1) Divide using synthetic division, and write a summary statement in fraction form.
two x to the fifth minus x to the fourth plus three x squared minus x plus five divided by quantity x minus one
a. 2x4 + x3 + 4x2 + 3x + eight divided by quantity x minus one
b. 2x4 + x3 - x2 + 2x + 1 + six divided by quantity x minus one
c. 2x4 + x3 + x2 + 4x + 3 + eight divided by quantity x minus one
d. 2x4 - 3x3 + x + six divided by quantity x minus one
2) Divide f(x) by d(x), and write a summary statement in the form indicated.
f(x) = x4 - 4x3 + 2x2 - 4x + 1; d(x) = x2 + 1
a. f(x) = (x2 + 1)( x2 + 4x + 1)
b. f(x) = (x2 + 1)( x2 - 4x + 1) + 12x + 3
c. f(x) = (x2 + 1)( x2 + 4x + 1) + 12x + 3
d. f(x) = (x2 + 1)( x2 - 4x + 1)
3) Find the remainder when f(x) is divided by (x - k).
f(x) = 3x3 - 4x2 - 3x + 14; k= 3
a. 50
b. 68
c. -12
d. 112
4) Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f.
k = -1; f(x) = 4x3 - 2x2 + 2x + 4; Lower bound?
a. yes
b. no
5) Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.
f(x) = -2x4 + 4x3 + 3x2 + 18
Answers
Refer to the first picture below
The synthetic division works by writing the coefficient only of the polynomials in question in order of the degree of the polynomials.
Our polynomial expression is given: 2x⁵ - x⁴ + 3x² - x + 5
The coefficient in order are 2, -1, 3, 0, -1, 5
The value '0' in the list is for the polynomial x²
Then divide these coefficients by 1 ⇒ you get this value by x - 1 = 0, x = 1
The rest of the step is explained in the picture.
We have an answer [tex]2x^+x^3+x^2+4x+3+ \frac{8}{x+1} [/tex] ⇒ The last term in fraction form is the remainder
Answer: Option C
----------------------------------------------------------------------------------------------------------------
Question 2
We can use the usual way of Algebraic division as shown in picture 2 below
We have no remainder, so the answer to the question is given in the form of factors ⇒ (x² + 1)(x² - 4x + 1)
Answer: Option D
-----------------------------------------------------------------------------------------------------------------
Question 3
We are given the remainder to be k = 3 when we divide f(x) by (x - k)
So, f(3) = 3(3)³ - 4(3)² - 3(3) + 14 = 50
Answer: Option A
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Question 4
k is upper bound when f(x) is divided by (x - k) where k > 0 using the synthetic division and the answer gives all positive numbers
k is lower bound when f(x) is divided by (x - k) where k < 0 using the synthetic division and the answer gives an alternating sign
Refer to picture 3 below, the values of the answer have alternating signs (+) then (-) then (+) then (-) again. This means k = -1 is a lower bound
Answer: YES
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Question 5
Focus on the coefficient of the leading term which is -2x⁴ and the last term, 18.
Factors of -2 is 1, -1, 2, -2 ⇒ Let's call this group as 'p'
Factors of 18 is 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18 ⇒ This is group 'q'
Possible values for p ÷ q are
1, -1, 0.5, -0.5, 2, -2, 1.5, -1.5, 6, -6, 3, -3, 9, -9, 4.5, -4.5, 18, -18 ⇒ These are the list for possible roots.
Related Questions
which function represents a vertical stretch of an exponential function
Answers
Sequence 13, 39, 65, 91,
Answers
hmmm, add 26? yep
the sequence is
[tex]a_n=a_{n-1}+26[/tex] when [tex]a_1=13[/tex]
or
[tex]a_n=13+26(n-1)[/tex] or [tex]a_n=26n-13[/tex]
Which statements describe acceleration? Check all that apply.
Negative acceleration occurs when an object slows down in the positive direction.
Negative acceleration occurs when an object slows down in the negative direction.
Negative acceleration occurs when an object speeds up in the negative direction.
Positive acceleration occurs when an object speeds up in the positive direction.
Positive acceleration occurs when an object speeds up in the negative direction.
Positive acceleration occurs when an object slows down in the negative direction.
Answers
Acceleration determines whether an object speeds up or slows down, which can be positive or negative based on the direction of motion and the chosen coordinate system. Negative acceleration occurs when an object slows down while moving in the positive direction or speeds up while moving in the negative direction. Positive acceleration occurs when an object speeds up in the positive direction or slows down in the negative direction.
