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
HELP!!! The probability that a male’s foot is between 10 and 12.5 inches is__
p(10
Answers
Answer:
I suggest you use Socratic, it solves questions like this.
Step-by-step explanation:
Simplify the following expression: -4(k - 7)
Answers
Answer:
-4k+28
Step-by-step explanation:
Answer:
-4k+28
Step-by-step explanation:
multiply -4k inside the parentheses
-4k x k
-4 x 7
= -4k+28
find slope please help
Answers
Answer:
slope = -5/2
Step-by-step explanation:
rise/run
down 5
right 2
I am so stressed can someone please help me
It’s 53 points
Answers
Answer:
(3,1)
Step-by-step explanation:
write a word problem for 8x - 5 = 40
Answers
Answer:
Bob only has 40 dollars but he wants to buy a membership at the gym. It cost 8 dollars per month to receive a gym card. Bob went to the Gym in person so they gave him a 5 dollar off coupon. How many months can Bob buy?
Step-by-step explanation:
Answer:
eight and a variable subtracted by five equals forty
Step-by-step explanation:
A boy weighs x pounds. His younger sister weighs 53 pounds less than him. His father weighs four times as much as his sister. A simplified expression that represents the fathers weight (in pounds) is (blank -blank)
Answers
Answer:
4x-53
Step-by-step explanation:
Boy=x
sis = x-53
father = 4x-53
What is the value of the expression when a = 4, b = 3 , and c = 10?
3a4b−c
a 1
b 4
c 6
d 12
Answers
Answer:
3a4b-c
3(4)4(3)-10
12(12)-10
144-10
=134
Step-by-step explanation:
Answer:
134
Step-by-step explanation:
3×4=12
4×3=12
12×12=144
144-10=134
thats what I got
hope it helps
The measurement of the complement of an angle is 40° more than the angle. What is the supplement for the angle?
Answers
if a dinosaur has a mass of 55g, what is his density
Answers
Answer:
32ounces I think
Step-by-step explanation:
Felicia has a stack of 10 cards. Each card is labeled with a number in the range 1 through 10 and no two cards have the same number. She picks three cards at random from the stack and adds the numbers on the three cards. What is the expected value of the sum
Answers
Answer:
The expected value of the sum of three numbers chosen out of 10 numbers will be 16.5.
Step-by-step explanation:
Felicia has a stack of 10 cards with number 1,2,3,4,5,6,7,8,9,10
Selecting 3 cards out of 10
10C3 = 120
Now she picks three cards to look at their numbers and sum it up
The possible three numbers are
(1 2 3), (1 3 2), (2 1 3) ,(2 3 1), (3 1 2), (3 2 1) ,(1 2 4), (1 4 2), (2 1 4), (2 4 1),
(4 1 2)│(4 2 1), (1 2 5), (1 5 2)│(2 1 5), (2 5 1) ,(5 1 2), (5 2 1), (1 2 6), (1 6 2), (2 1 6), (2 6 1), (6 1 2) ,(6 2 1) ,(1 2 7), (1 7 2) ,(2 1 7), (2 7 1), (7 1 2), (7 2 1), (1 2 8), (1 8 2), (2 1 8) ,(2 8 1), (8 1 2) ,(8 2 1), (1 2 9), (1 9 2), (2 1 9), (2 9 1), (9 1 2), (9 2 1),
(1 2... …, (6 10 8), (8 6 10), (8 10 6), (10 6 8), (10 8 6), (6 9 10), (6 10 9), (9 6 10),
(9 10 6), (10 6 9), (10 9 6), (7 8 9), (7 9 8), (8 7 9), (8 9 7), (9 7 8), (9 8 7), (7 8 10),
(7 10 8), (8 7 10), (8 10 7), (10 7 8), (10 8 7), (7 9 10), (7 10 9), (9 7 10), (9 10 7),
(10 7 9), (10 9 7) , (8 9 10), (8 10 9), (9 8 10), (9 10 8), (10 8 9), (10 9 8)
Now we sum it all up so minimum sum can be 1+2+3 = 6 andthe maximum can be 8+9+10 = 27
Let S denote the sum of the three numbers that are chosen and P(S=k) denotes its probability
P(S=6)=1/120
P(S=7)=1/120
P(S=8)=1/60
P(S=9)=1/40
P(S=10)=1/30
P(S=11)=1/24
P(S=12)=7/120
P(S=13)=1/15
P(S=14)=3/40
P(S=15)=1/12
P(S=16)=1/12
P(S=17)=1/12
P(S=18)=1/12
P(S=19)=3/40
P(S=20)=1/15
P(S=21)=7/120
P(S=22)=1/24
P(S=23)=1/30
P(S=24)=1/40
P(S=25)=1/60
P(S=26)=1/120
P(S=27)=1/120
Now adding all the sum in order to get the expected value
∑(K=6 to 27) k*P(S=k) = 33/2 = 16.5
Therefore the expected value of the sum is 16.5.
