Which equation is equivalent to
f(x) = 16x4 -81 = 0?
✓(4x² +9)(4x² - 9) = 0 ✓
COMPLETE
Select all of the zeroes of the function.
O
2/3
DONE
Answers
The given equation is equivalent to (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3). And the zero of the function are: [tex]\pm \frac{3}{2}[/tex] and [tex]\pm \frac{3}{2}i[/tex].
What is a Quadratic Function?The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: D=b²-4ac and after that use this variable in the formula: [tex]x=\frac{-b\pm\sqrt{D} }{2a}[/tex].
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
The question gives: [tex]16x^4-81=0[/tex], you can factor this equation. See below.
(4x²+9)*(4x²-9)
(4x²+9)*(2x-3)*(2x+3)
Therefore, you should choose one of options: (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3).
Next step is to solve the given equation. Solving for (4x²+9)*(2x-3)*(2x+3)=0, then:
For 2x-3=0
x=3/2
For 2x+3=0
x= -3/2
For 4x²+9=0
4x²=-9
x²= -9/4
x = [tex]\pm \sqrt{\frac{-9}{4} }[/tex]
x =[tex]\pm \frac{3}{2}*\sqrt{-1 }\\ \\ \pm \frac{3}{2}*i[/tex]
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Related Questions
Two friends have recently graduated from college and are now looking for jobs. They are debating which type of job is better: hourly or salary. One hourly position that pays $18 an hour, with time-and-a-half pay for overtime. One salary position for the same type of job pays $38,000, does not pay for overtime. If employees work exactly 40 hours per week, which job has a higher hourly rate? How can we calculate this? Describe (compare) how these two different hourly rates would look when graphed as a line. When interviewing for the salaried job, the friends learn that they may have to work about 10 hours of overtime each week. Explain why this math is crucial to determining which job pays more.
Answers
Answer: This is a CRQ so you will want to answer using R.A.C.E
Step-by-step explanation:
First, restate the question: "If employees work exactly 40 hours the job with the higher pay rate is..."
Now let's figure it out who gets paid more. The hourly employee gets $18 per hour, for 40 hours each week... 18 times 40. That's $720 for each week.
But they don't work for just one week, they have to work the whole year! So that's 52 weeks. Take the $720 and multiply by 52 weeks.
Now you have the total for how much hourly guy will make in a whole year.
Compare this number with the salary guy who is making $38,000 per year. Which person get's paid more? Hourly or Salary? Don't forget to include your calculations!
.............................................................................
Next part of the question: "When graphed as a line..." This part of the question you do not have to do because we did not cover slope of a line yet. (Hi, I'm your math teacher by the way lol)
.............................................................................
Next part of the question adds 10 hours of overtime to their work week. This changes everything! Remember, the salary guy gets $38,000 every year, no matter how many hours of overtime he works.
However, the hourly guy gets extra money for these extra hours! For overtime, the hourly employee gets "time and a half" pay whenever he has to work extra time. This means he gets his original $18 per hour, AND now also gets half of that ($9 per hour) ... which adds up to a whopping $27 per hour for overtime (nice!)
Hourly guy works 10 extra hours per week, at $27 per hour. Multiply that and you get $270 per week. Remember, 52 weeks per year, so now take the $270 and multiply by 52 weeks. This gives you the total amount of overtime money hourly guy makes.
Combine his overtime money with his regular money (the first thing we did at the start of this problem) to get his new grand total for the year.
Salary guy still makes $38,000 per year. So now that they work overtime... who gets paid more?
Remember to answer in R.A.C.E format. Restate your question, Answer all parts of the question, Cite a math term/definition/concept that supports your answer (maybe use "hourly rate" or "salary"), and Explain your steps and thinking.
Good luck! send me an email for more help.
Mrs. B
Find the value of X:
Answers
Answer:
x=9
Step-by-step explanation:
I took one side, and made proportions:
12:16
3:4
so, x-1:6=3:4
(x-1)/6=3/4
solve it for x=9
Answer:
9
Step-by-step explanation:
Hope this helps!
Plz Mark Brainliest!
An airplane can ascend at a rate of 54 1/2 meters in 2/3 of a second. How many meters can the airplane ascend in one second?
Answers
Answer:
The airplane ascends [tex]81\,\frac{3}{4}[/tex] meters in one second.
