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
Is y=12x proportional?
Answers
Answer:
yes, this line will pass through the point of origin
Step-by-step explanation:
The polynomial x3 4x2 â€"" 9x â€"" 36 has 4 terms. Use factoring by grouping to find the correct factorization. (x2 9)(x 4) (x2 â€"" 9)(x â€"" 4) (x2 9)(x â€"" 4) (x2 â€"" 9)(x 4).
Answers
The factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
The polynomial function is given as:
[tex]P(x) = x^3 + 4x^2 - 9x - 36[/tex]
Factorize the given expression.
[tex]P(x) = x^2(x + 4) - 9(x +4)[/tex]
Factor out x + 4
[tex]P(x) = (x^2 - 9)(x +4)[/tex]
Express 9 as the square of 3
[tex]P(x) = (x^2 - 3^2)(x +4)[/tex]
Apply the difference of two squares
[tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
Hence, the factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
Read more about factorization at:
https://brainly.com/question/11434122
I need help please it’s for school
Answers
From Sweatcoin, London to the residence of Santa Claus is about 4,280 km away.
Where is the Santa Clause's residence?
The residence of Santa Clause is popularly known as the North Pole.
According to the above, we have to roughly calculate the distance from Sweatcoin in London to the North Pole. This distance is equivalent to about 4,280 km
Learn more about London in: https://brainly.com/question/7416097
George's family is on a road trip. After driving for a while, they stopped for gas, and then traveled 5834 more miles before they decided to stop for lunch. After lunch, they tripled their distance traveled before stopping for the night. Their total distance traveled that day was 381 miles. How many miles had they traveled before their first stop for gas? Enter your answer as a simplified mixed number in the box.
Answers
Answer:
Step-by-step explanation:
68 1/4
The distance travelled before their first gas stop is 68 1/4 miles given in mixed fractions.
What is a mixed fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
Assume the distance covered before their first stop for gas be 'x'
Total distance travelled is 381 miles
We are given that after stopping for gas they travelled 58 3/4 miles and then tripled their distance. The equation formed is
x + 3x + 58 3/4 = 381
4x + 58 3/4 = 381
x=68 1/4 in mixed fraction
To know more about improper fraction visit:
brainly.com/question/21449807
#SPJ2
(0, 2), (1,7) create a equation that passes through each pair of points
Answers
Answer:
y = 5x + 2
Step-by-step explanation:
Given the equation 5x + 2
Plug in 0
y = 5(0) + 2
y = 2
(0,2)
Given the equation 5x + 2
Plug in 1
y = 5(1) + 2
y = 7
(1,7)
Please Help Question in picture
Answers
Answer:
(-3, 5.5)
Step-by-step explanation:
To find the midpoint, you add up the corresponding coordinates (x with x and y with y) and divide each by 2.
(-7+1)/2 = -3
(8+3)/2 = 5.5
Answer:
(-3,5.5)
Step-by-step explanation:
(-7,8)
(1,3)
(-7+1)/2,(8+3)/2
-3,5.5
Which values for A and B will create infiniely many solutions for this system of equations
Answers
Answer :
4x-ay=15
Step-by-step explanation:
Asha bought 60 fruit baskets.
25% of the fruit baskets have 12 pieces of fruit in each basket.
The remaining 75% of the baskets have 15 pieces of fruits in each basket.
Answers
Answer:
Answer: 855
Step-by-step explanation:
I take it you want the total number of fruit? You should state the question. I will assume I am correct.
So 25% of 60 baskets = 25/100 * 60 = 15 baskets.
Each basic contains 12 pieces of fruits 12 * 15 = 180
And 75% of 60 baskets = 0.75 * 60 = 45 baskets.
Each contains 15 pieces 45 * 15 = 675
The total number of fruit in all is 855
PLS HELP MEE :((
Write an equation representing the area Felicia covered, y, in terms of the number of tiles she used, x.
y =
Answers
Answer:
Check the picture below
Step-by-step explanation:
last one… someone help please.
Answers
Answer:
32 degrees
a triangle is = to 180 degrees
Find the perimeter of both ( they have the same perimeter)
Answers
Answer:
x=2
Step-by-step explanation:
6x+3+2x+1+4x=12x+4
5x+5x+3x+2=13x+2
12x+4=13x+2
4-2=13x-12x
2=x
what the sum of 9999x23
Answers
Answer:
suma is 229,997
Step-by-step explanation:
229,997
Lola's Suds costs $3.48 for a 12 ounce bottle. Bill's
Bubbles cost $1.60 for a 12 ounce bottle. Which
bottle cost less per ounce?
Answers
Answer: Bill's $0.1333333 per oz
Step-by-step explanation:
URGENT WILL MARK BRAINLIEST 1. Suppose Q is the midpoint of PR. Use the information to find the
missing value.
PQ = 32 + 10 and QR = 2 + 14
Find PR.
