Answer:-46
Step-by-step explanation: just took test
The remainder when f(x) is divided by (x - 3) is 8 and this can be determined by using the factorization method.
Given :
[tex]\rm f(x) = x^4-5x^2-6x-10[/tex]
The following steps can be used in order to determine the remainder if f(x) is divided by (x - 3):
Step 1 - Write the mathematical expression of the statement "f(x) is divided by (x - 3)".
[tex]=\dfrac{x^4-5x^2-6x-10}{x-3}[/tex]
Step 2 - Now, try to factorize the numerator in the above expression.
[tex]=\dfrac{x^4-3x^3+3x^3-9x^2+4x^2-12x+6x-18+18-10}{x-3}[/tex]
Step 3 - Further simplify the above expression.
[tex]=\dfrac{x^3(x-3)+3x^2(x-3)+4x(x-3)+6(x-3)+8}{x-3}[/tex]
[tex]=(x^3+3x^2+4x+6) +\dfrac{8}{x-3}[/tex]
So, the remainder when f(x) is divided by (x - 3) is 8.
For more information, refer to the link given below:
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What is the slope and y-intercept from the table?
a
m = 1/4, b = 0
b
m = -1/4, b = 5
c
m = -4, b = 5
d
m = 4, b = 0
What is the monthly payment for a $11,000 loan for 7 years with an annual interest rate of 2.5%?
Answer:
i d k
Step-by-step explanation:
look it up
The sum of two numbers is __________ greater than either number.
a) Always
b) Sometimes
c) Never
d) Not enough information
The correct answer is b) Sometimes.
Given that a statement,
"The sum of two numbers is __________ greater than either number."
We need to fill the blank from the options provided.
The sum of two numbers can be greater than either number depending on the specific values of the numbers.
Let's consider some examples:
Example 1: If we have two positive numbers, such as 3 and 4, their sum (3 + 4 = 7) is greater than either number individually.
Example 2: If we have one positive number and one negative number, such as 5 and -8, their sum (5 + (-8) = -3) is greater than -8 but less than 5.
Example 3: However, if we have two negative numbers, such as -2 and -4, their sum (-2 + (-4) = -6) is not greater than either number individually.
Therefore, since the statement holds true in some cases but not in others, the correct answer is sometimes (b).
Learn more about Sum click;
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Using the triangle in the diagram, what would be the coordinate of A' if reflected over the line x=2 ? *
(0, 3)
(0, -3)
(4, -3)
(-4, 3)
Which of these represents slope-intercept form of a linear equation?Immersive Reader
(1 Point)
y - y1 = m(x-x1)
Ax + By = C
y=kx
y = mx + b
Find all the zeros and multiplicities. Provide explanation. r(x)=x^2(x+5)(x-7)^3
Answer:
what do you mean by find all the zeros and multiplicities, you have me confused on that part, if you explain that part a little more then I might be able to help you out a little bit M8
can someone help please ?
Answer:
5 is the hight
Step-by-step explanation:
To harmandeep or someone else please help me
Answer: 3x+6=9
3x=3
x=1
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
To solve this, we must first isolate the variable 'x':
3x + 6 = 9
-6 -6
3x = 9 - 6
Combine like terms
3x = 3
Isolate 'x' fully
3x = 3
/3 /3
x = 1
Hope this helps :)
Rich weighed 320 pounds on June 1st. He lost 3 pounds per week by following a meal plan provided by a doctor for w Weeks write a function for R, Rich's weight.
5)
D
-10 + 7x
70°
E
12x + 10
А с
A) 12
C) 8
B) 10
D) 2
Answer:
B) 10
Step-by-step explanation:
Exterior angle property: Exterior angle equals the sum of opposite interior angles.
12x + 10 = -10 + 7x + 70 {Subtract 10 from both sides}
12x = -10 + 7x + 70 - 10
12x = -10 + 70 - 10 + 7x {Combine like terms}
12x = 50 + 7x {Subtract 7x from both sides}
12x - 7x = 50
5x = 50 {Divide both sides by 5}
x = 50/5
x = 10
Use the distributive property to write an expression equivalent to 3x+21. *
Answer:
3(x+7)
Step-by-step explanation:
Maria's job pays her $1500 a month what is her gross weekly wage
Answer:
annual: $18000
weekly: $346.15
Find the slope (-2,1)and (1,2.5)
Answer:
.5
Step-by-step explanation:
slope = rise/run= 1.5/ 3= 0.5
hope that helps if it does please mark as brainliest.
0.6h=13.02 show work
Answer:
21.7
Step-by-step explanation:
0.6h=13.02
h=13.02/0.6
h=21.7
Answer:
21.7
Step-by-step explanation:
0.6h=13.02
h=13.02/0.6
h=21.7
Sandeep used 8 litres of fuel to travel 76 miles.
He wants to know how many miles he will be able to travel with 22 litres of fuel.
