Given:
A fourth-degree polynomial function has zeros 4, -4, 4i , and -4i .
To find:
The fourth-degree polynomial function in factored form.
Solution:
The factor for of nth degree polynomial is:
[tex]P(x)=(x-a_1)(x-a_2)...(x-a_n)[/tex]
Where, [tex]a_1,a_2,...,a_n[/tex] are n zeros of the polynomial.
It is given that a fourth-degree polynomial function has zeros 4, -4, 4i , and -4i. So, the factor form of given polynomial is:
[tex]P(x)=(x-4)(x-(-4))(x-4i)(x-(-4i))[/tex]
[tex]P(x)=(x-4)(x+4)(x-4i)(x+4i)[/tex]
[tex]P(x)=(x-4)(x+4)(x^2-(4i)^2)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
On further simplification, we get
[tex]P(x)=(x-4)(x+4)(x^2-4^2i^2)[/tex]
[tex]P(x)=(x-4)(x+4)(x^2+16)[/tex] [tex][\because i^2=-1][/tex]
Therefore, the required fourth degree polynomial is [tex]P(x)=(x-4)(x+4)(x^2+16)[/tex].
The fourth degree polynomial is given by f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
Polynomial
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Polynomials can be classified based on degree as linear, quadratic, cubic, fourth degree.
Let f(x) represent the function with zeros 4, -4, 4i , and -4i. Hence:
x = 4; x = -4; x = 4i; x = -4i
x - 4 = 0; x + 4 = 0; x - 4i = 0; x + 4i = 0
f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
The fourth degree polynomial is given by f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
Find out more on polynomial at: https://brainly.com/question/2833285
The ratio of boys to girls in the 10th grade is 8 to 13. If there are 91 girls in 10th grade, then how many boys are there?
Answer: There are 56 boys in the 10th grade
Step-by-step explanation:
Step 1
ratio of boys to girls in the 10th grade is 8 :13
Number of girls= 91
To find the number of boys, we first find the total number of boys and girls in the 10th grade
Step 2
Now the total ratio= 8 +13=21
Number of girls = ratio of girls/ total ratio x Total number of students
91=13/ 21 x Total number of students
Total number of students =21 x 91 / 13 =147
Step 3
Therefore Number of boys =ratio of boys/ total ratio x Total number of student
8/21 x 147=56
Mrs. Lindsay doesn't have a cat crate and needs to take her cats to the vet. She's
going to make a box out of a 8 foot by 8 foot piece of cardboard. How many feet
should Mrs. Lindsay cut from the corners to have the maximum amount of space
inside the box?
Answer:
The amount to remove from each corner is a square, 4/3 ft by 4/3 ft.
Step-by-step explanation:
The piece of cardboard measures 8 ft by 8 ft.
Each corner will be cut to create the sides of the box.
Let the square cut from each corner measure x by x ft.
The base of the box will measure 8 - 2x by 8 - 2x, and the height of the box will be x.
V = (8 - 2x)^2 * x
V = 64x - 32x^2 + 4x^3
Now we differentiate and set the derivative equal to zero to find a maximum value.
64 - 64x + 12x^2 = 0
3x^2 - 16x + 16 = 0
(3x - 4)(x - 4) = 0
3x - 4 = 0 or x - 4 = 0
3x = 4 or x = 4
x = 4/3 or x = 4
The solution x = 4 must be discarded since 8 - 2x = 8 - 8 = 0, and the sides would have 0 length.
The amount to remove from each corner is a square, 4/3 ft by 4/3 ft.
hey in need of help please help me
Consider matrix L, a 13x7 matrix. How many elements are in matrix L?
Answer:
14
Step-by-step explanation:
Answer: 25
Step-by-step explanation:
I got it wrong so heres the right answer
A password contains five digits, such as 17467. How many different passwords can be formed? Help please
Answer:
Step-by-step explanation:
100,000
The number of different passwords can be formed by; 1,00,000
How to identify the place value of a digit in a number?The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths, and so on
Given that the password contains five digits, such as 17467.