what is the slope of the line shown in graph
A. -2
B. -1
C. 1/-2
D. 1/2
Answers
Answer:
-1/2
Step-by-step explanation:
using rise over run its 1/-2 which is just -1/2
translate this sentence to an equation
38 is the product of Malik's score and 2. Use the variable m to represent Malik's score.
Answers
Answer:
Step-by-step explanation:
m * 2 = 38
Equation: 2m = 38
Solution:
2m = 38
m = 38/2
m = 19
Malik's score = 19
Answer:
Given :-38 is the product of Malik's score and 2. Use the variable m to represent Malik's score
To Find :-Marks scored by Malik
Solution :-The equation will be
[tex] \frak{2m = 38}[/tex]
Total marks
[tex] \tt \: m \: = \dfrac{38}{2} [/tex]
[tex] \tt \: m \: = 19[/tex]
The marks scored by Malik is 19
Which graph shows the solution to the inequality -2x+10>20
Answers
Answer:
+20 bc 2x10= 20 so +20>20
Solve the inequality
Answers
Answer:
x<2
Step-by-step explanation:
5x+10>14x-8
18>9x
2>x
Write an equation for the n th term of the arithmetic sequence 56, 48, 40, 32, ....
Answers
Answer:
-8n+64
Step-by-step explanation:
Pran ran 29 miles less than Robin last week. Pran ran 19 miles. How many
miles did Robin run?
Answers
Robin= 29+19
29+19= 48
Does anyone know the answer to this question
Answers
Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality using the formula K = y/x
Answers
Answer:
Option C is correct option.
Step-by-step explanation:
We need to find k constant of proportionality
In the graph below let us take the values of x and y
x=150 , y=50
x=300, y=100
x=450, y=150
Now finding k using the formula: [tex]k=\frac{y}{x}[/tex]
Putting values of x and y to find k
For x=150 , y=50 k = 50/150, k =1/3
For x=300, y=100 , k=100/300 , k=1/3
For x=450, y=150, k= 150/450 , k=1/3
Since for values of x and y, k = 1/3 is constant so, the graph shows two quantities that vary directly.
So, Option C is correct option.
3. If Ted is making monthly payments of $77 on a loan of $4,000 for 5 years;
approximately what percent interest is he paying?
$
Answers
hope this helps
The percent of interest is he paying is,
⇒ R = 4.62%
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
We have to given that;
Ted is making monthly payments of $77 on a loan of $4,000 for 5 years.