Explanation:Acceleration is the rate of change in velocity, and it can be characterized as positive or negative depending on its direction relative to a chosen coordinate system. Understanding acceleration involves recognizing how it affects an object's speed in relation to its direction of motion. Let's clarify which statements describe acceleration correctly.
Negative acceleration occurs when an object speeds up in the negative direction or when an object slows down in the positive direction.Positive acceleration occurs when an object speeds up in the positive direction.It is important to distinguish between speeding up, slowing down, and the sign of acceleration. For example, if we assume rightward motion is positive:
An object moving to the right (positive direction) and slowing down has negative acceleration.An object moving to the left (negative direction) and speeding up also has negative acceleration.Contrarily, an object moving to the left and slowing down has positive acceleration.Summarizing these principles:
Negative acceleration occurs when an object slows down in the positive direction.Negative acceleration occurs when an object speeds up in the negative direction.Positive acceleration occurs when an object speeds up in the positive direction.Additionally, positive acceleration occurs when an object slows down in the negative direction.This understanding can help distinguish between deceleration, which always indicates slowing down, and negative acceleration, which may increase speed if the velocity is also negative.
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If you need how many days between two dates what function should be used
Answers
Your next problem is to work out the day number from the beginning of the year. On average there are between 30.4 and 30.5 days in a month, but this is only an approximation because the length of each month varies. So to aid in the calculation you need a table which gives you the day number for every date in the year, and the table is different for leap years.
So, you start by subtracting the years and counting how many leap years there are between. You consult the day number table for working out how many days there are from the beginning of the year.
Another way is to have a smaller table with just the months, so in a non-leap year Jan 1 would be 1, Feb 1 would be 32, Mar 1 would be 60, Apr 1 would be 91, and so on. Then we have to add in the day date. Mar 20 would be 19 days after Mar 1 so would have a day number of 79, not 80. Some diaries and calendars include the day number.
You can speed up the calculation by using one day number table or calculation and then adding in a day for each leap year between two dates. I hope this helps.
To calculate the number of days between two dates, subtract the start date from the end date and add 1.
Explanation:To find the number of days between two dates, you can use the formula:
Number of days = (End date) - (Start date) + 1
For example, if the start date is July 10, 2022, and the end date is July 15, 2022, the number of days between them would be:
Number of days = (15) - (10) + 1 = 6
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The length of a rectangle is 24 units. can the perimeter x of the rectangle be 60 units when its width y is 11 units? (1 point)
Answers
Okay, well we start out with the equation P=66, where P is perimeter. You should create equations using variables to explain each piece of information you are given. Follow the equations below and see if you can understand how to do another one like this. In this problem, l is length and w is width.
P = 66 The perimeter is equal to 66
l = 3 + w The length of one side is 3 more than the width
2l + 2w = 66 A rectangle's perimeter is calculated by adding the lengths and widths
2(3 + w) + 2w = 66 Use what you know about length from step 2 to replace the variable in step 3
6 + 2w + 2w = 66 Multiply
6 + 4w = 66 Add like terms
4w = 60 Subtract
w = 15 Divide
l = 3 + w Remember step 2?
l = 3 + 15 Replace the variable using your value for w
l = 18 Add
And you're done! Always check your work. It helps to create a picture of a rectangle while you're doing these problems as well. As you get used to these problems more and more, you can show more or less work than I've shown, but try to stay true to what the teacher asks of you. Good luck!
Perimeter (x) = 24 + 24 + 11 + 11 = 70.
There is no chance that the perimeter of the given rectangle will be 60. SO yeah thats the Answer
Given the following inverse variation find the missing value: (4, 33) (12, y)
PLEASE ANSWER AS SOON AS POSSIBLE!!!!!! THANKS I APPRECIATE YOU AND YOU'RE VALID
Answers
The function f(x)= -6x+11 has a range given by {-37,-25,-13,-1}.Select the domain values of the function from the list 1,2,3,4,5,6,7,8. explain how you arrived at your answer
Answers
function, ( f(x)=-6x+11 ), equals these numbers that are in the range {-37,-25,-13,-1}.