In general total digits = 10 [ from 0 to 9]
If a password contains five digits, then by the fundamental principal of counting, then the total number of different passwords;
[tex]10^5[/tex] = 1,00,000
Hence, the number of different passwords can be formed by; 1,00,000
Learn more about place value here:
https://brainly.com/question/17983725
#SPJ2
John can play 12 songs on the guitar and he
learns 1 new song each week. Aiden can play 4 songs.
but he learns 2 each week. How many weeks (w) will it
be before Aiden knows as many songs as John?
Answer:
8 weeks
Step-by-step explanation:
Let
w = number of weeks
John = 12 + w
Aiden = 4 + 2w
How many weeks (w) will it be before Aiden knows as many songs as John?
Equate both John and Aiden expression
John = Aiden
12 + w = 4 + 2w
Collect like terms
12 - 4 = 2w - w
8 = w
w = 8 weeks
It will take 8 weeks before Aiden knows as many songs as John
A scaled drawing of May’s room is a square with an area of 16 square inches. If her actual bedroom has a side length of 12 ft, what is the scale of the drawing? 1in = _____ ft
Answer:
9 ft
Step-by-step explanation:
your area in the model is 16 in, and to get area you do LxW or BxH same thing. The room is a square, which means all sides are going to be 12ft. multiply 12 by 12=144 now you have
16in=144ft
then you divide 144 by 16 and get 9.
1in=9ft
Sry if im wrong, have a great day/night :}
Edit: yes i was wrong
A number has the same digit in its hundreds place and its hundredths place. How many times greater is the value of the digit in the hundreds place than the value of the digit in the hundredths place?
Answer:
372
Step-by-step explanation:
that's my answer hope it's help
Answer:
1000
Step-by-step explanation:
7. Find the length of HP.
12
P
9
H
Step-by-step explanation:
hope it is helpful to you
Answer and Step-by-step explanation:
To find the length of HP, we must use the Pythagorean Theorem.
This theorem helps us solve for the sides of any right triangle.
The equation for the Pythagorean Theorem is:
[tex]a^{2}+ b^{2} = c^{2}[/tex], in which a and b are the legs, while c is the hypotenuse.
Let's plug in our values into the equation to find the length of HP.
We will use the variable x to represent HP.
[tex]9^{2}+ 12^{2} = x^{2} \\\\\\Square.the.9.and.the.12.\\\\\\81 + 144 = x^2\\\\\\Add.\\\\\\225 = x^2\\\\\\Square.both.sides.\\\\\\\sqrt{225} = \sqrt{x^2} \\\\\\15 = x = HP[/tex]
So, we get our answer to be 15.
The length of HP is 15.
#teamtrees #PAW (Plant And Water)
need help again!! with a similar question
Answer:
9 gal
Step-by-step explanation:
Which of the following could be true if y ≤ -75?
Hello!
Lets go through each choice, and determine if it is correct.
So, the symbol ≤, means less than or equal to. So our answer must be less than -75 or -75 on the dot.
A: y = 75
Okay, so we can tell this one is wrong off the bat. 75 is much more than -75. (Make sure you notice the symbol!) So it cannot be equal to said answer. A is wrong.
B: y =-74
Another trick question! When you are in the negatives, less is more! So -74 is actually greater than -75. This is also incorrect!
C: y > -75
This one is straight forward. Our equation up top strictly says less than or equal too, while C says greater than. Incorrect!
D: y = -75
The last answer! We see that the symbol in our equation up top says less than or equal too, and y = -75 is equal. This is the correct answer.
