According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?
ORX)-(3x? -x-5)(2x-5
1 x) = (3x* +2x)"
o 9x)= (4x2-7)
OM) - Bx - 4y - 1) (3,2-4
Answers
===========================================================
Explanation:
For each expression in the parenthesis of choice A, focus only on the leading terms. Those would be the terms to the very left. The leading terms 3x^2 and 2x^6 multiply to 6x^8. This is the leading term of the final expansion and it's of degree 8. Any degree 8 polynomial will have 8 roots according to the fundamental theorem of algebra. Some of those roots may be complex numbers, or they may be purely real numbers.
Choice B can be ruled out because the leading term 3x^4 is raised to the 4th power to get (3x^4)^4 = 81x^16 as the leading term of the final expansion. This polynomial has 16 roots, but we want 8 roots instead.
Choice C is a similar story to choice B. In this case, we have (4x^2)^3 = 64x^6 as the leading term when you expand everything out. This 6th degree polynomial has 6 roots.
And finally, choice D can be ruled out as well. We follow the same steps as choice A. The leading terms from each parenthesis group multiply to 6x^8*3x^2 = 18x^10 showing we have 10 roots (due to the 10th degree polynomial).
Related Questions
What’s a converse in mathematics
Answers
Answer:
A converse is the result of reversing its two constituent statements.
Example, P-Q. Converse would be Q-P
Find the circumference of a circle with diameter,
d
= 3.2m.
Give your answer rounded to 2 DP.
Answers
Answer:
[tex]circumference = \pi \: d \\ = 3.14 \times 3.2 \\ = 10.05 \: m[/tex]
Answer:
circumference=10.05 m
Step-by-step explanation:
radius =diameter/2
=3.2/2
=1.6 m
circumference=2πr
=2*3.14*1.6
=10.048 m
=10.05 m
Can pls someone help I need help
Answers
9^2 + b^2 = 15^2
81 + b^2 = 225
225 - 81 = b^2
144 = b^2
square root of 144 = 12
b = 12
Amelia is taking a road trip. She drove 250 miles the first day. If 250 is 40% of her total distance, how many miles is her roadtrip in all?
Answers
Answer: 625 miles
Step-by-step explanation:
100-40=60
so she has 60% for her distance so lets munis 40 from it and add 250 to 250
250+250=500
60-40=20
20 is half of 40 so whats half of 250? its 125
so she drove 625 miles for her road trip 2 and 1/2 a day
HELP ASAP- IF YOU ARE CORRECT I WILL MARK BRAINLY
Answers
The Answer is:
B) -3/2
can someone help with part A please??
Answers
Answer:
Step-by-step explanation:
4 days 9 hours 40 minutes
what is the volume of the following rectangular prism 9/5 units 2/3 units
Answers
Answer:
1.2
Step-by-step explanation:
9/5*2/3=1.2
can someone help please.
Answers
Answer:
if im not mistaken is d hope you get it right
asma is drawing a picture of a tree.she drawss a 15m tree as 3cm in her drawing book. if a fruit acctualy hangs from branch 3 m from the ground how high must asma draw it to keep the proportion correct?
Answers
Answer:
0.6 cm
Step-by-step explanation:
she divided the the height of the tree 500, so the same factor has to be applied to everything else
3m * 1/500 = 0.6cm
How many liters are equivalent to 25 ml
Answers
Answer:
0.025 liters
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
0.025 liters
Step-by-step explanation:
Subtract: (-137° + 6) - (-43°) Your answer should be in simplest terms. Enter the correct answer.
Answers
Answer:
-9y⁹ + 6
Step-by-step explanation:
Subtracting a negative makes it positive
-13y⁹ + 6 + 4y⁹
combine like terms
-9y⁹ + 6
Shelly purchased 6 25'-tape
measures and 2 chalk line reels for
$78. Sean purchased one 25'-tape
measure and 3 chalk line reels from
the same store for $29. What was
the price of each 25'-tape measure
and each chalk line reel?
Answers
Answer:
Price of one 25'-tape measure = $11
Price of one chalk line reels = $6
Step-by-step explanation:
Let t = price of one 25'-tape measure, and
let c = price of one chalk line reel
"Shelly purchased 6 25'-tape measures and 2 chalk line reels for $78."
6t + 2c = 78
"Sean purchased one 25'-tape measure and 3 chalk line reels ... for $29."
t + 3c = 29
We have a system of two equations in two variables. We will solve it with teh substitution method.
Solve the second equation for t.
t = 29 - 3c
Substitute 29 - 3c for t in the first equation.