Step-by-step explanation:
Given that the airplane ascends [tex]54\,\frac{1}{2}[/tex] ([tex]\frac{109}{2}[/tex]) meters in [tex]\frac{2}{3}[/tex] seconds, we calculate the ascent rate of the airplane by simple rule of three:
[tex]x = \frac{\frac{109}{2}\,m }{\frac{2}{3}\,s } \times 1\,s[/tex]
[tex]x = \frac{327}{4}\,m[/tex]
[tex]x = 81\,\frac{3}{4}\,m[/tex]
The airplane ascends [tex]81\,\frac{3}{4}[/tex] meters in one second.
pls answer this question
Answers
Answer:
id kkk what the quequestion is
Step-by-step explanation:
Find the midpoint of the interval [-3, 6] along the number line.
Answers
Answer:
1.5 or 3/2
Step-by-step explanation:
The midpoint of the interval [-3, 6] along the number line is 1.5.
The midpoint of an interval is the point that lies exactly in the middle of the two endpoints.
To find the midpoint of the interval [-3, 6], we use the midpoint formula:
Midpoint = (Endpoint1 + Endpoint2) / 2
In this case, Endpoint1 is -3, and Endpoint2 is 6:
Midpoint = (-3 + 6) / 2
Midpoint = 3 / 2
Midpoint = 1.5
The midpoint of the interval [-3, 6] is 3/2. This means that the point exactly halfway between -3 and 6 on the number line is 1.5 units to the right of -3 and 1.5 units to the left of 6.
Visually, if you plot -3 and 6 on a number line, the midpoint 3/2 (or 1.5) would be located at the center, equidistant from both endpoints.
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que es una organizacion
por favor es urgente
Answers
Step-by-step explanation:
Las organizaciones son estructuras administrativas y sistemas administrativos creadas para lograr metas u objetivos con el apoyo de las propias personas, o con apoyo del talento humano o de otras características similares.
(-10) + (-10) = 10 –
PLS HELPPPP
Answers
Answer:
Step-by-step explanation:
-10 + -10 = -20
so
10 - _ = -20
10 - 30 = -20
-10 + -10 = 10
Simplify:
-10 - 10 = 10
Simplify:
-20 = 10
It's false so there is no solution
Use the slope formula to find the slope between the given two points.
(-4, -1) and (-2, -5)
Answers
Answer:
y2 -y1 over x2 - x1
Step-by-step explanation: plz mark brainliest
The points represented by the table lie on a line. Find the slope of the line.
Answers
Step-by-step explanation:
11. step 1. m = (4 - 7)/(-3 - (-5))
step 2. m = -3/2.
Which multiplication expression does the model represent?
Answers
Answer: I think the answer is A. because it's 1/2 of 4 and it takes only one "quarter of the 4" all though it is split in half it still decared as a whole
Step-by-step explanation:
The multiplication expression represent the model is 1/2×4.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
In the given figure, there are 4 equal parts.
One part is divided into two equal parts.
1/2×4
Therefore, the multiplication expression represent the model is 1/2×4.
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Evaluate each expression when y=5.
B. 4(y+3)
Answers
Answer:
B. 4(y+3)=4(5+3)=4×8=32
Answer:
32
Step-by-step explanation:
Step 1: Sub y = 5 into the expression
Find anywhere that has a 'y' and replace it with a 5
4(y+3)
4(5+3)
Step 2: Solve
Use BEDMAS to solve the expression
4(5 + 3)
4(8)
32
Step 3: Therefore Statement
Therefore the expression is equal to 32
simplify e with an exponent of in6
Answers
Answer:
Step-by-step explanation:
I think the exponent is ln6, not in6.
e^(ln 6)= 6
P = R+C help I need to get out of class plz help
Answers
Answer:
People's Republic of China
PRC means People's Republic of China.
Step-by-step explanation:
What is PRC? History of rebranding
All products manufactured in China were automatically considered low-quality items for a long period. Even the famous brand or name of the manufacturing plant did not manage to change this stereotype.
China has been the world leader in exporting and manufacturing industrial output since 2014. For the last 50 years, over 370 thousand new factories have started working in the PRC. To reduce the prime cost of goods, a lot of factories have been moved from Europe to China. The remaining factories, for example, those in Germany, France, and Spain, make products for their home markets but produce all goods for export in China.
When you are choosing household appliances pay attention to labels. You will find that most products of highly popular brands are marked “Made in China”. However, it doesn’t mean that – say – a kitchen unit is an imitation of a real food processor from Moulinex, for instance. The fact is that this unit was made at the Moulinex factory in China and it was then sent to your country. The real cost of the food processor produced in China is several times lower than the same one manufactured in and delivered from France. When ordering goods to be produced in China the seller earns more than when producing a similar product in France. Therefore there are so many European brands in our stores, which were produced in China.
