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
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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 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
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!
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
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.
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
PLEASE HELP!!!!!!!!!!!!!
Answers
Answer: I think E
Step-by-step explanation:
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
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
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
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 %
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
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
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
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
HELP ASAP- IF YOU ARE CORRECT I WILL MARK BRAINLY
Answers
The Answer is:
B) -3/2
(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.
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
can someone help please.
Answers
Answer:
if im not mistaken is d hope you get it right
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
can someone help with part A please??
Answers
Answer:
Step-by-step explanation:
4 days 9 hours 40 minutes
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
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
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:
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...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
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
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!
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
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
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