6(29 - 3c) + 2c = 78
174 - 18c + 2c = 78
-16c = -96
c = 6
Substitute 6 for c in the second original equation.
t + 3(6) = 29
t + 18 = 29
t = 11
Answer:
Price of one 25'-tape measure = $11
Price of one chalk line reel = $6
14 is what % of 89 if you choose a random answer you will be reported
Answers
Answer:
15.73 %
Step-by-step explanation:
Given :-
14 is what % of 89 .For finding% :-
→ 14/89 * 100
→ 15.73 %
Answer:
15.73% to the nearest hundredth.
Step-by-step explanation:
14/89 = 0.157303
Now multiply by 100
This gives 15.7303 %
Lee ran a mile in 7 1/3 minutes. His friend Sam ran the same mile in 8 5/9 minutes. How many minutes faster did Lee run? (First answer will be the brainliest)
Answers
Complete the point-slope equation of the line through (-8,-8)(−8,−8)left parenthesis, minus, 8, comma, minus, 8, right parenthesis and (-7,9)(−7,9)left parenthesis, minus, 7, comma, 9, right parenthesis.
Use exact numbers.
y-9=y−9=y, minus, 9, equals
Answers
Answer:
[tex]y-9=17(x+7)[/tex]
Step-by-step explanation:
Hi there!
What we know:
The line goes through the points (-8,-8) and (-7,9)We need to write the equation of the line in point-slope formWhat we need to know:
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope of the line and [tex](x_1,y_1)[/tex] is a point that the line passes throughWe're given "[tex]y-9=[/tex]", which is the "[tex]y-y_1[/tex]" part of the point-slope form equation. This means that [tex](x_1,y_1)[/tex] is [tex](-7,9)[/tex] and we only need to solve for m.Our equation so far (plugging in the point (-7,9):
[tex]y-9=m(x-(-7))[/tex]
[tex]y-9=m(x+7)[/tex]
Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-8,-8) and (-7,9)
[tex]=\frac{-8-9}{-8-(-7)}\\=\frac{-8-9}{-8+7}\\=\frac{-17}{-1}\\= 17[/tex]
Therefore, the slope of the line is 17. Plug this into [tex]y-9=m(x+7)[/tex]:
[tex]y-9=17(x+7)[/tex]
I hope this helps!
How many four-digit integers contain only the digits 1, 2, 3, 4, and 5, with the property that no two consecutive digits are the same?
Answers
Answer:
120
Step-by-step explanation:
we solve this question by using permutation because the order matters
nPr
5P4 = 120
What is 2x^2(x-5) divided by 10x when x + 10?
Answers
Answer:
1000
Step-by-step explanation:
2x²(x - 5) ÷ 10x
x = 10
2(10)²(10 - 5) ÷ 10(10)
20²(5) ÷ 100
100² ÷ 100
100000 ÷ 100
1000
simplify 26a+4a-10a
Answers
Answer:
20a
Step-by-step explanation:
26a+4a-10a=30a-10a=20a
Answer:
20a
Step-by-step explanation:
26a+4a-10a
since they are like terms u can add and subtract them
=30a-10a
=20a
Which sequences are geometric? Check all that apply.
Answers
Step-by-step explanation:
A geometric sequence is when we multiply one number by a set rate to obtain the next number.
For the first one, we multiply 5 by 2 to get 10, 10 by 2 to get 20, and so on. This is geometric
Next, we multiply 3 by 4 to get 12, 12 by 4 to get 48, and so on. This is geometric
Next, we multiply 3 by 5 to get 15, 15 by 5 to get 75, and so on. This is geometric
Next, we multiply 8 by 15/8 to get 15, and 15 by 5 to get 75. 15/8 and 5 are not the same so this is not geometric
Next, we multiply 14 by 21/14 to get 21, and 21 by 28/21 to get 28. 21/14 and 28/21 are not the same so this is not geometric
Next, we multiply 17 by 20/17 to get 20, and 20 by 23/20 to get 23. 20/17 and 23/20 are not the same so this is not geometric.
Finally, we multiply 2 by 5 to get 10, 10 by 5 to get 50, and so on. This is geometric
HELPP!!!!!x
And thanks!
Answers
Answer:
7/10 > 17/25
Step-by-step explanation:
17/25 and 7/10
The common denominator is 50
17/25 *2/2 =34/50
7/10 *5/5 = 35/50
35 > 34 so
35/50 > 34/50
7/10 > 17/25
for the same girl again plz.
Answers
Answer:
Option A is correct
Step-by-step explanation:
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
Hope it is helpful...A• 3.7
B• 3.8
C• 5.3
D• 5.4
Answers
Answer:
D 5.4
Step-by-step explanation:
The pythagoras theorem states that a² + b² = c²
2² + 5² = ?²
4 + 25 = ?²
29=?²
? =
[tex] \sqrt{29} [/tex]
? = 5.4 rounded 2 sig fig one decimal place
Somebody help i need to find the value of x and classify the sides and angles
Answers
Answer:
a) x=18
b) 36 (2*18)
c) 54 (3*18)
d) I'm not exactly sure what it's asking for, so I don't know
Step-by-step explanation:
triangle sum theorem means the sum of every triangle is 180 degrees
so we can make this equation: 180 = 90 + 2x + 3x
solve and you get 18.
