Answers
1. If a polynomial function with rational coefficients has -4 and 8 as roots, it means we can factor this polynomial this way :
What is rational coefficients?
A coefficient is a number that is placed in front of a variable. A variable and a rational number are preceded by a rational coefficient, which may be an integer, decimal, or fraction.
(x - (-4))(x-8) = (x+4)(x-8) = x² - 8x + 4x - 32 = x² - 4x - 32
1x² - 4x - 32 is a polynomial function of least degree with rational coefficients that satisfices the given conditions. The leading coefficient here is 1, we call this a monic polynomial.
2. There may be something missing in the question here
3. We can use the factoring techniques to find the roots :
x^3 - 5x² + 9x - 45 let us group x^3 with -5x² and 9x with -45 :
(x^3 - 5x²) + (9x - 45) = x²(x - 5) + 9(x - 5)
We can notice now that there is a common factor : (x-5) this allows us to factor again by (x-5) :
Y = (x-5)(x²+9)
This is the maximum we can do on R, but on C the set of complex we can still factor again.
x² + 9 has a negative discriminant : Δ = b² - 4ac where b = 0 , a = 1, c = 9
Δ < 0, Δ = - 36
Applying the formulas for the roots x1 and x2 we get x1 = -3i, and x2 = + 3i
Y = (x-5)(x-3i)(x+3i)
So the solution is S = {5, 3i, -3i} the three roots of the function.
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Related Questions
7 3/10 - 3 9/10
Show work please
And no links
Answers
Yan na sagut ko sa module
Sana makatulong
follow me for more math answer
Answer:
3 4/5
Step-by-step explanation:
7 3/10 - 3 9/10=
In this case 3/10 - 9/10 is cannot be so we have to borrow 1 whole from 7
so, 7 3/10 will become 7 3/10 + 1 or to add we have to change 1 as 10/10, any way 1 and 10/10 is equal but in this case we will use 10/10 to add 1 whole to 3/10 and minus 1 whole to 7
so, 3/10 + 10/10 = 13/10
and 7 - 1 = 6
so, 7 3/10 as 6 13/10
any way 7 3/10 and 6 13/10 is equal but, in this case we have to use 6 13/10 to minus, because 7 3/10 is cannot be
so, 6 13/10 - 3 9/10 =
=3 4/10 or 3 2/5
Please pick me as brainliestWhat is 3785 divided by 30?
Answers
Enter the slope-intercept equation for the image of line ℓ after a clockwise rotation of 90°. (Hint: To find the image of line ℓ, choose two or more points on the line and find the images of the points.)
Answers
Answer:
y=-3x-3
Step-by-step explanation:
Rotate 90 degrees
find slope
find y intercept
write equation
HELP ASAP PLEASE!!!!!!
Answers
Answer:
the answer is 0
Step-by-step explanation:
The average snail can move 1.81 X 10³ mi in 5 hours. What is its rate of speed in miles per hour?
Answers
Answer:
Step-by-step explanation:
How Far Can A Snail Travel In One Hour
If a snail can travel over half an inch per minute, that means in one hour a snail can travel up to 40 inches. If you want to think about how far this is in feet, it means that snails move up to 3.5 feet per hour.
Consider the fact that the average human being can walk about a mile, or 5280 feet, in one hour.
This means that snails can take up to 1,500 days, or over 4 years, to travel just one mile.
please help i’ll mark u
Answers
Answer:
4:12
4/12
4 to 12
25. Critique Reasoning A student is given the rectangle and the square shown. The student states that the
two figures have the same perimeter. Is the student correct? Explain your reasoning.
Answers
You only attached the square. Edit the question to add it, and then I'll edit my answer.
a certain radioactive isotope has leaked into a small stream. one hundred days after the leak 8% of the original amount of substance remained. Determine the half life of this radioactive isotope
Answers
Answer:
The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. We can use the fact that 8% of the original amount remains after 100 days to determine the half-life of the isotope.
Let's assume that the initial amount of the substance is 1 unit (it could be any amount, but we're assuming 1 unit for simplicity). After one half-life, half of the original amount remains, or 0.5 units. After two half-lives, half of the remaining amount remains, or 0.25 units. After three half-lives, half of the remaining amount remains, or 0.125 units. We can see that the amount of substance remaining after each half-life is half of the previous amount.