He assumes that the distance travelled and the amount of fuel used are directly proportional.
How many miles can he drive with 22 litres of fuel?
Answer:
I got, when calculated, 209 miles. (It may be wrong)
Step-by-step explanation:
First, I calculated how many miles can Sandeep travel with 1L, therefore I divided 76 miles by 8L and got 9.5 miles on 1L.
Then I multiplied 9.2 miles by 22L and got 209 miles.
This may be wrong but if anyone else is able to work it out much appreciated if it's correct.. Your most welcome!
Find the positive value of x that makes the following equation true?
x^2 − 1 4 = 5x + 67 − 5x
Answer:
x=9
Step-by-step explanation:
x^2 = 5x + 81 -5x.
x^2 = 81
x=9
A color printer prints 13 pages in 8 minutes How many pages does it print per minute
Answer: 13/8 or 1.625
Step-by-step explanation:
Find the side of an equilateral triangle if its area is 25√3 cm2
Answer:
10
Step-by-step explanation:
area=√3/4×a^2
100√3 = √3×a^2
a^2 = 100
a=10
side = 10
if alpha and beta are the zeros of the quadratic polynomial f(x)=2x^2+11x+25. Find alpha^4+beta^4 and 1/alpha+1/beta-2alpha*beta
Step-by-step explanation:
[tex]2 {x}^{2} + 11x + 5 \\ {x}^{2} + 5.5x + 12.5 \\ = -2.75-2.222i \\ \: \: \: - 2.75 + 2.22i \\ \alpha = - 2.75 - 2.22i \\ \beta = - 2.75 + 2.22i[/tex]
[tex] { \alpha }^{4} + { \beta }^{4} = -284.2912344[/tex]
[tex]\frac{1}{ \beta } + \frac{1}{ \alpha } + 2 \alpha \beta = 24.9818[/tex]
Mount Mo is 5323 feet tall dawn climbed it in five days she climbed 821 feet on the last day how many feet did she climb in the first four days
Answer:
Step-by-step explanation:
d+821=5323
d=4502
So the distance she climbed in the first four days was 4502 feet.
Learning Task 3
Solve the word problems
1. The sides of the quadrilateral are consecutive numbers.
how long is each side?
2. Inzo is 10 years older than Migz. Five years ago Mig
Inzo. What are their present ages?
3. An express train travels 100 kph from station A to
travelling at 45 kph, takes 45 minutes longer for the
is station A from station B.
4. The sum of two consecutive even integers is less tha
Find at least 3 pairs of numbers
5. The perimeter of the square is less than 152 m. Find
sides of the square.
Answer:
1. The sides are: 38.5, 39.5, 40.5 and 41.5
2. Presently, Inzo is 15 years old and Miz is 10 years old
3. [tex]Distance = 3682km[/tex]
4. Possible pairs are: (12, 14), (16, 18) and (20, 24)
5. [tex]L < 38m[/tex]
Step-by-step explanation:
The question has lots of missing details. See the comment section for complete question
Solving (a):
Given
Shape: Quadrilateral
Sides: Consecutive
[tex]Perimeter = 160[/tex]
Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.
So, the perimeter is:
[tex]Perimeter = x + x + 1 + x + 2 + x + 3[/tex]
This gives:
[tex]160 = x + x + 1 + x + 2 + x + 3[/tex]
Collect Like Terms
[tex]160 -1-2-3= x+x+x+x[/tex]
[tex]154= 4x[/tex]
Divide both sides by 4
[tex]38.5 = x[/tex]
[tex]x =38.5[/tex]
So, the sides are: 38.5, 39.5, 40.5 and 41.5
Solving (b):
Given
Presently: [tex]Inzo = 10 + Miz[/tex]
Five years ago: [tex]Miz - 5= \frac{1}{3} * (Inzo-5)[/tex] --- (Missing from the question)
Required: Determine their present ages
Substitute [tex]10 + Miz[/tex] for Inzo in the second equation
[tex]Miz - 5 = \frac{1}{3} * (10 + Miz - 5)[/tex]
[tex]Miz - 5 = \frac{1}{3} * (Miz + 5)[/tex]
Multiply both sides by 3
[tex]3Miz - 15 = Miz + 5[/tex]
Collect Like Terms
[tex]3Miz -Miz = 15 + 5[/tex]
[tex]2Miz= 20[/tex]
Divide both sides by 2
[tex]Miz = 10[/tex]
Substitute 10 for Miz in [tex]Inzo = 10 + Miz[/tex]
[tex]Inzo = 10 + 5[/tex]
[tex]Inzo = 15[/tex]
So presently, Inzo is 15 years old and Miz is 10 years old
Solving (3):
Given
Express Train:
[tex]Speed = 100kph[/tex]
[tex]Time = t[/tex]
Local Train:
[tex]Speed = 45kph[/tex]
[tex]Time = t + 45[/tex]
Required: Determine the distance between A and B
Distance is calculated as:
[tex]Distance = Speed * Time[/tex]
For the express train:
[tex]Distance = 100 * t[/tex]
For the local train
[tex]Distance = 45 * (45 + t)[/tex]
Distance between both stations are equal; So,
[tex]100 * t = 45 * (45 + t)[/tex]
[tex]100 t = 2025 + 45t[/tex]
Collect Like Terms
[tex]100 t -45t= 2025[/tex]
[tex]55t= 2025[/tex]
Divide by 55
[tex]t = 36.82[/tex]
Substitute 36.82 for t in [tex]Distance = 100 * t[/tex]
[tex]Distance = 100 * 36.82[/tex]
[tex]Distance = 3682km[/tex]
Solving (4):
Let the even numbers be: n and n + 2.
