I WILL GIVE BRAINLIEST IF YOU CAN ANSWER THESE TWO QUESTIONS!!!!
2. Darwin believes that x + b is a factor of (x + b)3 + (x + c)2 – (b - c), while Eunju
believes it is not. Who is correct? Justify your response.
3. How can you prove that x2 + 5x + 6 is a factor of x* + 5x3 + 2x2 – 20x – 24, without
using long or synthetic division?
Answers
Answer:
2. Eunju is right
3. [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].
Step-by-step explanation:
Polynomial Remainder Theorem
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).
As a consequence, if a polynomial is divisible by x-a, f(a)=0.
Part 1:
Let's make:
[tex]f(x)=(x+b)^3+(x+c)^2-(b-c)[/tex]
To find out if x+b is a factor of f(x), we find f(-b):
[tex]f(-b)=(-b+b)^3+(-b+c)^2-(b-c)[/tex]
Operating:
[tex]f(-b)=(-b+c)^2-(b-c)[/tex]
The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).
Part 2:
We must find out if [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex] without using long division or synthetic division.
We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:
[tex]x^2+5x+6 =(x+2)(x+3)[/tex]
Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.
Let's make:
[tex]f(x)=x^4+5x^3+2x^2-20x-24[/tex]
Find f(-2):
[tex]f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24[/tex]
[tex]f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0[/tex]
Find f(-3):
[tex]f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24[/tex]
[tex]f(-3)=81-5*27+2*9+60-24[/tex]
[tex]f(-3)=81-135+18+60-24 =0[/tex]
Since both f(-2) and f(-3) are zero, [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].
Related Questions
PLEASEEEE HELPP !
A company sells bottles of vitamin capsules. The graph and table show the linear relationship between the cost per capsule in cents and the number of bottles ordered. What is the slope of the line that models this situation?
Answers
Answer:
[tex] slope (m) = -5 [/tex]
Step-by-step explanation:
The slope can be calculated using two points, (2, 60) and (4, 50) as shown below:
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex], where,
[tex] (2, 60) = (x_1, y_1) [/tex]
[tex] (4, 50) = (x_2, y_2) [/tex]
Plug in the values into the equation
[tex] slope (m) = \frac{50 - 60}{4 - 2} [/tex]
[tex] slope (m) = \frac{-10}{2} [/tex]
[tex] slope (m) = -5 [/tex]
Answer:
x=6
Step-by-step explanation:
You earn 90% on a quiz. If you earned 36 points, how many points was the quiz worth?
Answers
Reasoning: 36/40=0.9
Answer:
36/90%=40
Step-by-step explanation:
40 points in total
Point k lies at (-3,4). Point k is reflected over the y-axis and then translated 7
units down to produce K'. Which rule could have been used to produce K' from K?
K(x, y) +K'(x,y-7)
K(x,y) →K'(-x, y-7)
K(x,y) →K'(x, -y-7)
K(x,y) → K'(-x-7.-y-7)
Answers
Answer:
b
Step-by-step explanation:
Answer:B
Step-by-step explanation:
Tina is taking picture of her friends. if she sets a tripod level on the ground, will the bottom of each of the legs of tripod be coplanar
Answers
Answer:
Yes
Step-by-step explanation:
what is Evaluate 2. to the 2 power
Answers
Answer:
2^2 = 4
Step-by-step explanation:
2*2 = 4
The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers?
Just take the $ out
Answers
You're given
x + y + z = 165
7x = n
n = y - 9
n = 9 + z
and you want to find xyz.
Solve the last three equations for x, y, and z :
7x = n → x = n/7
n = y - 9 → y = n + 9
n = 9 + z → z = n - 9
Substitute x, y, and z into the first equation and solve for n :
n/7 + (n + 9) + (n - 9) = 165
n/7 + 2n = 165
n + 14n = 1155
15n = 1155
n = 77
Now solve for x, y, and z :
x = 77/7 = 11
y = 77 + 9 = 86
z = 77 - 9 = 68
Then the product is
xyz = 11 • 86 • 68 = 64,328
The product of the three numbers is 8,192,040. The sum of three numbers x, y, z is 165: x + y + z = 165
The problem states:
1. When the smallest number x is multiplied by 7, the result is n: 7x = n
2. The value n is obtained by subtracting 9 from the largest number y: n = y - 9
3. The value n is also obtained by adding 9 to the third number z: n = z + 9
Now, let's proceed to find the values of x, y, z, and n:
From equation (2), we can express x in terms of n:
x = n/7
Now, substitute the value of x in equation (1):
(n/7) + y + z = 165
From equation (3), we can express y in terms of n:
y = n + 9
Now, substitute the value of y in the equation above:
(n/7) + (n + 9) + z = 165
From equation (4), we can express z in terms of n:
z = n - 9
Now, substitute the value of z in the equation above:
(n/7) + (n + 9) + (n - 9) = 165
Combine the terms with n:
3n/7 = 165
To isolate n, multiply both sides by 7/3:
n = 165 * (7/3)
n = 385
Now, we have the value of n, which is 385. To find the values of x, y, and z, substitute n back into the respective equations:
x = n/7 = 385/7
≈ 55
y = n + 9 = 385 + 9
= 394
z = n - 9 = 385 - 9
= 376
Now, we have the values of x, y, z, and n:
x = 55,
y = 394,
z = 376,
n = 385
To find the product of the three numbers, simply multiply them:
Product = x * y * z
= 55 * 394 * 376
≈ 8,192,040
So, the product of the three numbers is 8,192,040.