PLEASE HELP!!!!!!!!!!!!!
Answers
Answer: I think E
Step-by-step explanation:
Alex accepted a job as a veterinarian that pays a salary of $78,500 in the first year. After the first year, his salary increased by 1.5% per year.
Alex works for the vet clinic for 10 years. What is the total of his earnings over the 10 years?
Round your answer to the nearest hundredth
$ = _______
Answers
Answer:
795.597,5
Step-by-step explanation:
let's consider the fact that Alex worked for the vet for 10 years. First year is off with $78,500 since that was his first payment, now there are nine years left. With some math operations we find that 1,5% in this problem is equal to 1.177,5$. So if we take that number and put it together with Alexs' first payment we get from now and on his yearly pay, which is $79.677,5. At last we take that number multiply it by 9 and add all the numbers together (78,500+79.677,5(×9)= 795.597,5)
The total of his earnings over the 10 years is $236677.5.
What is interest rate?The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time.
Given
P = $78,500
Interest rate = 1.5 %
Time t = 10 years
Total earning = P[tex](1+\frac{r}{100} )^{t}[/tex]
A = 78500[tex](1+\frac{1.5}{100} )^{t}[/tex]
A = 78500[tex](\frac{1015}{100} )^{10}[/tex]
A = 78500[tex](\frac{230}{200} )^{10}[/tex]
A = $236677.5
Hence, the total of his earnings over the 10 years is $236677.5.
Find out more information about interest rate here
https://brainly.com/question/7279636
#SPJ2
which expression is equivalent to 1/2r + 8p - 3/4r -2p
A. 1/4r -6p
B. 1/4r +10p
C. 1/4r + 10p
D. 5/4r + 6p
Answers
Answer:
D.5/4r+6p
Step-by-step explanation:
hula kong hahha
Can someone tell me which one it is?
Answers
Answer:
-16
Step-by-step explanation:
-16... using d = b²-4ac
Answer:
the discriminant is –16
hope this helps!
(04.02 MC)
4
What is the y-intercept of the line perpendicular to the line y = x + 1 that includes the point (4, 1)?
Answers
Answer:
The intercept of the line perpendicular to the line [tex]y = x + 1[/tex] is 5.
Step-by-step explanation:
The line [tex]y = x + 1[/tex] has a slope 1. By Analytic Geometry, the slope of the line perpendicular to the original line is determine by the following formula:
[tex]m_{\perp} = -\frac{1}{m}[/tex] (1)
Where:
[tex]m[/tex] - Slope of the original line.
[tex]m_{\perp}[/tex] - Slope of the line perpendicular to the original line.
If we know that [tex]m = 1[/tex], then the new slope is:
[tex]m_{\perp} = -\frac{1}{1}[/tex]
[tex]m_{\perp} = -1[/tex]
A line is defined by the following expression:
[tex]y = m\cdot x + b[/tex] (2)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m[/tex] - Slope.
[tex]b[/tex] - Intercept.
If we know that [tex](x,y) = (4,1)[/tex] and [tex]m = -1[/tex], then the intercept of the line perpendicular to the original line:
[tex]b = y - m\cdot x[/tex]
[tex]b = 1+4[/tex]
[tex]b = 5[/tex]
The intercept of the line perpendicular to the line [tex]y = x + 1[/tex] is 5.
Claire's music playlist contains songs she bought and songs her mother bought. The ratio of her songs to her mother's songs is 3:2. Which table shows this ratio and two equivalent ratios?
Answers
Answer:
B.
Step-by-step explanation:
The ratio of Claire's songs to her mother's songs = 3 : 2
A.
3 : 2 = 3/2
9 : 6 = 9/6 = 3/2
12 : 10 = 12/10 = 6/5
B.
3 : 2 = 3/2
6 : 4 = 6/4 = 3/2
15 : 10 = 15/10 = 3/2
C.
3 : 2 = 3/2
4 : 3 = 4/3
5 : 4 = 5/4
D.
3 : 2 = 3/2
4 : 6 = 4/6 = 2/3
20 : 30 = 20/30 = 2/3
The table which shows the correct ratio and two equivalent ratios is B
Find the circumference
Answers
Answer:
75.36 mi
Step-by-step explanation:
Given :-
Radius = 12 mi .We know :-
→ Circumference = 2 π r
→ C = 2 * 3.14 * 12 mi
→ C = 75.36 mi
Answer:
Step-by-step explanation:
circumference of a circle=2πr
=2*3.14*12
=24*3.14
=75.36 mi