Answers
Answer:
option D
[tex]x^4 + 6x^3 + 33x^2 + 150x + 200 = (x+2)(x+4)(x^2 +25)[/tex]
Step-by-step explanation:
Since no factors are mentioned at all. We use trial and error method to find a root of the polynomial.
Step 1 :
For that we will consider the factors of 200 :
± 1 , ±2, ± 4, ±5, ±8, ±10, ±20, ±25, ±40, ±50, ±100, ±200
[tex]Let \ f(x) = x^4 + 6x^3 + 33x^2 + 150x +200\\\\[/tex]
f ( -1 ) = (-1)⁴ + 6 (-1)³ + 33(-1)² + 150(-1) + 200
= 1 - 6 + 33 - 150 + 200
= 78 ≠ 0
So - 1 is not a root.
f ( - 2) = ( -2)⁴ + 6( - 2 )³ + 33 (- 2) ² + 150 (- 2) + 200
= 16 - 48 + 132 - 300 + 200
= 0
Therefore - 2 is a root of f( x ) and ( x + 2) is a factor of f( x) .
Step 2
Now we will use synthetic division to find other factors.
-2 | 1 6 33 150 200
| 0 -2 -8 -50 -200
|_______________________________
1 4 25 100 0
[tex]f(x) = x^4 + 6x^3 + 33x^2 + 150x + 200 \\\\f(x) = ( x^3 + 4x^2 + 25x + 100)(x + 2)[/tex]
We will use trial and error method again to further factorize the equation
g(x) = x³ + 4x² + 25x +100.
Proceed as in step 1
Consider the factors of 100 to find the root.
Factors of 100 :±1, ±2, ±4 , ±5 , ±8, ±10 , ± 20, ±25, ± 50, ±100
g( - 4) = ( -4)³ + 4 ( -4)² + 25(-4) + 100
= - 64 + 64 - 100 + 100
= 0
Therefore - 4 is a root of g(x) , that means (x + 4) is a factor.
Now we will use synthetic division :
- 4 | 1 4 25 100
| 0 -4 0 -100
|_____________________
1 0 25 0
Therefore g(x) = ( x² + 0x + 25)(x + 4)
= ( x² + 25 )( x + 4)
Therefore the factorized form of
x⁴ + 6x³ + 33x² + 150x + 200 = (x + 2)(x³ + 4x² + 25x + 100)
= ( x + 2 )( x + 4 )( x² + 25)
Related Questions
what is an expression showing the sum of 5 less than the number k
Answers
Answer:
5<k
Step-by-step explanation:
Answer:
k-5
Step-by-step explanation:
So, lets go over each part of the sentence, and turn it into a expression.
So it first says sum. This means addition, so we can start our expression with:
+
Next is says of 5. So we know its the addition of 5:
+5
Next it says less than. So now we know less than, which is subtraction. So we can swap the addition sign for a - sign:
-5
Finally it says the number k. So we know that the subtracted value is k:
k-5
So this is your expression!
Hope this helps!
If x = 2 and t = 4, what is the value of 2(x3 – 4)(t2 + 8)
Answers
Answer:
64
Step-by-step explanation:
Just add in the numbers and put the expression into a calculator.
20 POINTS !!!!!!!
ireflections
for each point or figure, give the coordinates of its reflections over the given line. draw and label the reflection on the graph. the first one is done for you.
Answers
2.
Point A'(4, 3)
Point B'(9, 7)
Point C'(6, 7)
3.
Point D'(-8, -2)
4.
Point E'(2, -4)
5.
Point F'(8, 2)
Hope this helps! :)
If valorie made five times more baskets than her brother Vance
But if she made 70 baskets how many baskets did Vance make
Answers
Answer:
I say its 14 because it says times more" so u would divide 70 by 5 but im debating between 14 and 65
Step-by-step explanation:
(Please help this is due by Tuesday)
Answers
Answer:
A
Step-by-step explanation:
ded the colour of each car going past his house one morning.
e results are shown below.
blue red red silver silver silver silver silver blue silver blue blue black red
red silver silver red black red
complete the table for Jay's results.
Colour
Frequency
blue
red
silver
black
Tally
4 4
= b
till
= 8
2
nich colour of car did Jay record most often?
Answers
Answer:
The correct answer is -
1. An image with correct tally marks and frequency values is attached.
2. Silver
Step-by-step explanation:
The given data of different color cars that going past his house one morning is given in 20 times. The frequency of each car is -
Blue cars - 4 times out of 20
red - 6 times out of 20
silver - 8 times out of 20
black - 2 times out of 20
The complete table is attached as an image -
2. the maximum frequency of the car is the silver car so Jay must have recorded the silver car most often.
