Answer:
-45 is the answer good luck
Answer:
-45 is your answer hope this helps
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
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
Example 5 Given m angle7=38^ and m angle10=102^ the measure of each missing angle
angle 1 - 78
angle 2- 102
angle 3- 78
angle 4- 102
angle 5- 38
angle 6- 142
angle 8- 142
angle 9- 78
angle 11- 78
angle 12- 102
angle 13- 38
angle 14- 142
angle 15- 38
angle 16- 142
Determine whether f(x) = 4x^2 – 16x + 6 has a maximum or a minimum value and find that value.
a
maximum; –10
b
minimum; –10
c
maximum; 2
d
minimum; 2
Answer:
minium:-2................
The function f(x) = 4x² – 16x + 6 has a minimum value is –10 when the value of x is 2. Then the correct option is B.
What is differentiation?
The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function is given below.
[tex]f(x) = 4x^2 -16x + 6[/tex]
Differentiate the function, then we have
[tex]\dfrac{d }{dx} f(x) =\dfrac{d}{dx}(4x^2 -16x + 6) \\\\ \dfrac{d }{dx} f(x) =8x - 16 \\[/tex]
The value of x will be
[tex]8x - 16 = 0\\x = 2[/tex]
Then again differentiate the function, if the value comes negative then maxima and if the value is positive then minima.
[tex]f''(x) = \dfrac{d }{dx} f'(x) \\\\f''(x)=8x - 16 \\\\f''(x) = 8\\\\ f''(x) > 0[/tex]
Then the function is minimum at 2.
More about the differentiation link is given below.
https://brainly.com/question/24062595
Properties to solve an equation
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
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)
Hansika paid $9.25 for 2.8 pounds of pretzels. About how much did she pay for a pound of pretzels? ( Round your answer to the nearest whole number )
$2.00
$3.00
$4.50
$5.00
Answer:
3.00
Step-by-step explanation:
Rounding down
Answer:
$3.00
Step-by-step explanation:
shaminapodiepooo
given the side lengths
of 10, 24,26, determine whether the triangle is acute, right, obtuse or not a triangle.
Answer:
Right angled triangle
Step-by-step explanation:
Longest side = hypotenuse = 26
26² = 676
24² + 10² = 576+ 100
= 676
= hypotenuse²
As Pythagorean rule is satisfied, this makes an right angled triangle
-4/5 x -7/6
Please help!
Answer:
0.93333333333
Step-by-step explanation:
-4/5 = 0.8
-7/6 = 1.16666666667
-1.16666666667 x -0.8 = 0.93333333333
I WILL MARK U BRAINLIEST ANSWERRRRRR PLS
Answer:
11000
Step-by-step explanation:
Keep the ratio and multiply. I will explain more later but you needed the answer
Answer:
The answers are correct so what do I do now?
Step-by-step explanation:
Please mark as brainliest
Which of the following best describes the slope of the line below ?
A) Undefined
B) Positive
C) Negative
D) Zero
Which best describes the expression b(4-n)?
Answer:
4b−bn
Step-by-step explanation:
Can i have brainliest pls?
Mathematics
12g - 16 =
Answer:
g= -4 is correct answer
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? *
what negative 8 in graphing
Answer:
The 8 is in the quadrant III and IIII
Step-by-step explanation:
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:
Which equations listed below contain like terms?
A. 2c-4x=13
B. 14p-3p=9
C. 12(13v-13)+3=14
D. 77-2x+ 15-3x=29
Answer:
B
Step-by-step explanation:
14p and 3p have the same variable
Please give me the correct answer.
Answer:
First ?: 4
Second ?: -6
Step-by-step explanation:
40-40=0, which leaves 4n left.
34-40=-6
The final answer would be n= 3/2.
Pls help due tomorrow just numbers 7 - 12
Answer:
Step-by-step explanation:
7). 5.75% = [tex]\frac{5.75}{100}[/tex] = [tex]\frac{575}{10000}[/tex] = [tex]\frac{23}{400}[/tex]
10). [tex]16\frac{2}{3}[/tex] % = [tex]\frac{50}{3}[/tex] % = [tex]\frac{50}{300}[/tex] = [tex]\frac{1}{6}[/tex]
12). [tex]79\frac{5}{6}[/tex] % = [tex]\frac{479}{6}[/tex] % = [tex]\frac{479}{600}[/tex]
Now is you turn. You can do it!
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
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
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
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:
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:
Urgent!! Find the length of B by using the Pythagorean Theorem
Answer:
Step-by-step explanation:
24^2 + b^2 = 40^2
576 + b^2 = 1600
b^2 = 1024
b = 32
32
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
a= 24 , b= b , c=40
In order to find b, you have to change the equation a bit. Your new equation will look like [tex] {c}^{2} - {a}^{2} = {b}^{2} [/tex]
here is the step by step now
[tex] {40}^{2} - {24}^{2} = {b}^{2} [/tex]
[tex] {1600} - {576} = {b}^{2} [/tex]
[tex] {1024} = {b}^{2} [/tex]
**now you need to take the square root of both sides and you get 32**
-3x + 7 y = -16
-9x + 5y = 16
Answer:
x = -4y = -4Step-by-step explanation:
-3x + 7y = -16 (-3) to eliminate x
-9x + 5y = 16
9x - 21y = 48
-16y = 64
y = 64/-16
y = -4
substitute y= -4 into eq. 1
-3x + 7y = -16
-3x + 7(-4) = -16
-3x = -16 + 28
x = 12 / -3
x = -4
check:
-3(-4) + 7(-4) = -16
- 16 = -16 ok
-9x + 5y = 16
-9(-4) + 5(-4) = 16
16 = 16 ok
Answer:
x=44/3, y=4
Step-by-step explanation:
Assuming you have to solve for x and y
-3x+ 7y = -16 (1)
-9x+ 5y =16 (2)
multiply (1) by -3 and add it to (2)
9x-21y=48
-9x+5y=16
Add up and get
-21y+5y=48+16 combine like terms
16y=64 divide both sides by 16 and get
y=4
Substitute y=4 in (1)
-3*x+7*4=-16
28+16=3x
44=3x
x=44/3
Solve the system of equations.
14r + 5y = 31
2r - 3y = -29
When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The equation of the least-squares regression line is Area = 0.010 + 3.141 (Time^2) . What is the predicted area, in cm2, of the circle 8 seconds after the stone was dropped?
A. 25.14cm^2
B. 50.27 cm^2
C. 64.01 cm^2
D. 201.03 cm^2
Answer: D.
Step-by-step explanation: calculator
Answer:
d) 201.03
Step-by-step explanation:
An artist sculpted a scale model of a giraffe for the zoo gift shop. The artist used the scale 1 inch: 4 feet to create the scale model giraffe. The actual giraffe at the zoo is 20 feet tall.
How tall is the scale model giraffe in inches?
Enter your answer in the box.
inches
Answer:
The scale model giraffe is 5 inches tall.
Step-by-step explanation:
To determine the size of the giraffe sculpted by the artist, knowing that it has been built on a scale of 1 inch for every 4 feet, and knowing that the real giraffe in the zoo is 20 feet, the following calculation must be performed:
20 feet / 4 inches = X
5 = X
Therefore, the size of the giraffe sculpted to scale by the artist is 5 inches.