So you apply each of these numbers (1,2,3,4,5,6,7,8) into the function (f(x)=-6x+11)
one by one.
f(1)=-6(1)+11=5
f(2)=-6(2)+11= -1
f(3)=-6(3)+11= -7
f(4)=-6(4)+11= -13
f(5)=-6(5)+11= -19
f(6)=-6(6)+11= -25
f(7)=-6(7)+11= -31
f(8)=-6(8)+11= -37
As you can see, f(2),f(4),f(6),and f(8) equal the numbers that are in the range {-37,-25,-13,-1}.
The domain of the given function f(x)= -6x+11 for the given range is
{2,4,6,8}
Given :
The function f(x)= -6x+11
range given by {-37,-25,-13,-1)
Range is the f(x) values . Domain are the x values .
To find out domain , we substitute the values of f(x) that is range and solve for x
First we substitute -37 for f(x) in the given function and solve for x
[tex]f(x)= -6x+11 \\x=-37\\-37=-6x+11\\-37-11=-6x\\-48=-6x\\x=8[/tex]
Now substitute -25 for f(x)
[tex]x=-25\\-25=-6x+11\\-25-11=-6x\\-36=-6x\\x=6\\\\\\x=-13\\-13=-6x+11\\-13-11=-6x\\-24=-6x\\x=4\\\\\\x=-1\\-1=-6x+11\\-1-11=-6x\\-12=-6x\\x=2[/tex]
x values are the domain
Domain is {2,4,6,8}
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The price of grapes at the grocery store is $1.44 per pound. There are approximately 0.45 kilograms in a pound. To the nearest cent, what is the price of grapes in dollars per kilogram?
Answers
1 lb / 0.45 = 2.22
so approximately 2.22 kilograms per pound
divide price per pound by kilometers per pound
1.44 / 2.22 = 0.648
round to 0.65, so it costs $0.65 per kilogram
Answer:
1 lb / 0.45 = 2.22
so approximately 2.22 kilograms per pound
divide price per pound by kilometers per pound
1.44 / 2.22 = 0.648
round to 0.65, so it costs $0.65 per kilogram
Step-by-step explanation:
got it right on the quiz
The length of a rectangle is three times its width. if the area of the rectangle is 243 in2 , find its perimeter.
Answers
John and 3 friends are going out for pizza for lunch. They split one pizza and 4 large drinks. The pizza cost $13.00. After using a $6.00 gift certificate, they spend a total of $13.20. Write an equation to model this situation, and find the cost of one large drink. a. 3d + $13.00 – $6.00 = $13.20; $2.07 b. 4d + $13.00 – $6.00 = $13.20; $1.55 c. 4d – $13.00 + $6.00 = $13.20; $6.73 d. 4d + $13.00 – $6.00 = $13.20; $1.60
Answers
4d +13.00 -6.00 = 13.20
4d = 7.00 = 13.20
4d = 6.20
d - 6.20/4 =1.55
answer is B
Deshawn multiplies 236 by 9. Which are the three partial products he could add to find the final product?
Answers
6 × 38 in parts,
writing the
numbers under
each other.3 8
× 6
4 8 First multiply
6 × 8.3 8
× 6
4 8
1 8 0
Then multiply 6 × 30 and
write the result under the 48.
Remember, the "3" is in the
tens place in the number 38
so it actually means 30.3 8
× 6
4 8
+ 1 8 0
2 2 8Lastly, add.
My question is 8n-(6n+7)=5
Answers
2n - 7 = 5
2n = 5 + 7
2n = 12
N = 6
2n -7 (+7) = 5 (+7)
2n/2 = 12/2
n = 6
Why are black people always watched so closely at a liquor store?
Answers
A lot of people assume that because of the forced situations blacks have been in the past, that they're all bad people. Which is not always true. Although black people can still steal(like any other capable human being), so can white people. And hispanics, and middle easterns. But based on the history of America, specifically, black people have been the most common to shoplift or vandalize. But that was in the past, anyone today can easily steal a bottle of beer or a pack of gum from any store just like everyone else. I think the issue is that most priveledged people haven't let go of the past. Or at least what the media filtered as the past.
Hope this helps. :)
Solve 2a − 5d = 30 for d
Answers
-5d = -2a + 30....divide both sides by -5
d = (-2a + 30) / -5 or d = 2/5a - 6
The Opera House sells an average of 1,700 tickets per night when the price of each ticket is $25. An employee of the Opera House noticed that with every one-dollar decrease in the cost of each ticket, the number of tickets sold increased by 200 tickets. Write an equation that could be used to determine the number of one-dollar decreases, x, that would yield a revenue of $55,000.