HELP ASAP
Write the equation in standard form for the circle x2 + 32 = -y² + 12x.
Answers
Step-by-step explanation:
Move
26
to the right side of the equation because it does not contain a variable.
3x2−12x−2y2+16y=26
Answer:
(x - 6)² + y² = 4
Step-by-step explanation:
x² + 32 = -y² + 12x
Rearrange
x² - 12x + y² = -32
Complete the square for x
(x - 6)² + y² = -32 + (-6)²
(x - 6)² + y² = -32 + 36
(x - 6)² + y² = 4
Match each power of a power expression with its simplified expression
Answers
= 4⁰×-⁹
= 4⁰
(-4⁹)²= -4⁹ײ
= -4¹⁸
=( -4)¹⁸
(4-³)-³= 4-³ × -³
= 4⁹
(4⁶)-³= 4⁶ × -³
= 4-¹⁸
= 1/4¹⁸
what is x+43434343434= 34344
Answers
Answer:
x=−43434309090
Step-by-step explanation:
HELP HURRY PLEASE! circumference of R
Answers
Answer:
To calculate the circumference, you need the radius of the circle: Multiply the radius by 2 to get the diameter. Multiply the result by π, or 3.14 for an estimation. That's it; you found the circumference of the circle.
Step-by-step explanation:
I am confused with this
Answers
Answer:
C ) 7
Step-by-step explanation:
Constant is value in equation that DOES NOT change. Varibales such as x and y will change. Coefficent are things that are written in front of variable.
HURRYYYYY HELLPP MEEE PLEASEEEEE
Answers
Answer:
8/17
Step-by-step explanation:
sin 28 degree = opposite / hypotenuse
= 8/17
Which ordered pair is a solution to the linear system?
2x + y = 5
x - y = 13
A) (6,-7)
B) (7,6)
C) (-6,-7)
D) (-7,-6)
Answers
Answer:
The Answer is option A) .( 6 , -7 )
Write the decimal as a fraction or mixed number in simplest form. .45454545
Answers
Answer:
45454545 as a fraction equals 454545450/10
Step-by-step explanation:
Answer: i think its 454
Step-by-step explanation:
A line with a slope of 0 passes through the points (–4,q) and (6,–10). What is the value of q?
Answers
Answer:
q = - 10
Step-by-step explanation:
A line with a slope of zero is a horizontal line parallel to the x- axis
The y- coordinates of the points the line passes through are equal
Given the line passes through (- 4, q) and (6, - 10 ) with y- coordinate - 10
Then q = - 10
While performing a piece of music, Tommy strikes the cymbals every 7 beats and the triangle is every 12 beats. If he just struck both at the same time, how many beats will pass before he again strikes them at the same time?
Answers
Answer:
84
Step-by-step explanation:
In interval questions we use LCM
LCM of 7, 12=84
Therefore, the number of beats will pass before he again strikes them at the same time is 84
Help please if you don’t mind!!
Thankyou so much
Answers
Answer:
Step-by-step explanation:
[tex]F = \frac{9}{5}C+32[/tex]
Subtract 32 from both sides
[tex]F-32= \frac{9}{5}C\\[/tex]
Multiply both side by 5/9
[tex]\frac{5}{9}(F-32)=( \frac{5}{9})* \frac{9}{5}C\\\\ \frac{5}{9}(F-32)=C\\[/tex]
F= 41
[tex]\frac{5(41-32)}{9}=C\\\\ \frac{5*9}{9}=C\\\\ \frac{45}{9}=C\\\\C = 5\\\\[/tex]
41° F = 5° C
What is the product of (b2 - 2b + 4) and (b - 2)?
Answers
B2=-1
These are the correct answer
16.83 rounded to 1 significant figure
Answers
Answer:
20
Step-by-step explanation:
1 being the first number you then approximate to 2 cause 16 is larger than 5
afterwards round the 6 down to 0
therefore the answer is 20
Find an equation of a line that is parallel to y = 5x - 21 and passes through the point (3, 7)
Answers
Answer:
y=5x-8 is the parallel line that passes through the point (3,7)
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula y-y₁=m(x-x₁) to find the parallel line to y=5x-21, which if done correctly you should end up with y=5x-8
hope this helps!