European brands produced in China
Spare parts for smartphones from China
The case of spare parts for smartphones, tablets and laptops is even more complicated. It is commonly known that almost all spare parts are produced in China. Nevertheless, to buy a spare part for Samsung or Apple here is almost impossible. Their factories are protected by all means available. Spare parts from these factories are sent to Europe, where they are distributed among branches. Therefore you can buy the Original item only in the company's official representative office.
However, the Chinese people would not be Chinese if they were not able to make money on such expensive products. They manufacture the same spare parts but not at official factories. After learning the manufacturing technology of displays, touchscreens and flat cables, the local craftsmen create a device that can make spares identical to the original. Such spare parts are considered high quality products and belong to the High Copy level.
Original PRC means that the spare part consists of original components. For example, the seller has original LCDs and doesn’t have original touchscreens. In such cases, the High Copy touchscreen is installed on the original display. Such LCD module will be classified as Original PRC because one of its components is original. There can also be another scenario. Imagine that the seller has both the original LCD and touchscreen but the customer needs a module, not a separate spare part. In this situation, a handyman sticks together the LCD and the touchscreen and here is the module. Such a spare part is called Original PRC because it’s made of original components even though it is not manufactured at the official factory. The main difference between Original PRC and Original is the place where they were made. The quality of Original PRC spares doesn’t differ from Original. Still the difference in price is significant.
(hope this helps can i plz have brainlist :D hehe)
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing
A. calculator, but he could only see one line. Why is this?
B. because the system of equations actually has only one solution
C. because the system of equations actually has no solution
D. because the graphs of the two equations overlap each other
because the graph of one of the equations does not exist
Answers
What is the unit ratio for 360 oranges growing to 9 trees
Answers
Answer:
360/9=40
Step-by-step explanation:
Answer:
40
all you have to do is divide the first term by the second term
example: 360 divided by 9 = 40
What is X - 8 = 15.
Answers
Answer:
X = 23
Step-by-step explanation:
X - 8 = 15.
Add 8 to each side
X - 8+8 = 15+8
X = 23
the answer is 23
hope that helped^^
what is the distance between (-1,-2) and (8,10)
Answers
Answer:
x1 = 2, x2 =-8
y1=-2, y2 =-2
y2-y1 = |-2+2| =0
x2-x1= |-8-2|= 10
So distance is 10 units
Step-by-step explanation:
Find the requested information based on the given facts.
Total sales is $55,000.
The commission is 3.5%.
Determine the commission.
Answers
Using proportions, it is found that the commission is of $1,925.
What is a proportion?A proportion is a fraction of a total amount, and operations such as multiplication or division are used to find the desired measures in the problem.
One example of application of proportions is for percentage problems, as the percentage is the desired amount divided by the total amount. To find the amount equivalent to a percentage, we multiply the decimal coefficient of the percentage by the total amount.
For this problem, the percentage is of:
3.5%.
Hence the decimal equivalent is:
3.5/100 = 0.035.
The commission is 3.5% of the total sales of $55,000, hence:
C = 0.035 x 55000 = $1,925.
Hence the commission is of $1,925.
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Part B: The weatherman claimed that the temperature on Friday was the opposite of Thursday’s temperature. Which of the following statements support this claim? Select all that apply.
A.
The temperatures on Thursday and Friday are opposites because they are on different sides of 0 on the number line.
B.
The temperatures on Thursday and Friday are opposites because they have a sum of 0.
C.
The temperatures on Thursday and Friday are opposites because they both contain a 3.
D.
The temperatures on Thursday and Friday are opposites because they are the same distance from 0 on the number line.
Answers
Answer:
it will be d
Step-by-step explanation:
because I had a assignment over this and I put d and got it correct
Please guys I need help
Answers
[tex]8000 \: pounds \times \frac{1 \: ton}{2000 \: pounds} = 4 \: tons[/tex]
[tex]7 + 4 = 11 \: tons[/tex]
Which expression is equal to 4(2+3)
Question 1 options:
A.4+5
B.8+12
C.2+12
D. 8+3
Answers
Answer:
B, 8+12
Step-by-step explanation:
2 + 3 is 5, 4 × 5 = 20
Therefore the only option which equals 20 is B.