Answers
To determine the number of one-dollar decreases that would yield a revenue of $55,000, set up the equation (1,700 + 200y) * (25 - x) = 55,000 and solve for x.
Explanation:To determine the number of one-dollar decreases, x, that would yield a revenue of $55,000, we can set up an equation based on the given information.
Let y be the number of one-dollar decreases and (1,700 + 200y) be the number of tickets sold. The revenue can be calculated by multiplying the number of tickets sold by the price of each ticket. So in this case, the equation can be written as:
(1,700 + 200y) * (25 - x) = 55,000
Now we can solve this equation to find the value of x.
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A census is taken every 10 years to determine to determine the apportionment of
Answers
The US Constitution requires that there be a census every ten years in order to apportion the seats in the House of Representatives among the states. Census information is also used by federal, state, and local governments to assess needs and allocate funding, by academics to study the changing population, by individuals to trace their genealogy, and for many other purposes.
In the diagram below, ∠Q is bisected.
Find the perimeter of ΔPQS.
Answers
QP/QR = SP/SR
To be able to calculate the perimeter we need to know SP, which can be extracted from the formula QP/QR = SP/SR
QP/QR = SP/SR → 36/15 =SP/11 ; SP = (11x36)/15 = 26.4
And the perimeter is : 36+15+ (11+26.4) = 77.4 units
What is f(–3) if f(x) = |2x – 1| – 5?
Answers
f(-3) = |2x - 1| - 5
f(-3) = |-6 - 1| -5
f(-3) = |-7| - 5
f(-3) = 7 - 5 Absolute value of -7 = 7
f(-3) = 2
f(-3) = |2(-3) – 1| – 5
f(-3) = |-6 - 1| - 5
f(-3) = |-7| - 5
f(-3) = 7 -5
f(-3) = 2
A subway ride for a student costs $1.25. A monthly pass costs $35.Write an inequality that represents the number of times, x , you must ride the subway for the monthly pass to be a better deal.
Answers
From 29 Trips you have a better deal.
Answer:
1.25x>35
Step-by-step explanation:
If x is the number of times you must ride the subway and the monthly pass is $35, we must determine the expression where the cost per ride is greater than $35. Therefore:
1.25x>35
We can solve x to determine the number of rides you must ride for the monthly pass to be a better deal.
x>35/1.25
x>28
The student must take more than 28 rides for the mothly pass to be a better deal.
TDC, Inc's . net profits were $-2000 each month last year . What was TDC's net profits for the year ?
Answers
The TDC's net profits for the year were -$24,000 if TDC, Inc's. net profits were $-2000 each month last year option (A) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
TDC, Inc.'s net profits were $-2000 each month last year.
Let x be the net profit for the year
As we know there are 12 months in 1 year.
So the net profit:
x = $-2000×12
x = -$24,000
Thus, the TDC's net profits for the year were -$24,000 if TDC, Inc. net profits were $-2000 each month last year option (A) is correct.
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Emily designed a robot that could climb down steps. She drew a graph to show the results from a test of her new robot. The graph shows the number of steps remaining over time.
Which equation represents Emily’s situation, where x is the number of seconds and y is the number of steps?
Answers
y intercept= 15
y= -1/10x + 15
The equation that describes Emily's robot's movement is y = -mx + c where 'm' is the number of steps per second the robot climbs down, and 'c' is the initial number of steps. The equation would be negative because the number of steps decreases over time.
Explanation:In the given context, Emily's robot is being tested for its ability to climb down steps. As it performs this task, the number of steps it needs to climb down decreases over time. This relationship could be described by a linear equation. If every second the robot climbs down a fixed number of steps, this would translate to a constant rate of change or slope in the graph. Therefore, the equation would be of the form y = mx + c, where 'm' is the slope (representing the number of steps per second the robot climbs down) and 'c' is the y-intercept (representing the initial number of steps).
For instance, if the robot climbs down 1 step per second, and we started with 10 steps, the equation would be y = -x + 10 (negative because the number of steps is decreasing).
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Suppose you have 100 mL cup 300 mL cup in a 500 mL cup list two different ways you can measure exactly 1 L
Answers
A) 500 mL + 500 mL
B) 100 mL + 100 mL + 300 mL + 500 mL
Final answer:
To measure 1 liter, one could fill a 500 mL cup twice, or fill a 300 mL cup once, a 500 mL cup once, and a 100 mL cup twice, summing to a total of 1,000 mL which equals 1 liter.