We can use this information to set up the following equation:
0.08 = (1/2)^n
where n is the number of half-lives that have elapsed. We want to solve for n.
Taking the logarithm of both sides, we get:
log(0.08) = n*log(1/2)
Solving for n, we get:
n = log(0.08) / log(1/2) = 3.42
So the number of half-lives that have elapsed is approximately 3.42. Since we know that 100 days is the time for three half-lives (from the previous calculation), we can find the half-life by dividing 100 days by 3.42:
Half-life = 100 days / 3.42 = 29.2 days (rounded to one decimal place)
Therefore, the half-life of the radioactive isotope that leaked into the stream is approximately 29.2 days.
Can anyone please help me which statement is not correct? (use estimation to decide please)
Answers
Answer:
Step-by-step explanation:
A is correct.
2/3 > 4/8
5/9 > 7/12 This one is close. They are both nearly 1/2, but 9<12 and when you divide something by 9 the remainder is going to be larger than if you divide by 12.
The second one is incorrect.
3/4 > 5/9 5/9 is close to 1/2. Three quarters is much greater than 1/2
3/10 is much smaller than 5/9
The third one is correct. 1/10 and 5/6 are much larger than the two fractions on the right. The right side = 56/60 which is very nearly one. The left side is nowhere near that large. (I did estimate the right side).
The fourth one is correct. 9/10 is much larger than 2/3 and 5/9 is larger than 5/12. 5/9 is over 1/2 and 5/12 is under one half. So the arrow in the fourth one is going the right way.
FIND MULTIPLICITY AND ZEROS OF THE GRAPH!
Answers
Answer: The Zeros Are(in order) -3,-2,-1,1, 1.5 ALL have a multiplicity of 1.
Step-by-step explanation: Since the 0's cross the graph and don't "bounce" on the x-axis, they're all for a multiplicity of 1.
Help please!! I’ll give brainliest if you show work as well. Thank you!!!
Answers
Answer:
TWO CRACKERS
Step-by-step explanation:
I'm assuming they want to find x. Here we see that these two are similar triangles, so the sides are reflective. 5x/5 should be equal to 4/x, so 5x/5 = 4/x. If we use cross multiplying we get 5x^2 = 20. divide both sides by 5 and we get x^2 = 4 or x = 2.
Hope this helped
Wednesda
P
Which is greater: 5/8 or 3/5?
Answers
Answer:
5/8 is greater
Step-by-step explanation:
you can divide 8 into 5 to get the decimal equivalent of 5/8, which is 0.625
you can divide 5 into 3 to get the decimal equivalent of 3/5, which is 0.600
so 5/8 is greater
or . . .
you can create equivalent fractions using a common denominator and then compare numerators
\(\frac{5}{8}\) = \(\frac{25}{40}\)
\(\frac{3}{5}\) = \(\frac{24}{40}\)
this proves, again, that 5/8 is greater but only by \(\frac{1}{40}\)
Answer:
Given fractions are 5/8 and 3/5
LCM of 8 and 5=40
Now, making the denominator the same of both fractions
5/8=5 x 5/8 x 5=25/40
3/5=3 x 8/5 x 8=24/40
Since, 25/40>24/40
Hence, 5/8 > 3/8
Step-by-step explanation:
Y and X can both be proportional if:
A. product is constant
B. quotient is constant
C. increase by x + 2
D. increase by 2x
Answers
Y and X can both be proportional if:
A. product is constant
B. quotient is constant
C. increase by x + 2
D. increase by 2x
Answer:
B
Step-by-step explanation:
Martina created this box plot to represent the number of inches of snow that fell during the winter in several different cities. (a) What was the least amount of snowfall in any of the cities? (b) In which quarter is the data most concentrated? Explain how you know. (c) In which quarter is the data most spread out? Explain how you know.
Answers
Answer:
c
Step-by-step explanation:
I can do this so fast I know I am a high school
A parallelogram has an area of 20.4 square units. If the height that corresponds to a base is 4 units,what is the base
Answers
Answer:
5.1 units
Step-by-step explanation:
A=b x h divide by 2
20.4=4b
b=5.1 units
Which has a greater effect on the volume-changing the radius by a given amount or changing the height by the same amount? Why?