Three numbers have a ratio of 2: 3: 4. If the largest number if their sum is 24 what is the sum of the three numbers?
Answers
Answer:
Step-by-step explanation:
Let r be a multiplier. Then 2r + 3r + 4r = 24, or
9r = 24, or r = 24/9 = 8/3
The three numbers are then (8/3)(2), (8/3)(3), (8/3)(4), and their sum is
(8/3)(2 + 3 + 4) = (8/3)(9) = 24. But the problem tells us that! Please check the wording of your question; something's not quite right there!
how do you solve 3 divided by x -1 = x + 1
Answers
Answer:
multiply (x-1) to both sides and then subtract three from both sides
3 = (x-1)(x+1)
3 = (x^2 -1)
0 = x^2 - 4
(x-2)(x+2) = 0
x = 2
x = -2
Step-by-step explanation:
PLS PLS PLS THIS IS VOCAB FOR MATH ONLY HAVE UNTILL 7:30 TO DO SEVERAL ASSIGHNMENTS1. a number belonging to the set made up of the counting numbers: 1, 2, 3, and so on
2. a number that is greater than zero
3. a line that graphically represents all numbers
4. a pair of numbers whose sum is zero
5. any number belonging to the set of counting number, or zero
6. a number that is less than zero
7. a number belonging to the set made up of the whole numbers and their opposites
8. two numbers that are the same distance from zero on the number line but in opposite directions
Answers
Answer:
1. natural numbers
2. positive
3. number line
4. zero pair
5. whole number
6. negative
7. integer
8. opposite
Step-by-step explanation:
This is my guess. Take it with a grain of salt. Have a great day!
Answer:
2. positive integers
3. number line
4. I don't know
5. whole number
6. negative integer
7. integers
8. absolute value???
Things that are equivalent to 5 : 2
Answers
Answer:
2/5
Step-by-step explanation:
Answer:
10 : 4, 15 : 6, 20 : 8,
Step-by-step explanation:
increase the first number by 5 then add two to the second number
please help me solve this problem
Answers
Step-by-step explanation:
it seems the answer is four (option a)
In 1995, there were 85 rabbits in Central Park. The population increased by 8.5% each year. How much rabbits were in Central Park in 2005
Answers
==============================================
Work Shown:
A = P*(1+r)^t
A = 85*(1+0.085)^10
A = 192.183592562981
A = 192
-----------
Notes:
P = 85 is the starting population.r = 0.085 is the decimal form of 8.5%, so we can say 8.5% = (8.5)/100 = 0.085t = 10 years have elapsed from 1995 to 2005.The formula shown above helps with exponential growth and decay problems.The rabbit population in Central Park in 2005 is 192 rabbits.
To find the rabbit population in Central Park in 2005, we need to calculate the growth from 1995 to 2005.
From 1995 to 2005, there is a total of 10 years.
Using the growth rate of 8.5% per year, we can calculate the population in 2005:
Population in 2005 = 85 rabbits(1 + 0.085)¹⁰
Calculating this expression:
Population in 2005 = 85 rabbits(1.085)¹⁰
= 85 rabbits × 2.2609
= 192 rabbits
Therefore, the estimated rabbit population in Central Park in 2005 is 192 rabbits.
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It says 33cm it’s messed up because it’s on a laptop but what’s the volume of this sphere :)
Answers
Answer:
1.51*10^5 cm^3
Step-by-step explanation:
the formula for the volume of a sphere is (4/3)pi(radius)^3
I can't really tell if the 33 cm is for the radius or the diameter, but it looks like the radius, so
(4/3)*(33)^3*pi
simplify
Im assuming you can use a calculator because it's too hard to do without because it's a huge number
Isabel put $4,000 into a saving account that pays interest monthly at a simple-interest rate of 2.5% per year. If she takes the interest interest out of the account each month, how much money should she expect to earn after 6 months?
Answers
9514 1404 393
Answer:
$49.98
Step-by-step explanation:
The interest credited to Isabel's account each month is ...
I = Prt
I = $4000·(0.025)(1/12) = $8.33
If she withdraws that amount each month, the original balance is restored, and she will earn the same amount the next month.
Isabel's total earnings in 6 months will be ...
$8.33 · 6 = $49.98
help. mee
Write an equivalent expression for 3(3x + 5). Explain what property you used to write your equivalent expression.
Answers
Answer:
distributive property
9x+15
Step-by-step explanation:
The distributive property is whenever you have () and distribute until you have zero of these ()
The equivalent expression simply means write this equation differently.