Explanation:
To measure exactly 1 liter using cups of 100 mL, 300 mL, and 500 mL, we can use two different methods. It's important to note that 1 liter (L) equals 1,000 milliliters (mL). Here are the steps for each method:
Method 1:
Fill the 500 mL cup twice and pour the contents into another container. (500 mL + 500 mL = 1,000 mL)
This gives you exactly 1 liter, since 1,000 milliliters is equivalent to 1 liter.
Method 2:
First, fill the 300 mL cup and pour it into an empty container.
Then, fill the 500 mL cup and add it to the same container. (300 mL + 500 mL = 800 mL)
Lastly, fill the 200 mL remaining by using the 100 mL cup twice. (100 mL + 100 mL = 200 mL)
Combining all the measurements gives you 1,000 mL, which is exactly 1 liter. (800 mL + 200 mL = 1,000 mL)
What number can you add to √7 to get a rational number?
−7√
7√
7
0
Answers
So if a=0 the answer is -√7, option answer 1.
Given ΔABC, m∠A = 120°, b = 13 cm, and c= 15 cm. Find the triangle's area. Round to the nearest tenth.
Answers
m∠A = 120°
b = 13 cm
c = 15 cm
From the Law of Sines, the area of the triangle is
Area = (1/2)*b*c*sin(A)
= 0.5*13*15*sin(120°)
= 84.4375 cm²
Answer: 84.4 cm² (nearest tenth)
Final answer:
The area of triangle ΔABC with m∠A = 120°, side b = 13 cm, and side c = 15 cm, when calculated using the formula for area ½ bc sin A, is approximately 84.2 cm² when rounded to the nearest tenth.
Explanation:
To find the area of triangle ΔABC with m∠A = 120°, side b = 13 cm, and side c = 15 cm, we will use the formula for the area of a triangle when two sides and the included angle are known:
Area = ½ bc sin A
First, we need to find the sine of angle A, which is sin(120°). Using a calculator, we find that sin(120°) ≈ 0.866. Now, we can plug in the values into the area formula:
Area = ½ × 13 cm × 15 cm × sin(120°)
Area = ½ × 13 cm × 15 cm × 0.866
Area ≈ ½ × 13 cm × 15 cm × 0.866 ≈ 84.225 cm²
Rounding to the nearest tenth, the area is approximately 84.2 cm².
Isabella competed in a triathlon. She completed the swimming event in 12.9 minutes, the biking event in 13.05 minutes, and the running event in 23.125 minutes. What was Isabella’s total time in the triathlon?
Answers
Add up (12.9 + 13.05 + 23.125)
12.9 + 13.05 + 23.125
25.95
25.95 + 23.125
49.075
Answer:
49.075 minutes
HOPE I HELPED!!!!!!!!!!!!!!!!!!!!
P.S. If you need anymore help do not hesitate to ask!!!!!
Answer:
49.075 minutes
Step-by-step explanation:
Your welcome :]
how can you use a number to explain what an integer and rational number are??
Answers
The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.
Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10,which is even.
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what is the equation of this graphed line (in slope intercept form)
thank you!
Answers
slope =
7- - 2 =9
8-0 = 8
slope = -9/8
y intercept = 7
equation: y=-9/8x+7
What is the measure of ∠ABC?
Enter your answer in the box.
Answers
The measure of the angle ∠ABC will be 95 degrees.
What is a quadrilateral?A quadrilateral is a shape made up of four sides having the sum of the angles 360 degrees. The given shape is like a parallelogram in which two sides are equal and at the same angles.
Given that angle A in the quadrilateral is 85 degrees. The value of the angle B will be calculated as:-
∠A + ∠B +∠C + ∠D = 360
85 + ∠B + 85 + ∠B = 360 ∠B = ∠D
170 + 2∠B = 360
2∠B = 360 - 170
2∠B = 190
∠B = 190 / 2
∠B = 95
Therefore, the measure of the angle ∠ABC will be 95 degrees.
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if a = 0.6(the 6 repeating) and b= 0.75, then a·b= (blank) and a/b=(blank)
Answers
0.6666 (repeating) / 0.75 = 0.8888888 (repeating)
If h(x)= 5 for the function h(x)= 2x+1, what is the value of x?