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
Show that 0-58200-48826-5 is a valid UPC number.
Answers
Answer:
Proved
Step-by-step explanation:
Given
[tex]UPC = 0-58200-48826-5[/tex]
Required
Show that it is valid
Add up the elements at odd positions
[tex]Odd = 0 + 8 + 0 + 4+8+6[/tex]
[tex]Odd = 26[/tex]
Multiply by 3
[tex]Product = 26 * 3[/tex]
[tex]Product = 78[/tex]
Add up the elements at even positions
[tex]Even = 5 + 2 + 0 + 8 + 2 + 5[/tex]
[tex]Even = 22[/tex]
Add up both results
[tex]Result = 78 +22[/tex]
[tex]Result = 100[/tex]
Take modulus of 10
[tex]Result \% 10 = 100 \% 10[/tex]
[tex]Result \% 10 = 0[/tex]
Since the result of the modulus is 0, then the number is valid
in a cave, a stalactite gets 4 millimeters longer each year. This year it is 72 centimeters long. How many years until it is 1 meter long?
Answers
lmk if this helped :)
Which is NOT a way to state the meaning of the expression c+5?
Answers
what is the word capacity mean
Answers
Answer:
the maximum amount that something can contain. hope this helps :)
Step-by-step explanation:
A hula hoop is 113 inches around. What is its diameter to the nearest inch?
HURRY PLEASE
Answers
Answer:
35.97
Step-by-step explanation:
113 divided by pie (3.14)
Question 1
Researchers want to find a way to increase the growth rate of corn so it can be harvested more often. To test the effectiveness of a new type of spray fertilizer, plants grown from 200 corn seeds were divided equally into two groups: a treatment group and a control group. The treatment group was frequently sprayed with the new type of fertilizer. The growth in centimeters of each corn plant was noted before and after the treatment.
The results showed that the mean change in the growth rate by the treatment group is 8 points more than that of the control group. To test whether the results could be explained by random chance, researchers created a table that summarizes the results of 1,000 re-randomizations of the data with differences of means rounded to the nearest 2 points.
Consider the significance level to be set at 5%, so results less than 5% can be considered statistically significant.
Part B
Question
Which statement is true about the result considering a significance level of 5%?
The result is not statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.
The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.
The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does not increase the growth rate.
The result is not statistically significant, which implies that this result could be due to random chance.
Answers
Answer:
So what are you asking me to do
Answer:
A.
Step-by-step explanation:
Question and choices are in the photo please explain the answer
Answers
Answer: The correct option is B.
Step-by-step explanation:
(x+5)(2x-1)=3(x+5)
Multiply the parentheses
2x^2 - x + 10x - 5 = 3x + 15
Collect like terms
2x^2 + 9x - 5 = 3x + 15
Move the expression to the left hand side and change its sign, then equate it to 0
2x^2 + 9x - 5 - 3x -15 = 0
Collect like terms
2x^2 + 6x - 20 = 0
Divide each term of the equation by 2
x^2 + 3x - 10 = 0
Rewrite the expression in factorized form
x^2 + 5x - 2x - 10 = 0
Factor the expression
x(x + 5) - 2(x + 5) = 0
(x + 5) (x - 2) = 0
Separate into possible cases but when the product of factors equals 0, at least one factor is 0.
x + 5 = 0———equation (1)
x - 2 = 0———-equation (2)
Solve the equations
x + 5 = 0———equation (1)
Make x the subject
x = 0 - 5
x = -5
x - 2 = 0———equation (2)
Make x the subject
x = 0 + 2
x = 2
Hence, the possible values of x are -5 and 2.
A computer store bought a program at a cost of $40 and sold it at a selling price of $32.5. Find the percent markdown (Rounded to a whole number) .
Answers
Answer:
answer is 18.76 percent.
Step-by-step explanation:
CP= $40
SP= $32.5
Markdown percent=?
now,
markdown %= CP-Sp/CP×100%
=7.5/40×100%
=750/40
=18.75%
The amount to be reduced is: $40 - $32.5 = $7.5
The percentage decrease is: (7.5 : 40) * 100 = 18.25%
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11 feet cubed.
Which equation gives the volume of the sphere?
V = four-thirds (11) pi
V = two-thirds (11) pi
V = four-thirds (11)
V = two-thirds (11)
Answers
Answer:
A
Step-by-step explanation:
What is the product?
Answers
Answer:
[tex]21x^{7}y^{11}[/tex]
Step-by-step explanation:
Remove the parentheses and take out the constansts.