Hence, Yearly payments to pay is,
⇒ 12 × 77
⇒ $924
Hence, We get;
⇒ Interest = PRT/ 100
⇒ 924 = 4000 × R × 5 / 100
⇒ 92400 / 20,000 = R
⇒ R = 4.62%
Thus, The percent of interest is he paying is,
⇒ R = 4.62%
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ2
A bakery is making apple pies and carrot cakes. Each
apple pie nets $5 profit. For each carrot cake, they
make $10 profit. Each pie take 4 hours to prepare and
1.5 hours to bake. The carrot cakes take 0.5 hours to
prepare and 0.5 hours to bake. The maximum
preparation time is 20 hours. The maximum baking
time is 10 hours. How many pies and cakes should be
made to maximize profits?
Answers
Answer:
8 thats how many pies and cakes you can do
Step-by-step explanation:
you have 20 minutes and 10 and the most cakes you can get with left over is 8
The pies and cakes should be made to maximize profits is 8 pies.
What is profit?Profit is defined as the sum of revenue and income after all costs have been deducted by a business. A function with a business-oriented focus is called a profit function. The main goal of a business is to generate income through the sale of goods and services, minus the costs associated with producing those goods and services, in order to turn a profit.
Revenue minus costs equals profit.
Costs comprise both variable costs and fixed costs, whereas revenue is the total amount of positive cash flow that a business generates.
The maximum number of cakes you can get with leftovers in 20 minutes and 10 is 8.
Thus, the pies and cakes should be made to maximize profits is 8 pies.
To learn more about profit, refer to the link below:
https://brainly.com/question/15036999
#SPJ2
Laura can finish payroll in 3
hours. It takes Ben 5 hours
to do the same job. If they
work together, how long
should it take them?
hours
Answers
Answer:
1/2
Step-by-step explanation:
First we divide 3 and 5, which gives us 0.6, then we use the LA Hypothalamus formula which is x2, so then we substitute the x with 0.6, 0.6 multiplied by 2 is 1.2, so then we transform it to a fraction, your welcome
Answer:
15/8
Step-by-step explanation:
5. Past experience shows that the standard deviation of the distances traveled by consumers to patronize Chinese restaurants is 2 km. How large a sample is needed to estimate the population mean distance traveled to within 0.4 km
Answers
Answer:
96
Step-by-step explanation:
Given that :
Standard deviation (s) = 2km
Error in estimation is within 0.4 km ; Error (E) = 0.4 km
Using the relation :
Sample size = ((Zα/2 * s) /E)^2
Using α = 0.05
The Zcritical at 0.05 = Z0.025 = 1.96
Sample size = ((1.96 * 2) / 0.4)^2
Sample size = (3.92 / 0.4)^2
Sample size = 9.8²
Sample size = 96.04
Required sample size = 96
Rewrite in simpliest terms-
−0.2(3p−0.9)+0.4(−0.9p−5)
Answers
Answer:
-0.96p - 1.82
Step-by-step explanation:
What is 5/8 ÷ 3/4 I need to know this please hurry
Answers
Answer:
5/6
Step-by-step explanation:
i used a caculater
BRAINLIEST PLEASE
Find the slope between the following points (2,5) and (-3,-9)
Answers
Answer: 14/5
Step-by-step explanation: Use Algebra calculator on math papá.com
Answer:
[tex]m=\frac{14}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (2, 5)
Point (-3, -9)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute [SF]: [tex]m=\frac{-9-5}{-3-2}[/tex]Subtract: [tex]m=\frac{-14}{-5}[/tex]Simplify: [tex]m=\frac{14}{5}[/tex]Calculate the amount of simple interest earned
$1,000 at 4% for 4 years
Answers
Answer:
$160
Step-by-step explanation:
A = $1,160.00
I = A - P = $160.00
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year.
Solving our equation:
A = 1000(1 + (0.04 × 4)) = 1160
A = $1,160.00
The total amount accrued, principal plus interest, from simple interest on a principal of $1,000.00 at a rate of 4% per year for 4 years is $1,160.00.
Does this graph represent a function? Why or why not?
Answers
6. Slope =
Y-Intercept
Equation in slope-intercept form:
Answers
Y intercept = 1
Equation: 0.5x +1
