Given:
The degree of the polynomial = 3
Leading coefficient = 1
Zeros of the polynomial are 5 and 4i.
To find:
The expanded form of the polynomial.
Solution:
According to the complex conjugate root theorem, if a+ib is a zero of a polynomial, then a-ib is also a zero of that polynomial.
Here, zeros of the polynomial are 5 and 4i. It means the third zero of the polynomial is -4i. So, the factors of the polynomial are [tex](x-5),(x-4i),(x+4i)[/tex].
The required polynomial is the product of its all factor and a constant which is equal to the leading coefficient. Here, the constant is 1. So, the required polynomial is
[tex]P(x)=1(x-5)(x-4i)(x+4i)[/tex]
[tex]P(x)=(x-5)(x^2-(4i)^2)[/tex]
[tex]P(x)=(x-5)(x^2+16)[/tex] [tex][\because i^2=-1][/tex]
[tex]P(x)=(x-5)(x^2+16)[/tex]
On further simplification, we get
[tex]P(x)=x^3+16x-5x^2-80[/tex]
[tex]P(x)=x^3-5x^2+16x-80[/tex]
Therefore, the required polynomial P is [tex]P(x)=x^3-5x^2+16x-80[/tex].
SOMEBODY PLSSSSSSS HELP!! :(
Answer:
What's your question?
Step-by-step explanation:
Answer:
Where is the question?
Mr.Robin assign 3/4 hour of homework each day to his students for 4 days in a row. How many total hours of homework does Mr.Robin assign his students?
The event of picking a number less than 13 from a jar with papers labeled from 1 to 12 is.
PLZ FAST ANSWER
Answer:
100 %
Step-by-step explanation:
n<13, you only have numbers from 1 to 12. This means that any number that you will pick will be less than 13
Nine times a number, added to 4, is 58.
Find the number n.
Answer:
6
Step-by-step explanation:
n - number
9n + 4 = 58
9n = 54
n = 54/9 = 6
ILL GIVE BRAINIEST IF SOMEONE CAN HELP
f(t) =
2(t-1)
(t-4) (t + 2)
What is the domain off (t)?
Answer:
{t element R : t!=-2 and t!=4}
(assuming a function from reals to reals)
Step-by-step explanation:
Can you help me on algebra?
Answer:
the answer is :c^5 b^3
Write the log equation as an exponential equation. You do not need to solve for x.
log, (5x + 4) = 3x – 4
Awesome Autos creates the following advertisement to compare the prices of its used cars to those of Cool Cars. Which statement best explains how Awesome Autos misrepresented the data? (could someone please help)
1
Step-by-step explanation:
Answer: A. The graph for Awesome Autos does not begin at 0 and makes its prices appear less than those of Cool Cars.
please anybody can help me to solve this question btw im from malaysia but the questions have the eng subtitle so you can read the eng subtitle, no worries! please help me to answer the questions
A store offers a discount of 40% off any one regular-price item. The price paid after this discount is represented by $(<). Employees also receive 10% off any purchases; the price paid alter
this discount is represented by e(x). Which of the following represents the composite function of applying the store discount first, and the employee discount second?
O e(s(x) = 0.04
O c(s(x)) = 0.54
Os(e(x) = 0.54
Os(e(x)) = 0.04
Answer:
O s(e(x)= 0.54
Step-by-step explanation:
sana makatulong
A). You plan to invest $1978 in an account with two different options. Option 1 earns 8.5% annually, with interest to be compounded continuously. How much money would you have in the account after 2 years?
B). You plan to invest $1978 in an account with two different options. Option 2 earns 8.5% annually, with interest to be compounded quarterly. How much money would you have in the account after 2 years?
C). You plan to invest $1978 in an account with two different options. Based on your two previous answers, which option would you choose and why?
Please hep me i will mark as the best please....
Answer:
A) $2,344.53
B) $2,340.36
C) Based on my answer in A and B, the Option i would choose is Option A. This is because the amount i would receive after 2 years in Option A is higher than that of Option B
Step-by-step explanation:
We solve for A and B using Compound Interest formula
A). You plan to invest $1978 in an account with two different options. Option 1 earns 8.5% annually, with interest to be compounded continuously. How much money would you have in the account after 2 years?