Answers
Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.
how many ping pong balls do you need if you want to arrange them in the shape of an equilateral triangle with 23 rows
Answers
You would need a total of 276 ping pong balls
Step by step explanation:
To determine the number of ping pong balls needed to form an equilateral triangle with 23 rows, we can calculate the total number of balls in the triangle. In an equilateral triangle, each row has one more ball than the previous row. The formula for the sum of the first n natural numbers is given by:
Sum = (n * (n + 1)) / 2
In this case, we want to find the sum of the first 23 natural numbers. Substituting n = 23 into the formula, we get:
Sum = (23 * (23 + 1)) / 2 = 276
Therefore, you would need 276 ping pong balls to arrange them in the shape of an equilateral triangle with 23 rows.
If the side length of of rectangle is 3x-3 and the top length is 6, how do I write a linear equation the represents the area and a linear equation that represents the perimeter, all measurements are in cm if that is useful.
Answers
Perimeter of the rectangle is: 6x + 6 cm
Area of the rectangle is: 18x - 18 cm²
What is the Area and Perimeter of a Rectangle?Area = (length)(width)
Perimeter = 2(length + width).
Given the following:
Length of rectangle = 3x - 3
Width = 6
Area = (3x - 3)(6)
Area = 18x - 18 cm²
Perimeter = 2(3x - 3 + 6) = 2(3x + 3)
Perimeter = 6x + 6 cm
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Marvin runs on a regular basis, but he knows he could get injured if he runs long distances too frequently. How far will he run if he wants to run 75% of his distance from last week, when he ran 20 total miles
Answers
Consider an experiment of tossing a coin twice in a row.
The probability of occurrence of two heads in a row is
A) 0.25
B) 0.20
C) 0.50
Answers
Which equation will solve the following word problem? Four roommates share the cost of an apartment: rent, electricity, and gas. Rent costs $1200/month and gas costs $50/month. Each roommate pays $345/month. How much is the electric bill per month?
($1200 + $50)/4 = E + $345
($1200 + $50 + $345)/4 = E
($1200 + $50 + E)/4 = $345
($345)4 + E = $1200 + $50
Answers
Given that,
Four roommates share the cost of an apartment: rent, electricity, and gas. Rent costs $1200/month and gas costs $50/month. Each roommate pays $345/month.
To find,
The electric bill per month.
Solution,
Bill of each roommates = $1200+$500+E, E is electricity bill
Total bill = $345/month
Bill of each roommates = 4($1200+$500+E), E is electricity bill
ATQ,
4($1200+$500+E) = $345
So, the correct option is (c).
What is the Circumference of the circle below? (Use 3 for π)
Answers
Answer: The circumference of this circle with 3 for pi is 108 m.
Step-by-step explanation: The formula for the circumference of a circle is 2 pi r. So, plug in the values. 2 x 3 x 18 is equal to 108. Therefore, the circumference of this circle is 108 m.
PLZ HURRY IT'S URGENT!!! 20 POINTS!!
1. Write an equivalent expression for −4(3x−2y−1).
−12x−2y−1
−12x+8y+4
−12x−8y−4
−12x+8y−4
2. A triangle has lengths measuring 42‾√ cm, 218‾‾‾√ cm, 48‾√ cm. What is its perimeter? Express your answer in simplest terms.
options:
182‾√ cm
1028‾‾‾√ cm
122‾√+218‾‾‾√ cm
102‾√+48‾√ cm
3. The formula for the area of a trapezoid is A=12h(b1+b2).
Solve the formula for b1.
options:
A/2h−b2=b1
2/Ah−b2=b1
2A−2b2/h=b1
2A/hb2=b1
4. Gemma earns $575 a week plus $180 commission for each car she sells. She earned $1835 last week. How many cars did she sell?
options:
She sold 6 cars.
She sold 7 cars.
She sold 8 cars.
She sold 9 cars.
5. For the function f(x) = 12 – 5x, evaluate f(–3).
options:
27
-3
-27
3
6. Which of these is NOT a way to describe the slope of a line?
options:
rise over run
run over rise
the steepness of a line
the rate of change
Answers
Answer:
4 she sold 6 cars
Step-by-step explanation:
Which statement correctly compares functions fand g?
ОА.
They have the same end behavior as x approaches -oo but different end behavior as x approaches.co.
OB. They have different end behavior as x approaches -- and different end behavior as x approaches .
O C. They have different end behavior as x approaches - but the same end behavior as x approaches co.
OD. They have the same end behavior as x approaches-co and the same end behavior as x approaches co.