To know more about three numbers:
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Solve the equation
(- 5 + 7)5x+ 4=16
The solutions are:
Answers
Answer:
x=2
Step-by-step explanation:
Answer:
x=1.2
Step-by-step explanation:
Please help. I will brainliest!!
Answers
Answer:
12. 20 ft
13. 4.5
Step-by-step explanation:
12. (29x29)-(21x21)=400
sq root 400= 20
13. (2x2)+(4x4)= 20
sq root 20= 4.5
What is the first step to solving the division problem below?
Divide 15 into 82 to get 5.
Divide 15 into 82 to get 6.
Multiply 15 by 5 to get 75.
Multiply 15 by 6 to get 80.
Answers
Answer:
divide 15 into 82 to get 5 is the first step
Step-by-step explanation:
Answer:
The answer is A, ¨Divide 15 into 82 to get 5.¨
Step-by-step explanation:
Please make as brainliest! Thanks and i hope it is right!!! Pls say if wrong. Bye
Which of the following ratios is not equivalent to the rest: *
6 to 8
54 : 72
36 : 56
3 to 4
Answers
Answer:
36:56
Step-by-step explanation:
Answer: C 34:55
Step-by-step explanation:
start with 6:8 that’s the first one multiply by 9 on each side you get 54:72 so that’s the same and then 6:8 divide by 2 and you get 3:4 but for 36:56 you’d have to multiply by 6 and that would give you 36:48 not 36:56
What is the area of a rectangle with a length of 1/3 yards and width of 3/4 yard?
Answers
Answer:
1/4 yards squared
Step-by-step explanation:
Area of a rectangle equals length times width.
1/3 x 3/4 = 3/12, or 1/4
Answer:
It would be 1/4 and if not try 3/12
Step-by-step explanation:
I hope this helped
solve x 3+3(x+2)=-24
Answers
Answer:
x=-11
Step-by-step explanation:
3+3x=6=-24
3x+9=-24
3x=-33
x=-11
Answer:
x = -11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
3 + 3(x + 2) = -24
Step 2: Solve for x
Distribute 3: 3 + 3x + 6 = -24Combine like terms: 3x + 9 = -24Isolate x term: 3x = -33Isolate x: x = -11Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 3 + 3(-11 + 2) = -24Add: 3 + 3(-9) = -24Multiply: 3 - 27 = -24Subtract: -24 = -24Here we see that -24 does indeed equal -24.
∴ x = -11 is the solution to the equation.
find m
right anwser gets brainliest
Answers
Answer:
The measure of <FDE is 18°
A typical tip in a restaurant is 15% of the total bill. If the bill is $160, what would the typical tip be?
Answers
Answer:
24$
Step-by-step explanation:
15%=0.15
160*0.15=24
Which solution would make this equation have infinitely many solutions?
A.-18
B.-9
C.9
D.18
Answers
Answer: -18
Step-by-step explanation:
Abbey receives a $40 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $2.89 a. Let m represents the number of songs downloaded. Write an inequality that represents this given situation? b. What is the maximum number of songs Abbey can download?
Answers
Answer:
A. $2.89(m)=$40
B. 13 songs
Step-by-step explanation:
$2.89(m)=$40
m=$40/$2.89
m=13.84
She can download a maximum of 13 songs
Check:
$2.89 (13 songs)=$37.57
$40-$37.57=$2.43 left on her gift card
m=13.84, check that 0.84 of the cost of a song is left over 0.84*$2.89=$2.43
Answer:
13 songs
Step-by-step explanation:
40 divided by 2.89 is 13.84. DO NOT ROUND TO 14
So its a maximum of 13 songs, otherwise it will cost 40.46 for 14 songs
Please help me in struggling!!!!!!!!!!!!!