Pythagorus 17 is the long side and one of the short sides is 12 how do I figure out the other side
Answers
Answer:
x = [tex]\sqrt{145}[/tex]
Step-by-step explanation:
Use pythagorean theorem.
17^2 - 12^2 = x^2
145 = x^2
x = [tex]\sqrt{145}[/tex]
The straight line 3x + 4y = 24 cuts the y - axis at the point A and cuts the x - axis at the point B. What is the distance AB?
Answers
Step-by-step explanation:
the answer is in the above image
The distance between point A and point B is 10 units.
What is the distance between two points on a plane?The distance between two points on a coordinate plane (x, y) and (x, y) is
= √[(x₂ - x₁)² + (y₂ - y₁)²] units
The given straight line is 3x + 4y = 24.
This straight line will cut the x-axis at a point where y = 0.
Therefore, 3x + 4(0) = 24
⇒ 3x = 24
⇒ x = 8
Therefore, the coordinates of the point A is (8, 0).
Similarly, this straight line will cut the y-axis at a point where x = 0.
Therefore, 3(0) + 4y = 24
⇒ 4y = 24
⇒ y = 6
Therefore, the coordinates of the point B is (0, 6).
Therefore, the distance between point A and point B is
= √[(0 - 8)² + (6 - 0)²] units
= √(64 + 36) units
= √100 units
= 10 units (negative sign is avoided.)
Learn more about the distance between two points here: https://brainly.com/question/12538676
#SPJ3
If I put $80 into an account offering 2%
interest per year, how much interest would
I earn in five years?
Answers
Answer:
$88
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Simple Interest Rate Formula: A = P(1 + rt)
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify
P = 80
r = 2% = 0.02
t = 5
Step 2: Find Interest
Substitute in variables [Simple Interest Rate Formula]: A = 80(1 + 0.02 · 5)(Parenthesis) Multiply: A = 80(1 + 0.1)(Parenthesis) Add: A = 80(1.1)Multiply: A = 88(e+8)°
(3e-4°
Need help asap thx
Answers
Answer:
e=44°
Step-by-step explanation:
3e-4+e+8 = 180 degree (being linear pair)
4e+4=180
4e=180-4
4e=176
e=176/4
e=44 degree
what's bigger -3 or -4?
Answers
Answer:
-4
Step-by-step explanation: -4 is colder than -3 and bigger. Hope this helps!
Answer: negative three is greater than negative four
Step-by-step explanation: negative three is closer to zero
If n is an even number, find the next consecutive even number.
Answers
Answer:
n+2 is the next even number as n is an even number so adding 2 will make it an even number again.
Some students equally share 2 baskets of oranges. Each basket has 12 oranges. Write an algebraic expression to represent this situation. Then explain how you chose which variable and operations to use.
Answers
Answer:
y = 24 /x
The operations used were: Multiplication and Division
Step-by-step explanation:
Let the number of students who shared the basket = x
Amount of oranges = y
Some students equally share 2 baskets of oranges. Each basket has 12 oranges.
The total number of oranges in basket = 2 baskets × 12 oranges
= 24 oranges
Therefore, the algebraic expression to represent this situation is written as:
y = 24 /x
The operations used were: Multiplication and Division
Divide 63 into two parts such that one part is 2/7 of the other .
Answers
Answer:
49 and 14
Step-by-step explanation:
Answer:
14 and 49
Step-by-step explanation:
14+49= 63
[tex] = \frac{14}{49} \\ = \frac{2}{7} [/tex]
Based on histogram above what is the average number of hours worked by 20 salesperson in company G
Answers
Answer:
[tex]Average = 38[/tex]
Step-by-step explanation:
Given
The attached histogram
Required
The average work hours by 20 salespeople
First, we get the total hours worked as follows:
[tex]Hours = 3 * 30 + 5 * 34 + 9 * 40 + 2 * 45 + 1 * 50[/tex]
[tex]Hours = 760[/tex]
Divide by number of salespeople
[tex]Average = Hours/n[/tex]
[tex]Average = 760/20[/tex]
[tex]Average = 38[/tex]
Ivy bought 10 packs of cups for her holiday
party. A pack of MEDIUM cups costs $1.80
and a pack of LARGE cups costs $2.40. She
paid a total of $21.60. How many packs of
each size cup did she buy?
Answers
Step-by-step explanation:
1.80x + 2.40y = 21.60
1.80(4) + 2.40(6) = 21.60
7.2 + 14.4 = 21.60
21.60 = 21.60