Our correct answer is D: y = -75
waffletowne
PLS ACTUALLY HELP ME , I WILL MARK BRAINLIEST
Answer: 15/8
Step-by-step explanation:
100 points / i suck at this
Alison runs a mile in 5 minutes and 50 seconds. Elizabeth runs a mile in 6 minutes and 40 seconds. What is the ratio of Alison's time to Elizabeth's time?
a) 7:8
b) 5.5:6.4
c) 55:64
d) 8:7
Answer:
7:8
Step-by-step explanation:
First, convert their times to common units. You'll want to put it in seconds:
5 minutes and 50 seconds = 350 seconds
- multiply 5 minutes by 60 to get it into seconds and then add the other 50 seconds to it
- for Elizabeth's time, multiply 6 by 60 seconds and add 40 to it
To get the ratio of their times, divide Alison's time by Elizabeth's time:
350 ÷ 400 = 7:8
Answer:
a) 7:8
Step-by-step explanation:
Alison: 5 minutes and 50 seconds = 355 seconds
Elizabeth: 6 minutes and 40 seconds = 400 seconds
355:400, reduces to 71:80 or 7:8
QUICK will give brainlist
What is the shape of each half of the pentagon?
Answer:
trapezoid
Step-by-step explanation:
Answer:
Trapezoids and diamonds but you really have to look closely
Step-by-step explanation:
Using Angle Relationships to Solve Equations
Answer:
x+x+4+3x-9=90
5x-5=90
5x=95
x=19
9. 19
10. 19+4=23
11. 3×19-9=48
determine the domain of the following graph
Answer:
[-5, 10) or you can write [tex]-5\le x < 10[/tex]
Step-by-step explanation:
The domain is the set of all values of x used in the function. Scan across the graph from left to right (much as you do when reading). The first point you find on the graph has an x-coordinate 5 (see the solid dot?). Then, as you continue reading across the graph, there are values of x used until you get to 10. The dot at x = 10 is open, not filled in. That indicates that the number x = 10 is NOT used by the function.
So the domain is all real numbers greater than or equal to -5 and less than 10.
[-5, 10) is called interval notation; a square bracket means the value next to it IS used by the function, a parenthesis means the value next to it is NOT used.
what is the surface area, in centimeters, of a cube with a side length, s. of 1/3cm?
Please help me will give brainliest!
Answer:
3a) -22 + 5 = -17
3b) -22 - (-5) = -22 + 5 = -17
3c) (-22)(-5) = 110
3d) -22 ÷ 5 = -4.4
Hope this helps!
Step-by-step explanation:
a) -22+5=-17
b)-22+5=-17
c)-22_5=-27
d)-22÷5=-4.4
......help due in a minute
Answer:
The answer is ''C''
Hope this helps!! Have a great day! <3
Answer: D ( I really don’t have a good explanation for this question.)
b) A men earns Rs.50000 in a month. He spends 30% of his income on foood
2/5 on his child's Education,0.25% on transportation and rest he saves.
i) Find the amount that he spends on each topic.
ii)Find his saving percentage.
Answer:
[tex]\huge\mathfrak\pink{ here's your solution } \\ \\ im \: soo \: happy \: [/tex]
help will be appreciated ty :)
Answer:
7 Gallons and 6 pints !
Step-by-step explanation:
62 ÷ 8 = 7.75 gal.
0.75 gallons is 6 pints.
So, Its 7 gallons and 6 pints
Answer:
7 gallons 4 pints
Step-by-step explanation:
2 pints = 1 quart and 4 quarts = 1 gallon, and so 8 pints = 1 gallon
Write and solve an equation of proportions to answer this question:
8 pints 1 gal
--------------- = -----------
62 pints x
Cross-multiplying, we get 8x = 62, or 7 1/2.
That's 7 gallons 4 pints.
If cosec theta-cot theta is equal to 1/M then what is the value of cosec theta +cot theta
Given:
[tex]\text{cosec}\theta -\cot \theta =\dfrac{1}{M}[/tex]
To find:
The value of [tex]\text{cosec}\theta +\cot \theta [/tex].
Solution:
We have,
[tex]\text{cosec}\theta -\cot \theta =\dfrac{1}{M}[/tex]
We know that,
[tex]\text{cosec}^2\theta -\cot^2 \theta=1[/tex]
It can be written as:
[tex](\text{cosec}\theta -\cot \theta)(\text{cosec}\theta +\cot \theta)=1[/tex]
[tex]\dfrac{1}{M}\times (\text{cosec}\theta +\cot \theta)=1[/tex]
[tex]\text{cosec}\theta +\cot \theta=1\times M[/tex]
[tex]\text{cosec}\theta +\cot \theta=M[/tex]
Therefore, the value of [tex]\text{cosec}\theta +\cot \theta [/tex] is [tex]M[/tex].
sum of 20 and 8 minus the product of 3 and 5
Answer and Step-by-step explanation:
The sum of 20 and 8 would look like
20 + 8
Then we have to subtract the product of 3 and 5 from the sum of 20 and 8.