First, convert R as a percent to r as a decimal
r = R/100
r = 8.5/100
r = 0.085 rate per year,
Then solve the equation for A
The formula is given as
A = Pe^rt
A = 1,978.00(2.71828)(0.085)(2)
A = $2,344.53
B). You plan to invest $1978 in an account with two different options. Option 2 earns 8.5% annually, with interest to be compounded quarterly. How much money would you have in the account after 2 years?
First, convert R as a percent to r as a decimal
r = R/100
r = 8.5/100
r = 0.085 rate per year,
Then solve the equation for A
The formula is given as
A = P(1 + r/n)^nt
P = Principal = $1978
r = 0.085
n = compounded quarterly = 4
A = 1,978.00(1 + 0.085/4)(4)(2)
A = 1,978.00(1 + 0.02125)(8)
A = $2,340.36
C). You plan to invest $1978 in an account with two different options. Based on your two previous answers, which option would you choose and why?
Based on my answer in A and B, the Option i would choose is Option A. This is because the amount i would receive after 2 years in Option A is higher than that of Option B
You start at (2, 3). You move up 6 units. Where do you end?
Answer:
(2,9)
Step-by-step explanation:
we start at the point (2,3) and moving up 6 units
when we move up or down, we are changing the value of the y-coordinate. Since we are moving up, the value of the y-coordinate increases (makes sense, if you are thinking about a graph. The further you go up, the larger the y value becomes).
However, the x-coordinate will stay the same (no instructions on moving left or right {that changes the x value}). That means the y value will increase by 6 while the x value will stay the same.
so add 6 to 3 and get 9, and add nothing to 2
therefore, the point we end on will be (2,9)
if you would like to see a graph for clarity/visualization, please see below
Can anyone help me with this math equation??
Answer:
The person above me is right, it is 0.3 or 1/3
Step-by-step explanation:
Please answer correctly !!!! Will mark Brianliest !!!!!!!!!!!
Step-by-step explanation:
since they are in order points p and q are in the middle and points O and R are on the end so they say that OR=36 since you don't know the exact lengths of all of the lengths in the middle from O to R then you multiply 5,6 and 1 by x and add
5x+6x+1x=12x
so then the whole length is equal to the ratio of 12x and also 36 so set those to equal each other
12x=36
x=3
so that is just the ratio and since they are asking for the length of O to Q that means that it is just 5x+6x=OQ
11x=OQ
insert x=3
33=OQ
Hope that helps :)
Algebraically find the inverse for each of the following equations
A. y = 3x-8
B. y = 1/2x+6
C. y = x+6/2
Step-by-step explanation:
A. y= 3x -8
x = 3y -8
3y = x +8
y = (x+8)/3
B x = 1/2y +6
1/2y = x-6
y = 2x - 12
C x = y + 6/2
y = x - 6/2
solve for w what is w ÷ 1 = 6.6
Answer:
Step-by-step explanation:
solution is w = 6.6
Which two expressions are equivalent?
Answer:
7(x+8) and 7(x) + 7(8)
Step-by-step explanation:
Answer:
none are correct but d is I think the answer
Step-by-step explanation:
becuase of the way you are suppose to do the work
Please help me with this math question.
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 4 ← is in slope- intercept form
with y- intercept c = 4 → D
Order the measurements from largest to smallest.
4.9L , 4090ml , 1.4km , 4901m
Answer:
4090 ml - 4.9L
1.4km - 4901m
Step-by-step explanation:
A liter is made up of 1000 ml so 4.9 l is equvilant to 4,900 ml.