[tex](7 x 3) x^{2} x^{5} y^{3} y^{8}[/tex]
Simplify 7 x 3 to 21.
[tex]21x^{2} x^{5} y^{3} y^{8}[/tex]
Use the product rule: [tex]x^{a} x^{b} = x^{a + b}[/tex]
[tex]21x^{2 + 5}y^{3+8}[/tex]
Simplify 2+5 to 7.
[tex]21x^{7}y^{3+8}[/tex]
Simplfiy 3 + 8 to 11.
[tex]21x^{7}y^{11}[/tex]
Frida goes shopping and buys one sweater for $35 and jeans that cost $25 per pair. She has $115. Which inequality represents the number of jeans Dalecia can buy.
Answers
Answer: i have no idea how do i get rid of this answer
Step-by-step explanation:
John had to pay a combined electric and gas bill $150. The electric portion of the bill was $90. What is the ratio of money spent on electric to that on gas?
Answers
Given:
John had to pay a combined electric and gas bill $150.
The electric portion of the bill was $90.
To find:
The ratio of money spent on electric to that on gas.
Solution:
Let x be the amount of gas bill.
The electric portion of the bill was $90 and John had to pay a combined electric and gas bill $150. So,
[tex]90+x=150[/tex]
[tex]x=150-90[/tex]
[tex]x=60[/tex]
The gas portion of the bill was $60.
The ratio of money spent on electric to that on gas is:
[tex]\text{Required Ratio}=\dfrac{\text{Electric bill}}{\text{Gas bill}}[/tex]
[tex]\text{Required Ratio}=\dfrac{90}{60}[/tex]
[tex]\text{Required Ratio}=\dfrac{3}{2}[/tex]
[tex]\text{Required Ratio}=3:2[/tex]
Therefore, the ratio of money spent on electric to that on gas is 3:2.
A bag contains three red marbles and two blue marbles.
(1.) What is the probability of reaching in and pulling out a red marble?
(2.) Chloe reaches in the bag, pulls out a marble, puts it back in the bag, and pulls out another marble. What is the probability that both marbles are blue?
(3.) Chloe reaches in the bag, pulls out a marble, does NOT put it back in the bag, then pulls out another marble. What is the probability that both marbles are blue?
Thank you
Answers
Answer:
1. 3/5
2. 2/5
3. 1/5
Step-by-step explanation:
I'm pretty sure this is the answer :)
2. 2/5
3. 1/5
I hope this helps!
Mark is building a sandbox inside a play area. How much play area remains outside of the sandbox?
Answers
Answer:125
Step-by-step explanation:
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.
If one of the longer si
des is 6.3 centimeters, which equation can be used to find the length of the base
Answers
Answer:
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 3.1
If equation is x + y = 3 and x - y = 7 then the value of x will be?
A) 0
B) -3
C)-2
D)2
Its on the topic Simultaneous equations
Answers
Answer:
x = 5
Step-by-step explanation:
Add the equations
x + y = 3
x - y = 7
––––––––
2x = 10
Divide both sides by2
x = 5
Note: for the equations in the question,
none of the given answers are correct.
Have a nice day
Which set of numbers includes only integers?
Rational Numbers
Integers
Whole Numbers
-5, - 32.1,
23
Answers
Answer:
Second one
Step-by-step explanation:
Integers are any whole numbers ( can be negative or positive )
The only answer choice that contains only whole numbers is the second one
pleaseeee answer as fast as possible
Rohan went to bank with Rs. 75,000 to buy American dollars. Then he brings ______ USD. If selling rate = Rs. 76/USD & buying rate = Rs. 75/USD *
Answers
Answer:
$986.84
Step-by-step explanation:
exchange rate is the rate at which one currency is exchanged for another currency
Amount of dollars bought = amount of RS / selling rate
75,000 / 76 = $986.84
statement of pythagoras theorm no need proof only statement plz need fast
Answers
Answer:
Pythagoras Theorem: It is a basic relation in Euclidean geometry among the sides of a right-angled triangle. Pythagoras Theorem is commonly used to find the length of an unknown side in a right-angled triangle. It describes the interrelationship between the base, perpendicular and hypotenuse of a right-angled triangle. The converse of Pythagoras Theorem is used to check whether a triangle is a right-angled triangle or not
Step-by-step explanation:
Statement of Pythagoras Theorem
The Pythagoras Theorem states that in a right-angled triangle the sum of square of the base and square of the perpendicular is equal to the square of the hypotenuse.