Answers
They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. The correct option is C.
What is exponential function?An exponential function is a mathematical function with the formula f (x) = \(a^x\), where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero.
There are four possible types of end behavior for a function: as x approaches infinity, the function may approach a constant value, approach positive infinity, approach negative infinity, or oscillate without approaching any value.
The solution shown in the given graph illustrates that they have varying end behavior as x approaches -∞ but the same end behavior as x approaches ∞.
Thus, the correct option is C.
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Find an equation of the tangent line to f(x) = 5x2 − 2x + 10 at x = 7.
PLEASE HELP WORTH 30 POINT ....
Answers
Answer:
= 241
Step-by-step explanation:
\(5 {x}^{2} - 2x + 10 \\ 5 {(7)}^{2} - 2(7) + 10 \\ 5(49) - 14 + 10 \\ 245 - 14 + 10 \\ 245 + 10 - 14 \\ 255 - 14 \\ = 241\)
A caterer prepares twice as many pizzas as she usually prepares for a large party. The caterer usually prepares 5 pizzas. The caterer also estimates that each party guest will eat
1
2
of a pizza.
Drag and drop each expression into the correct boxes to complete the explanation.
The expression that represents how many guests the pizzas can serve is .
How many party guests will the pizzas serve? Drag and drop the number of guests into the box.
The pizzas can serve guests.
Answers
d Bula drives to work and
back every day. One way,
the trip is fifty miles.
How many miles does
she drive in five days?
Answers
The number of miles that she drives in five days will be 250 miles.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
Bula drives to work and back every day. One way, the trip is fifty miles.
The number of miles that she drives in five days will be given as,
50 = D / 5
D = 50 x 5
D = 250 miles
The number of miles that she drives in five days will be 250 miles.
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QUESTION 5. The Mets drew 1,750,400 fans this season (counting all their home games). This is 28.6%
less than their total attendance in the most recent comparable season, before the pandemic. How
many fans attended Mets games in that prior comparable season?
Answers
Answer:
Step-by-step explanation:
The physician’s order reads to administer Lasix 80 mg PO STAT. You have Lasix 20 mg tablets on hand. How many tablets will you administer to the patient ?
Answers
The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.
To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.
Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.
Number of tablets = Prescribed dose / Dosage strength per tablet
Number of tablets = 80 mg / 20 mg
Number of tablets = 4 tablets
Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.
It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.
Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.
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Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line x2 (a) the x-axis (b) the y-axis (c) the line x = 5 Need Help? Read ItTalk to a Tutor +-4 points LarCalc11 7.3.030.MI. Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line 10 x2 (a) the x-axis (b) the y-axis (c) the line y 10
Answers
Using either shell method, the volume of the solid generated by revolving the region bounded by y = \(x^{3}\) and y = 0 around the lines x = 2 (a), x = 0 (b), and x = 9 (c) can be determined to be 8π, 0, and 54π, respectively.
To solve this problem using the disk method, we first need to determine the area of the region bounded by the two equations. This can be done by integrating y = \(x^{3}\) from x = 0 to x = 2, which gives us A = 8/4 = 2. We then need to determine the radius of the disk, which is the distance from the line of rotation to the point of intersection of the two equations.
For (a), this is the distance from x = 2 to y = 2, which is 2. For (b), this is the distance from x = 0 to y = 0, which is 0. For (c), this is the distance from x = 9 to y = 27, which is 27/3. We can now use the formula for the volume of a solid generated by revolving a region around a line to calculate the volume for each of the three lines:
(a) V = π(2)2 × 2 = 8π
(b) V = π(0)2 × 2 = 0
(c) V = π(27/3)2 × 2 = 54π
To solve this problem using the shell method, we first need to determine the limits of integration, which is the same as for the disk method. We then need to determine the radius of the shell, which is the distance from the line of rotation to the point of intersection of the two equations.
This is the same as for the disk method. We can now use the formula for the volume of a solid generated by revolving a region around a line to calculate the volume for each of the three lines:
(a) V = 2π ∫(2) (\(x^{3}\)) dx = 8π
(b) V = 2π ∫(0) (\(x^{3}\)) dx = 0
(c) V = 2π ∫(27/3) (\(x^{3}\)) dx = 54π
The disk and shell methods are two methods used to find the volume of a solid generated by revolving a region bounded by the graphs of two equations around a given line.
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