A kilometre same as litre is made up of a 1000 m. So 1.4 km is 1400m
However, ml and l is a measurement of volume while m and km is a measurement of distance.
determine the speed in metres per second if it takes 10 minutes to walk 1,2 kilometre
Step-by-step explanation:
[tex]speed = \frac{distance}{time} \\ = \frac{(1.2 \times 1000)m}{(10 \times 60)s} \\ = \frac{1200m}{600s} \\ = 2 \frac{m}{s} [/tex]
Help? Pleaseee! : ))
Answer:
A.) 1.2
Step-by-step explanation:
A cell phone is in the shape of a rectangular prism, with a length of 4 inches, a width of 2 inches, and a height of 1 inch. What is the volume of the cell phone?
Answer:
8
Step-by-step explanation:
V=whl=2·1·4=8
Volume = width times length times height = 2 x 1 x 4 =8
I hope this helps!!
What operation do we use to solve unit rate?
FAST PLEASE
Answer:
Step-by-step explanation:
Calculator Use
A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Answer:
A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
I suck at math.
A slice of a pie weighs 8 ounces. How many pounds do 6 slices of pie weigh? (2 points)
Group of answer choices
2 pounds
3 pounds
4 pounds
5 pounds
Answer:
3 lbs
Step-by-step explanation:
There are 16oz in 1 lb
Therefore, 2 pieces of pie is 1 lb
Divide 6 by 2 and you get 3 lbs
What two plane geometric figures are ALWAYS similar?
What can be used to show the difference in variation for two populations that have equivalent measures of center?
A.
minimum
B.
maximum
C.
median
D.
mean absolute deviation
1. C
2. D
3. A
4. A
5. C
6. A
7. Do yourself
At Lincoln Middle School, 1/3 of the students play a musical instrument. Of the students who play instruments, 3/4 tried out for the class play. What is the probability that a student
selected at random plays a musical instrument and tried out for the class play?
25%
33%
66%
75%
The probability that a student selected at random plays a musical instrument and tried out for the class play is 25%.
To find the probability that a student selected at random plays a musical instrument and tried out for the class play, we need to multiply the probabilities of each event happening.
Given:
Probability of a student playing a musical instrument = 1/3
Probability of a student who plays an instrument trying out for the class play = 3/4
To find the combined probability, we multiply these probabilities:
Probability = (1/3) * (3/4)
Simplifying the multiplication:
Probability = 1/4
Converting the fraction to a percentage:
Probability = 1/4 * 100% = 25%
Therefore, the probability that a student selected at random plays a musical instrument and tried out for the class play is 25%.
To know more about probability here
https://brainly.com/question/23417919
#SPJ2
Otis has saved $18,500 so far to buy a house. He can put this amount into account that earns 5.1% simple interest, or another with 5.1% compounded annually. Which method of earning interest should he choose simpler compound and how much more interest will the account earn using that method after four years?
F. Compound interest $15,106.30
G. Simple interest $15,106.30
H. Simple interest $298.65
J. Compound interest $298.65
Answer:
J Compound interest; $298.65
Step-by-step explanation:
Interest compounding pays interest on the interest. For the same annual rate, any amount of compounding will earn more interest.
For short time periods, the effect of compounding is not great. In general, it will be a fraction of the equivalent simple interest rate. Here, the effective multiplier for annual compounding is ...
1.051^4 = 1.22024337
and the effective multiplier for simple interest is ...
1 +0.051·4 = 1.204
Then the difference in interest rate multiplier for the 4-year period is ...
1.22024337 -1.204 = 0.01614337
That fraction of the $18500 principal is $298.65.
Compound interest earns $298.65 more than simple interest in this scenario.
Hope this helps, have an amazing day!
Mona is going shopping! She bought 3 teeshirts, each costing the same price of -$15.00. This can be modeled with the equation: 3(-15).
Answer:
Yes
Step-by-step explanation:
Yes, equation 3(-15) is basically saying that you are spending -15, 3 times and that those two numbers are being multiplied together which would give you the total cost of all the shirts you are buying. That being said, no purchase would be a negative value, this is most likely an error made when writing the question but the cost of each individual shirt should be $15 and not -$15. Therefore making the actual equation 3(15). We can even equal this to the variable C which would represent the total cost of the purchase and make it more of a real equation.
C = 3(15)