
Answers
Answer:
$6347.26Step-by-step explanation:
Given:
Initial amount P = 5483Interest rate r = 5% or 0.05Compound number n = 1Time t = 3 yearsFind the total amount in 3 years:
[tex]A = P(1+r/n)^{nt}[/tex][tex]A = 5483*(1+0.05/1)^{1*3}=5483*(1.05)^3 = 6347.26[/tex]Here we've been given,
Principal amount (p) = $5843 Compound number (n) = 1 Rate of Interest (r) = 5% = 5 × 1/100 = 0.05 Time (t) = 3 years A = ?The standard formula for Compound interest (C.P) is given by,
[tex]:\implies\tt{A = p( { \frac{1 + r}{n} )}^{n \times t} } \\ \\ \\ :\implies\tt{A = 5483( { \frac{1 + 0.05}{1}) }^{1 \times 3} } \\ \\ \\ :\implies\tt{A = 5483 \times {1.05}^{3} } \\ \\ \\ :\implies\tt{A = 6347.26}[/tex]
X
18. MODELING WITH MATHEMATICS The inequality
3x + 2y 2 93 represents the numbers x of multiple-
choice questions and the numbers y of matching
questions you can answer correctly to receive an A on
a test. You answer 20 multiple-choice questions and
18 matching questions correctly. Do you receive an A
on the test? Explain.
Answers
Answer:
yes
Step-by-step explanation:
Put the numbers into the inequality and see if it is true.
Given x = 20, y = 18, ...
3x + 2y = 3(20) +2(18) = 60 +36 = 96 ≥ 93 . . . . true
You have met the requirements for an A on the test.