A. 32
B. 16
C. 4
D. 2
Answers
Answer:
A.32
Step-by-step explanation:
-g + 2 (3 + g) = -4 (g + 1)
Answers
g+6=-4g-4
-6. -6
g=-4g-10
+g. +g
5g=-10
g=-2
(6, 10)
(a, 8)
(4,5)
(2, 2)
1. Find the slope of the line. Explain or show your reasoning
2. Write an equations for the line.
3. Find the values for a and b. Explain or show your reasoning
4. What is the y-coordinate when x = 0? Explain or show your reasoning.
Answers
2) y=2x-2
3) a=5, b=6 because using the slope(2) you can find these values
4) y coordinate when x = 0 is -2
Can someone plz help Me?
Answers
Answer:
A
[tex]^{}[/tex]
PLEASE PLEASE HELP!!! i’m struggglingggg
Answers
Not sure bout the first one tho
Can someone please help me with this? Tysm!! ^^
Answers
Answer:
90 feet
1080 inches
Step-by-step explanation:
I hope it helps you!
90 feet
How many inches is this?
1080 inches
2x+5=10-3x please help
Answers
Step by step
2x + 5 = 10 - 3x
Let’s start with 2x + 5 = 7 and you bring the x with you which is 7x
Now you do 7x = 10 - 3x , equal sign is plus am guessing and then 10 - 3x is 7x so
7x + 7x = 14x
Find a quadratic function that includes the set of values below.
(0,8), (2,16), (4,0)
The equation of the parabola is y =
Answers
Answer:
Let y=ax^2+bx+c be the equation of the parabola. Set up equations.
Using (0,5). 5=a(0)2+b(0)+c
5
=
a
(
0
)
2
+
b
(
0
)
+
c
Using (2,15), 15=a(2)2+b(2)+5
15
=
a
(
2
)
2
+
b
(
2
)
+
5
4a+2b=10
2a+b=5
Using (4,9)
9=a(4)2+b(4)+5
9
=
a
(
4
)
2
+
b
(
4
)
+
5
16a+4b=4
4a+b=1
Subtract each side of (1) and (2) to eliminate b and solve for a: -2a=4
a=-2
Solve for b using (1): 2(-2)+b=5
-4+b=5
b=9
So, the equation is y=−2x2+9x+5
Step-by-step explanation:
Please help Question in picture
Also could you please dm me on insta gram: yourdealerjeremi
I need some help with a few more questions but im out of brainly points
Answers
Answer:
10,9
Step-by-step explanation:
On the coordinate plane you see that the point A has to go 6 to the right and 3 up. So the ratio is: for every 2 side, there is one up. Point A does this 3 times to get to M so do three times. 6 to the right and 3 up and B is on 10,9.
it's all i the picture help!! i don't remember how to solve it
Answers
1.
Which expression is equivalent to 5(3x + 1)(x − 2)(x – 3)?
Answers
Answer:
15x^3-70x^2+65x+30
Step-by-step explanation:
1) 5(3x+1)= (15x+5)
2) (15x+5)(x-2)=15x^2-25x-10
3) (15x^2-25x-10)(x-3)=15x^3-70x^2+65x+30
Solve for x.
32-8
=
-6
Enter your answer in the box
X=
Answers
Answer:
X = -2
Step-by-step explanation:
3x - 8/2 = x - 6
3x - 8 = x - 6 × 2
3x - 8 = x - 12
3x - x = -12 + 8
2x = -4
X = -4/2
X = -2
Hopes that it will help u...✌
1. Multiply both sides of the equation by 2
3x - 8 = 2x - 12
2. Move the terms over and collect like terms
3x - 2x = -12 + 8
X = -12 + 8
X = -4
there are 64 female performers in a dance recital. the ratio of men to woman is 5:8 how many men are in the dance recital
Answers
Answer:
40
Step-by-step explanation:
64 female
ratio of men to women is 5:8
5x:8x
where 8x = 64
so x = 8
5(8):8(8)
40:64
So there are 40 men.
Can anyone solve and explain part b
Answers
Answer:
Below in bold.
Step-by-step explanation:
b.
If we drop a perpendicular line from B to AC and mark the point D on AC, we have 2 right triangles, with AD = DC = 16 cm.
So tan O = BD/16 = 15/8
BD = (16*15)/8
= 2*15
= 30.
So the area of triangle ABC = 16*30
= 480 cm^2.
Noah is making grilled cheese sandwiches for friends. He has 24 ounces of cheese. He plans to split the
cheese evenly between 6 sandwiches.
Write an equation to determine how many ounces of cheese, c, Noah can use on each sandwich
How many ounces of cheese can Noah use on each sandwich?
Answers
Answer:
4 ounces
Step-by-step explanation:
6c = 24
c = 4
Answer: Noah can use 4 ounces per sandwich
an equation is c=24/6
Step-by-step explanation:
The distance between two cities on a map is 6cm. If the scale one the map is 2 cm=50 miles, how many miles apart are the two cities
Answers
Work Shown:
2 cm : 50 miles
3*(2 cm) : 3*(50 miles)
6 cm : 150 miles
The length of a certain rectangular prism is 3 less than twice the width. The height of the same prism is 4 more than
the width. Write an expression to represent the volume of the rectangular prism in terms of width (w).
V=2w? + 5w-12
V= -2w3 + 11w2 + 12w
V=2w3 +5w? - 12w
В.
С.
D
V=4w + 1
Answers
Answer:
it is c
Step-by-step explanation:
me big brain