Sum greater than 24: [tex]n + n + 2 > 24[/tex]
Sum less than 60: [tex]n + n + 2 < 60[/tex]
So, we have:
[tex]n + n + 2 > 24[/tex]
[tex]2n + 2 > 24[/tex]
Collect Like Terms
[tex]2n > 24-2[/tex]
[tex]2n > 22[/tex]
[tex]n > 11[/tex]
[tex]n + n + 2 < 60[/tex]
[tex]2n + 2< 60[/tex]
Collect Like Terms
[tex]2n < 60-2[/tex]
[tex]2n < 58[/tex]
Divide by 2
[tex]n<29[/tex]
So, we have:
[tex]n > 11[/tex] and [tex]n < 29[/tex]
So, possible pairs are: (12, 14), (16, 18) and (20, 24)
Solving (5):
Given
[tex]Perimeter < 152m[/tex]
Required: Find the possible lengths
Let the length be L.
Perimeter is calculated as:
[tex]Perimeter =4 * L[/tex]
[tex]Perimeter =4 L[/tex]
So, we have:
[tex]4L < 152m[/tex]
Divide through by 4
[tex]L < 38m[/tex]
Hence, length is less than 38m (e.g. 37m)
please and thank you
Answer: 6 units
Step-by-step explanation:
Since this is just a reflection, the length of A'C' shouldn't be different from the length of AC.
A value is decreased by 85% for a new value of 17.1. Find the original value.
Answer:
114
Step-by-step explanation:
let 'n' = original value
(17.1 - n) / n = -85/100
cross-multiply:
1710 - 100n = -85n
1710 = 15n
n = 1710/15
n = 114
Daniel jarred 12 liters of jam after 4 days. How much jam did Daniel jar if he spent 7 days
making jam? Assume the relationship is directly proportional.
liters
Step-by-step explanation:
He jarred 21 in 7 days because there is 3 liters per day
25 points
Solve for x, y, and z.
Answer:
Step-by-step explanation:
x=57
y=57
z=66
What is the height of a triangle that has a base of 8 in. and an area of [tex]28in^{2}[/tex]
Answer:
height is 7 inches
Step-by-step explanation:
a=1/2bh
28=1/2(8)h
28=4h
/4
7=h
check your work
8x7= 56
56/2=28
Help me pls pls pls pls
Answer:
sorry but all i got from this is the first one should be -3
Step-by-step explanation:
sorry that i couldn't answer all :)
A fence is being built around a rectangular garden that is 8 1/2 feet by 6 1/3 feet. Fencing comes in panels. Each panel is 2/3 of a foot wide. how many panels are needed?
Answer:
The quadratic equations and their solutions are;
9 ± √33 /4 = 2x² - 9x + 6.
4 ± √6 /2 = 2x² - 8x + 5.
9 ± √89 /4 = 2x² - 9x - 1.
4 ± √22 /2 = 2x² - 8x - 3.
Explanation:
Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.
We have to solve all of the five equations to be able to match the equations with their solutions.
2x² - 8x + 5, here a = 2, b = -8, c = 5. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4. 24 can also be written as 4 × 6 and √4 = 2. So x = 8 ± 2√6 / 2×2= 4±√6/2.
2x² - 10x + 3, here a = 2, b = -10, c = 3. x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.
2x² - 8x - 3, here a = 2, b = -8, c = -3. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4. 88 can also be written as 4 × 22 and √4 = 2. So x = 8 ± 2√22 / 2×2 = 4± √22/2.
2x² - 9x - 1, here a = 2, b = -9, c = -1. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4. x = 9 ± √89 / 4.
2x² - 9x + 6, here a = 2, b = -9, c = 6. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4. x = 9 ± √33 / 4 .
Choose Yes or No to tell whether each value of p is a solution for this inequality.
10p – 8 ≥ 12
Answer:
2 is what is it
Step-by-step explanation:
CAN SOMEONE PLEASE CHECK MY ANSWER!!
Answer:
Yesss, that's correct!
Step-by-step explanation:
Good luck!!!!