Answers
Answer:
Here’s the answer
Step-by-step explanation:
Henry is using a total of 16 ft. of lumber to make a bookcase. The left and right sides of the bookcase are each
4 ft. high. The top, bottom, and two shelves are all the same length, labeled S. How long is each shelf?
Answers
Answer: Each shelf is 2ft
Step-by-step explanation:
16 = (2 x 4) + 4s
16 = 8 + 4s
8 = 4s (subtract 8 from both sides)
8/4 = 4s/4 (divide both sides by 4)
2 = s
Bob wants to make a profit of $1.25 on each fish. How much should he sell each fish for to make this profit? Show your calculation.
note that each fish costs 2.14
Answers
Bob would have to sell each fish at $3.39 in order to make a profit of $1.25 on each fish sold
What is the selling price per fish?
The selling price per fish can be determined as the sum of the cost price of $2.14 and the profit per fish which is $1.25, in essence, the selling price in this case is the sum of the cost and profit or alternatively, we can model the profit as the selling price minus the cost price as shown below:
profit per fish=selling price-cost price
profit per fish=$1.25
selling price=unknown
cost price=$2.14
By making the selling price the subject of the formula, we can determine the selling price using the formula above
$1.25=selling price-$2.14
selling price=$2.14+$1.25
selling price=$3.39
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d=1/2at^2+s, solve for a
Answers
Step-by-step explanation:
Perhaps the equation is d=1/2at2 and you are given the distance (40 m) and acceleration (9.8 m/s2) and asked to find the time. or convert the equation in terms of t and then plug in the numbers to solve.
how much change did she receive?
Answers
Which polynomial is in standard form?
N
O 26x5 + 12x7-8x3 + 6x
O 3x5 +x-6x2 + 5
11x5-6x2-9x+12
5x2 + 18x3 - 12x4 +4x7
Answers
Answer:
i am pretty sure it is D
Step-by-step explanation:
Answer:
Its C.) 11x^5 - 6x^2 - 9x + 12
Step-by-step explanation:
ejenuwitee
=D
=P
Can anyone help me out solving this?
Answers
Answer: 25
Step-by-step explanation: When you divide exponents with the same base, you can subtract the exponents. It becomes 5^4-2, which is 5^2, which is 25
Angela is planting flowers in her flowerbed. She wants the ratio of tulips to roses to be 5 to 2. If a total of 63 flowers are planted, how many tulips should there be?
Answers
Answer:
45 Tulips
Step-by-step explanation:
63/7=9
Tulips: Roses=5:2
Tulips=9x5=45
Roses=9x2=18
1. The temperature was very cold. Then the temperature doubled. Then the temperature dropped by 10 degrees. Then the temperature increased by 40 degrees. The temperature is now 16 degrees. What was the starting temperature?
Answers
Answer:
10,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Steve's bedroom measures 12 feet by 13 feet. Ricardo's bedroom measures 8 feet by 14
feet. Assuming that both bedrooms are rectangular, whose room has the greater area?
Answers
Answer: Steve's bedroom has the greater area.
Step-by-step explanation: The formula for area is Area = Length x Width.
So all you have to do to figure this out is multiply the Width of the rooms by the length.
So Steve's room is 12ft X 13ft = 156ft
Ricardo's room is 8ft X 14ft = 112ft
156ft > 112ft
Steve's room has a greater area.
How many blueberries on the on cake roof
Answers
Answer:
say what
Step-by-step explanation:
Find the slope of the line graphed below.
Answers
Answer:
-3/5
Step-by-step explanation:
So first, you have to find out the two points :
(-1,-1), and (4,-4)
Next, you have to put into this formula:
y1-y2/x1-x2
The y values in our points are -4 and -1, and our x values are 4 and -1. Lets now substitute:
-4-(-1)/4-(-1)
Now simplify: -4+1/4+1, and solve and you will get -3/5 as the slope
If you liked it, please give me a good rating and please mark me as the brainliest... Thanks!
Hope you do well on your assignment!
Please help i was crying :(
Also there is another one
“Subtract. Write Your answer in simplest form” which is: 6 3/4 - 2 3/20
Answers
Answer:
is it 4 3/5 it might be
Step-by-step explanation:
Can you help me with this question please
Answers
Answer:
34
Step-by-step explanation:
Answer:
34 just subtract
Step-by-step explanation: