Answer:
6 + x / 3 = 4
Step-by-step explanation:
sorry if this is wrong, i believe this is how it needed to be written!
If the expression ax^4 + bx^3 – x² + 2x + 3 has a remainder
3x+5
when it is divided x^2-x-2 find the values a and b
There's probably a more efficient way to do it, but the following method works.
First, note that
x² - x - 2 = (x + 1) (x - 2)
Now use synthetic division to divide
a x⁴ + b x³ - x² + 2x + 3
by the two factors above.
Division by x + 1 :
-1 | a b -1 2 3
… | -a a - b -a + b + 1 a - b - 3
= = = = = = = = = = = = = = = = = = = = = = = = = = = = =
… | a b - a a - b - 1 -a + b + 3 a - b
which is to say,
(a x⁴ + b x³ - x² + 2x + 3) / (x + 1)
= a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3) + (a - b) / (x + 1)
Division by x - 2 :
2 | a b - a a - b - 1 -a + b + 3
… | 2a 2a + 2b 6a + 2b - 2
= = = = = = = = = = = = = = = = = = = = = = = = = = =
… | a a + b 3a + b - 1 5a + 3b + 1
meaning,
(a x³ + (b - a) x² + (a - b - 1) x + (-a + b + 3)) / (x - 2)
= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2)
Putting everything together, we have
(a x⁴ + b x³ - x² + 2x + 3) / (x² - x - 2)
= a x² + (a + b) x + (3a + b - 1) + (5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)
Combine the remainder terms:
(5a + 3b + 1) / (x - 2) + (a - b) / (x² - x - 2)
= ((5a + 3b + 1) x + (6a + 2b + 1)) / (x² - x - 2)
We're given that the remainder is 3x + 5, so
5a + 3b + 1 = 3
6a + 2b + 1 = 5
Solve this system for a and b :
5a + 3b = 2
6a + 2b = 4
5a + 3b = 2
3a + b = 2
5a + 3b = 2
-9a - 3b = -6
(5a + 3b) + (-9a - 3b) = 2 + (-6)
-4a = -4
a = 1
5 • 1 + 3b = 2
3b = -3
b = -1
Match the terms to their definition.
1. speed
a rate with a denominator of 1; a rate that shows an amount of something compared to 1 of something else
2. rate
an average rate comparing distance to time
3. unit rate
a type of ratio that compares two different kinds of quantities or numbers
4. complex fraction
a fraction with fractions in both the numerator and denominator
Answer:
2 goes to a type of ratio that compares two different kinds of quantities or numbers
Step-by-step explanation:
a type of ratio that compares two different kinds of quantities or numbers
In a 6th grade class there are 30 students. Out of these students, 3/5 achieved AL in Math and 2/6 achieved ML. Assuming that no student failed, find the number of students that achieved CL.
Answer: 2
Step-by-step explanation:
3/5 of 30 = 18(AL)
2/6 of 30 = 10 (ML)
18+10 = 28 (AL+ ML)
the remainder
30-28 = 2 (CL)
On January 1, 2012, Instaform Company issued 10% bonds with a principal amount of $ 50 million, dated January 1. The bonds mature in 2031 (20 years). The market yield for bonds of similar risk and maturity is 12% Interest is paid semiannually.
Required:
1. Determine the price of the bonds at January 1, 2012, and prepare the journal entry to record their issuance by Instaform.
2. Assume the market rate was 9%. Determine the price of the bonds at January 1, 2012, and prepare the journal entry to record their issuance by Instaform.
3. Assume Broadcourt Electronics purchased the entire issue in a private placement the bonds. Using the data in requirement 2. prepare the journal entry to record their purchase by broadcourt
Answer:
Step-by-step explanation:
There are 80 tickets in a bag and the ratio of winning tickets to losing tickets is 2:8. How many of each kind of ticket are in the bag?
Answer:
There are 16 winning tickets and 64 losing tickets
Step-by-step explanation:
Total no of tickets in a bag = 80
The ratio of winning tickets to losing tickets is 2:8.
Let there are 2x winning tickets and 8x losing tickets.
ATQ,
2x+8x=80
10x=80
x = 8
Winning tickets = 2x = 2(8) = 16
Losing tickets = 8x = 8(8) = 64
Hence, there are 16 winning tickets and 64 losing tickets.
An individual chooses a prime number that is less than 13. What is the probability that the number is odd? Write your answer as an exact fraction which is reduced as much as possible.
Answer:
4/5
Step-by-step explanation:
Okay, I'm pretty sure about this one! I might be wrong but:
If the number is prime and LESS than 13 (so it can't be 13 either), it's either 2, 3, 5, 7, or 11. Those are 5 numbers in all, and 4 of those are odd. So the fraction would be 4/5!
I might have done this wrong, but I hope it helps!! Have a nice day c:
Which show a way to factor the expression 32t-48? Select all that apply.
A 2(16t-24)
B 4(12t-48)
C 6(26t-42)
D 8(4t-6)
E 16(2t-3)
Simplify the following expression:
-13^2=?
Answer: -13 x -13 = 169
Step-by-step explanation: you have to multiply -13 two times and a negative time a negative equals a positive
Help please this sucks lol
Answer:
x = -4
Step-by-step explanation:
Equation of the Line
It can be written in the slope-intercept form as:
y = mx + b
Where m is the slope of the line and b is the y-intercept.
For horizontal lines, m=0. For slanted lines, m can have any real value.
Vertical lines have an infinite slope and the above equation cannot be used.
Vertical lines have a fixed value for x, thus the equation is:
x = h
If the vertical line goes through the point (-4,1), then its equation is:
x = -4
14 black balls and 6 white balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball?a) 0.3333
b) 0.2381
c) 0.0952
d) 0.2143
e) 0.3111
Answer:
[tex]Probability = 0.30[/tex]
Step-by-step explanation:
Given
Represent Black with B and White with W
[tex]B = 14[/tex]
[tex]W = 6[/tex]
Required
Probability of the second selection being white
This means that: The first selection could be white or black but the second must be white.
This probability would be represented as thus:
[tex]Probability = (P(W)\ and\ P(W))\ or\ (P(B)\ and\ P(W))[/tex]
And it is calculated as:
[tex]Probability = (\frac{n(W)}{Total} * \frac{n(W)-1}{Total - 1}) + (\frac{n(B)}{Total} * \frac{n(W)}{Total - 1})[/tex]
Notice that, the second selection has total -1 has its denominator. This is so because, the first selection was made without replacement
So, the formula becomes
[tex]Probability = (\frac{6}{20} * \frac{6-1}{20- 1}) + (\frac{14}{20} * \frac{6}{20- 1})[/tex]
[tex]Probability = (\frac{6}{20} * \frac{5}{19}) + (\frac{14}{20} * \frac{6}{19})[/tex]
[tex]Probability = \frac{30}{380}+ \frac{84}{380}[/tex]
[tex]Probability = \frac{30 + 84}{380}[/tex]
[tex]Probability = \frac{114}{380}[/tex]
[tex]Probability = 0.30[/tex]
The probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is 0.33.
Given :
14 black balls and 6 white balls are placed in an urn. Two balls are then drawn in succession.The formula given below can be used in order to determine the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.
[tex]\rm P = \left(\dfrac{n(W)}{Total}\times \dfrac{n(W)-1}{Total-1}\right)+ \left(\dfrac{n(B)}{Total}\times \dfrac{n(W)}{Total-1}\right)[/tex]
Now, substitute the values of known terms in the above formula.
[tex]\rm P = \left(\dfrac{6}{20}\times \dfrac{6-1}{20-1}\right)+ \left(\dfrac{14}{20}\times \dfrac{6}{20-1}\right)[/tex]
Simplify the above expression.
[tex]\rm P = \dfrac{30}{380}+\dfrac{84}{380}[/tex]
[tex]\rm P =\dfrac{114}{380}[/tex]
P = 0.33
So, the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball is 0.33.
Therefore, the correct option is a).
For more information, refer to the link given below:
https://brainly.com/question/23044118
What is 6x3-69+12x4-7x(9x3)+7-1?
Answer:
44
Step-by-step explanation:
6 times 3 is 18 so.. 18 minus 69 would be -36 plus 12 is a positive 1 times 14 would be 14 minus 7 would be 7 7 times 27 would 38 plus 7 would be 45 minus one would be 44
Answer:
-186
Step-by-step explanation:
6x3-69+12x4-7(27)+7-1
18-69+48-189+7-1
-51+48-189+7-1
-3-189+7-1
-192+7-1
-185-1
-186
Which values from the set make this inequality true?
4n<16 ; {1, 2, 3, 4}
Select each correct answer.
1
2
3
4
Answer:
4
Step-by-step explanation:
The answer would be D
Answer:
1,2,3
Step-by-step explanation:
you cant let them be equal its an inequality
its due in 1 hour please i need help i give brainliest 2/9 x 3/10 *
This is a required question
There are 10 students in a class. 1/2 of the class are playing a game. How many of the students are playing the game? *
6/10 ÷ 1/2 *
3/5
8/10 ÷ 4/5 *
This is a required question
0.56 + 1.452
Aliyah has 19.8 feet of rope. She uses a 13.5 foot piece to hang a plant. How much rope does she have left?
0.9 ÷ 0.3
What does 4 cubed look like written out?
What does 12 to the fourth power look like written out? *
first to help me with this gets the brainliest
Answer: -26 i think srry if im wrong
Step-by-step explanation:
A package of 24 pencils costs $3.60. What is the cost per pencil?
Answer:
6.66666666667
Step-by-step explanation:
Answer: 6.66
Step-by-step explanation: because you have to divide 24/3.6
2. Solve the following pair of simultaneous equations
0.6x - 4y=-1
1
0.8x -3.5y =0.5
2
Answer:
After solving the pair of simultaneous equations we get x=5 and y=1. Solution Set = {5,1}
Step-by-step explanation:
We need to solve the pair of simultaneous equations
[tex]0.6x-4y=-1\\0.8x-3.5y=0.5[/tex]
We can solve using substitution method.
Let:
[tex]0.6x-4y=-1--eq(1)\\0.8x-3.5y=0.5--eq(2)[/tex]
Find value of x from eq(1) and put it in eq(2)
[tex]From \ eq(1):\\0.6x-4y=-1\\0.6x=-1+4y\\x=\frac{-1+4y}{0.6}[/tex]
Putting in equation 2
[tex]0.8x -3.5y =0.5\\0.8(\frac{-1+4y}{0.6})-3.5y=0.5\\1.33(-1+4y)-3.5y=0.5\\-1.33+5.32y-3.5y=0.5\\-1.33+1.82y=0.5\\1.82y=0.5+1.33\\1.82y=1.83\\y=\frac{1.83}{1.82}\\y=1.00[/tex]
So, we get value of y= 1.00
Now finding value of x by putting value of y in eq(1)
[tex]x=\frac{-1+4y}{0.6}\\x= \frac{-1+4(1.00)}{0.6}\\x=\frac{3}{0.6}\\x=5[/tex]
We get value of x = 5
So, After solving the pair of simultaneous equations we get x=5 and y=1. Solution Set = {5,1}
Mathematics
12g - 16 =
Answer:
g= -4 is correct answer
8 pencils and one eraser cost $1.35 and 6 pencils and one eraser cost $1.05. How much does one pencil cost?
Answer:
one pencil cost $0.15
Step-by-step explanation:
2x−3, find h(6)h(6).
Answer:
90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you
Step-by-step explanation:
Answer:
654
Step-by-step explanation:
Which values of k are solutions to the inequality?
k>12
Select each correct answer.
k = 11.9
k = 12.1
k = 13.0
k = 19.9
k = 10.2
Answer:
B: k = 12.1
C: k = 13.0
D: k = 19.9 ARE THE CORRECT ANSWERS
Step-by-step explanation:
Answer:B: k = 12.1
Step-by-step explanation:
Solve the system of equations.
14r + 5y = 31
2r - 3y = -29
1. Three times a number added to four
times a number, subtract five.
Answer:
45
Step-by-step explanation:
Answer:
3x 4x and -5 so
3x+4x-5 is the answer
What is 2.27 kg in pounds
Answer:
5.004493
Step-by-step explanation:
Answer:
2.27 kg is about 5 pounds.
Step-by-step explanation:
1 kilogram = 2.2 pounds
So, we have to multiply 2.2 by the amount of kilograms, which in this case, is 2.27.
2.27 x 2.2 = 4.994 or 5 when rounded to the nearest whole number.
Therefore, 2.27 kg = 5 lbs
Hope this helps! :)
Help! - 20 POINTS!!!
Thanks!
Answer:
b
Step-by-step explanation:
Evaluate the expression
if a = 3, b = 4, c = 12
(2c + ab)
с
Answer:
Answer- 432
Step-by-step explanation:
a= 3
b=4
c=12
(2(12) + (3)(4))12
(24 + 12)12
288 +144 = 432
You are looking for your first credit card. You plan to use this credit card only for emergencies and to pay the credit card balance in full each month. Which credit card feature is most important?
a.
No annual fee
b.
Low APR
c.
Generous rewards program
d.
No balance transfer fee
Please select the best answer from the choices provided
A
B
C
D
Answer:
A No Annual Fee
Step-by-step explanation:
Edge 100%
Pappi
Each sentence shows the number of pages a student reads a book and the amount of time it takes to read those pages.
Answer:
65 mins
Step-by-step explanation:
I well help anyone because I’m a hero and I well always be one thanks to all of you
CAN SOMEONE TRANSLATE THIS INTO NUMBERS PLZ ITS DUE IN 10 minutes
Twice a number plus nine is negative seventeen.
Answer:
2x+9=-17
Step-by-step explanation:
hopefully this helps :)
Answer: I’m not sure what the number is but it’s a negative number, probably somewhere around 26. Take 9 from it and you will get 17.
Step-by-step explanation:
A department store sells a pair of shoes with an 87% markup. If the store sells the shoes for 193.21 what is the non-markup price
Answer:
$222.08
Step-by-step explanation:
To find the original price, divide 193.21 by 0.87:
193.21/0.87
= 222.08
So, the non-markup price was $222.08
What is the greatest common factor of 72 and 34?
Answer:
2 is GCF
Step-by-step explanation:
The greatest common factor of 72 and 34 is 2
What is greatest common factor ?
GCF means Greatest Common Factor.
By one examples we can understand this concept more easily.
We are taking four numbers 20,50,70,100.
By prime factorisation,
[tex]20 = 2 \times 2 \times 5 \\ 50 = 2 \times 5 \times 5 \\ 70 = 2 \times 5 \times 7 \\ 100 = 2 \times 2 \times 5 \times 5[/tex]
Here greatest common factor of 20,50,70 and 100 is [tex](2 \times 5) = 10[/tex]
So,GCF of 20,50,70 and 100 is 10.
Here numbers are 72 and 34
By prime factorisation,
[tex]72 = 2 \times 2 \times 2 \times 3 \times 3 \\ 34 = 2 \times 17[/tex]
So, greatest common factor of 72 and 34 is 2
So,GCF of 72 and 34 is 2
Greatest common factor related one more question:
https://brainly.com/question/11444998
#SPJ2