Pythagorean theorem
In the right angled triangle there is a relationship that governs the length of the three sides. if we knows the length of any two sides, the third side may be calculated by the use of the Pythagorean theorem. this theorem States the square on the hypotenuse of a right angle triangle is equal to the sum of the squares on the remaining two sides.
Very easy question I will mark you brainliest
1. Is 29 monomial or not monomial ?
Yes or No
2. 5x^7 monomial or not monomial
yes or no
Answers
Answer:
1. Yes
2. Yes
Step-by-step explanation:
A monomial is an algebraic expression consisting of one term. So, 29 is a monomial.
[tex]5x^{7}[/tex] has only one term. So, [tex]5x^{7}[/tex] is a monomial.
True or false, with method of elimination, think about what you can multiply one equation by so that a variable will be eliminated when the two equations are added.
Answers
Answer:
True i think
Step-by-step explanation:
what is (2x2 + 4x − 3)(x2 + 2) distributived ?
Answers
Answer:
2x⁴ + 4x³ + x² + 8x - 6
Step-by-step explanation:
(2x² + 4x - 3)(x² + 2)
2(x² + 2) · x² + 4x(x² + 2) - 3(x² + 2)
2x⁴ + 4x² + 4x(x² + 2) - 3(x² + 2)
2x⁴ + 4x² + 4x³ + 8x - 3x² - 6
2x⁴ + x² + 4x³ + 8x - 6
2x⁴ + 4x³ + x² + 8x - 6
What value of c is needed to complete the square?
X2 + 10x + c = -3+ c
Answers
Answer:
Step-by-step explanation:Let's solve for c.
x2+10x+c=−3+c
Step 1: Add -c to both sides.
x2+c+10x+−c=c−3+−c
x2+10x=−3
Step 2: Add -x^2 to both sides.
x2+10x+−x2=−3+−x2
10x=−x2−3
Step 3: Add -10x to both sides.
10x+−10x=−x2−3+−10x
0=−x2−10x−3
Step 4: Divide both sides by 0.
0
0
=
−x2−10x−3
0
c=
−x2−10x−3
0
Answer:
c=
−x2−10x−3/0
hope it helps :D
Encuentra la factorizacion
Answers
Answer for points
3(3x3)(45x6)(45x7)(56x5)(5x5)x0
Answers
Answer:
0
Step-by-step explanation:
3(3x3)(45x6)(45x7)(56x5)(5x5)x0 =0
A full waterbed mattress is 6 ft by 2 ft by 1 ft. The mattress is to be filled with water that weighs 62.4 lb /ft3. Find the weight of the water in the mattress to the nearest pound.
Answers
Answer:
749 lbs
Step-by-step explanation:
weight of the water in the mattress = volume of the mattress x weight of water
volume of the mattress = volume of a cuboid = length x width x height
6 x 2 x 1 = 12 ft³
weight of the water in the mattress = 12 x 62.4 = 748.8 lbs
749 lbs to the nearest pound
The values in the table represent a function.
A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12.
Use the drop-down menus to complete the statements.
The ordered pair given in the first row of the table can be written using function notation as
.
f(3) is
.
f(x) = –5 when x is
.
Answers
Answer:
4rfjq3yr i
Step-by-step explanation:
Answer:
✔ f(–6) = 8
✔ –2
✔4
Step-by-step explanation:
Got them right just now on Edge !!!
Help! What is the answer?
Answers
Answer:
c ......................
help guys pls i beg u cannot do the math this so hard someone help ☺️☺️☺️☺️☺️☺️☺️☺️
Answers
200 because that’s what she needs to equal. Then multiple 13.5 by V because you are accounting for how many times she visits and how many points she will get per visit. Then you add 65 because she already has that amount from signing up.
V >= 10
What is the range of the function shown below?
Answers
Answer:
y ≤ 0
Step-by-step explanation:
The correct option is option C. The range of the given function is less than or equal to zero i.e., y ≤ 0.
What are domain and range of a function?
Range is the set of all values that the given function can output, whereas domain is the input or set of values for which the function is defined.
The graph of a function is shown. We know that the range of function is the output of the input of values we give to the function. Another thing to keep in mind is that we often plot functions with the outputs on the vertical axis and the inputs on the horizontal axis.
From graph it is clear that the function is going down from axis to negative y - axis.
So , it is clear that range will be less than or equal to zero.
i.e.,
Range is :
y ≤ 0
Therefore , the correct option is option C. The range of the given function is less than or equal to zero i.e., y ≤ 0.
Learn more about range of a function here :
https://brainly.com/question/10197594
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