(20 + 8) - 3(5)
^That is the expression^
The answer, when you evaluate the expression, is:
28 - 15 = 13
#teamtrees #PAW (Plant And Water)
Ke'Andre joined the swim team. His high dive jump is modeled by the following equation: f(x) = -16x² + 24x +6.
25. A sequence of positive integers with 2020 terms is called an FT sequence if each term
after the second is the sum of the previous two terms. For example, if the first two
terms of an FT sequence are 8 and 7, the sequence would begin 8,7,15,22,37,....
For some positive integer m, there are exactly 2415 FT sequences where the first two
terms are each less than 2m and the number of odd-valued terms is more than twice
the number of even-valued terms. What is the value of m?
(A) 21
(B) 69 (C) 115 (D) 35 (E) 105
Answer:
The first term in the sequence is odd-valued and so there are m choices for it.2020 Gauss Contest Solutions Page 19
The second term in the sequence is even-valued and so there are m − 1 choices for it.
Thus, there are a total of m × (m − 1) FT sequences that begin with an odd-valued term
followed by an even-valued term.
Finally, we consider the FT sequences that begin with an even-valued term followed by an
odd-valued term (Parity #4).
Again, there are exactly twice as many odd-valued terms as there are even-valued terms in the
first 2019 terms (since the pattern repeats even, odd, odd).
However in this case, the 2020th term is even and so there are fewer than twice as many odd valued terms as there are even-valued terms.
Thus, there are m2 + m × (m − 1) FT sequences that satisfy the required conditions.
Since there are 2415 such FT sequences, we may solve m2 + m × (m − 1) = 2415 by trial and
error.
Evaluating m2 + m × (m − 1) when m = 30, we get 302 + 30 × 29 = 1770, and so m is greater
than 30.
When m = 33, we get 332 + 33 × 32 = 2145.
When m = 34, we get 342 + 34 × 33 = 2278.
When m = 35, we get 352 + 35 × 34 = 2415, as required.
Answer: (D)
Step-by-step explanation:
Hey can you help me fast!!
(PS. I used to HATE i-ready)
In the XY coordinate plane, the slope of a line is 4 and it passes through the point (1,3). Find the equation of a line that is perpendicular to the given line and intersects it at the given point.
A. y=4x-1
B. y=-4x+7
C. y=1/4x -1
D. y=4x+13/4
E. y=-1/4x+13/4
Answer:
E?
Step-by-step explanation:
I'm sorry of this answer is wrong
x+y=1212
x-y=518
please help me with it
Here,
x+y=1212••••••[tex]\bold{equation~I }[/tex] x-y=518••••••[tex]\bold{equation~II }[/tex]ADDITIONALL,both two equation.
we get that,
x+y+x-y=1212+5182x=1730x=865so,
x-y=518865-y=518y=860-518y=347Find a description this equation represents. Of the numbers 1, 2, 3, 4, and 5, which are solutions to the equation? 3x-8=7
Answer:
5
Step-by-step explanation:
3x - 8 = 7
collect like terms
3x = 8 + 7
3x = 15
divide both sides of the equation by 3
x = 15/3 = 5
Lilly sells 4 boxes of cookies in 60 minutes, at this rate how long will it take her to sell 10 boxes?
Answer:
150 minutes ! 60/4 multiplied by 10!
Step-by-step explanation:
Answer:
Step-by-step explanation:To find out how long it takes her to sell one box you see how many times 4 can go into 60 to get how long it takes to sell one box. So in this case it takes 15 minutes to sell one box. So you take 15 and multiply it by 10. 15 * 10= 150
60/4=15
15*10=150
So it takes 150 minutes to sell 10 boxes of cookies.