Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, [tex]\pm i, \pm 2i, \pm 3i[/tex], a sixth degree function with no real zeros is formed, so the answer is Yes.
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
What are the coordinates of point B' after
AABC is reflected across the y-axis?
5 y
А
В'
?
?
с
B (3,2
-5
0
-5
Answer:
B'(-3, 2)
Step-by-step explanation:
The rule for a reflection over the y-axis is (x, y) → (-x, y)
This means that the x-values change while the y-values stay the same.
B(x, y) → (-x, y)
B(3, 2) → (-3, 2)
B'(-3, 2)
Hope this helps!
Derek saves 10% of his paycheck each week to buy a mountain bike the mountain bike costs 340.00 Derek receives a paycheck in the amount of $280.50 each week how many paychecks will Derek have to receive before he has saved enough money to buy the mountain bike
Answer: 13 weeks
Step-by-step explanation:
First you have to find 10% of 340.00 which is 28, so each week he saves 28.00 for his bike. To find how many paychecks he has to recieve you divide 340.00 by 28.00, which is 12.1, since there is a decimal place you have to round it up to 13 because it is a little bit more than 12 paychecks. ;)
its 8th grade math super easy
[tex] {15}^{2} + {x}^{2} = {39}^{2} [/tex]
x = 36
^● ●^
Answer:
36
Step-by-step explanation:
You can use Pythagorus to solve this. 39^2-15^2=1296. √1296 is 36
PLEASE CHOSE THE RIGHT ANSWER AND EXPLAIN WHY YOU CHOSE IT PLEASE
Answer:
D
Step-by-step explanation:
See attached image.
Ramon and Hector ride their bikes at constant rates during a race. Ramon rides 45 miles in 3 hours. The distance, y, in miles, Hector rides in x hours is given by the equation y = 18x. Which statement is true?
No answer text provided.
No answer text provided.
Ramon rides his bike 3 miles per hour faster than Hector rides his bike.
Ramon rides his bike 27 miles per hour faster than Hector rides his bike.
Ramon rides his bike 3 miles per hour slower than Hector rides his bike.
Ramon rides his bike 27 miles per hour slower than Hector rides his bike.
We will find the speeds of both persons, the correct option is:
"Ramon rides his bike 3 miles per hour slower than Hector rides his bike."
Which statement is correct?First, we know that Ramon rides 45 miles in 3 hours, then its speed is:
S = 45mi/3h = 15mi/h
And we know that Hector position is given by:
y = 18x
Where x is time in hours, so his velocity is 18mi/h.
Then we can see that:
Ramon's speed = 15mi/hHector's speed = 18mi/hSo the correct statement is:
"Ramon rides his bike 3 miles per hour slower than Hector rides his bike."
If you want to learn more about speed, you can read:
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Answer:
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<<<<<<<<<<<<<<<<<<<<
hope it helps...!!!
Please help with this easy math problem. Due soon.
Answer:
Step-by-step explanation:
Exponential equation:
[tex]\boxed{y=a*b^{x}}[/tex]
Choose the point whose x-coordiante is 0, so that we can find the value of a. (0,2)
[tex]2 = a*b^0\\\\2 = a*1 \ [\text{\bf any \ variable raised to 0 is 1}][/tex]
[tex]\sf \boxed{a = 2}[/tex]
Now, choose (1 , 1) and find the value of b
[tex]1 = 2*b^{1}\\\\1 = 2*b\\\\\dfrac{1}{2}=b[/tex]
Exponential equation:
[tex]\bf \boxed{y =2* \left(\dfrac{1}{2}\right)^{x}}[/tex]
A 26 foot ladder is set against the side of a house so that it reaches up 24 feet. If Mila grabs the ladder at its base and pulls it 12 feet farther from the house, how far up the side of the house will the ladder reach now?
Answer
12 feet high
Step-by-step explanation:
The school auditorium has 448 seats arranges in 32 equal rows. How many seats are in each row?
Two-thirds of a number increased by 3 is 11. What is the number?
The Farmer Supply is building storage building for fertilizer shaped top. The that has cylindrica base and cone county laws say that the storage building must have maximum maximum height of 14 feet. Width of 8 feet and trucks deliver fertilizer in loads that are feet tall; feet wide, and 12 feet long_ Farmer Supply Dump wants t0 be able to store dump-truck loads of fertilizer: and height of the cone, h2 that Farmer Supply should use in Determine height of the cylinder; h1 will be able to store at least two dump-truck loads of fertilizer: the design: Show that your design Enter your answer and your work in the space provided
Assuming ℎ1 = 11 feet and ℎ 2 = 3 feet, the storage of the facility is going to be 603 cubic feet, which is more than 576 cubic feet
The diameter of the building has been given as 8cm
radius = d/2 = 8/2 = 4
Maximum height = h1 + h2 = 14
Find the volume of the fertilizer that is containeed in both of the trucks
2(12x4x6) = 576 feet
From the height of 14 feets we have to assume
h1 = 11 ft,
h2 = 3 ft
How to solve for volume[tex]volume =\frac{1}{3} \pi r^{2} h2 + \pi r^{2} h1[/tex]
= 0.333*3.14*4²*3 + 3.14*4²*11
= 602.8 ft ≈ 603
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Lin goal is to drink 8 cups of water every day she drags 37 oz of for lunch today how much more water does Linda need to drink today to reach her goal
Answer: 27
Step-by-step explanation:
8 cups of water is 64 Ounce. If she had 37, She needs 64 - 37 To balance up
PLS HELP
No links pls and Ty <33!!!
Answer:
C = 2πr = 2·π·20 ≈ 40π ft (125.6)
Where is the removable discontinuity of f (x) = startfraction x 5 over x squared 3 x minus 10 endfraction located? x = –5 x = –2 x = 2 x = 5
The removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).
What are discontinuities?Holes in the graph of function, where its undefined, or non-continuous, is called discontinuity.
The points in the domain of the function over which its not continuous, is called point of discontinuity for that function.
What is removable discontinuity?A discontinuity is removable if the limit of the function at the point of discontinuity exists but this limiting value is not the value of the function at that point.
We can remove that discontinuity by making the value of the function equate to the limiting value of the function at that point.
The given function is:
[tex]f(x) = \dfrac{(x+5)}{(x^2 +3x-10)}[/tex]
Factoring the denominator, we get:
[tex]x^2 + 3x -10 = x^2 + 5x - 2x - 10 =x(x+5) - 2(x+5) = (x+5)(x-2)[/tex]
Therefore, we get:
[tex]f(x) = \dfrac{(x+5)}{(x+5)(x-2)}[/tex]
The function is not defined if x = -5, or x = 2 since at those places, the denominator would become 0. (we cannot cancel out (x+5) from numerator and denominator for all x, as it isn't defined for x = -5
Also, we have:
[tex]\lim_{x\rightarrow 2}f(x)= \infty\\\lim_{x\rightarrow -5}f(x) = \lim_{x\rightarrow -5}\dfrac{(x+5)}{(x+5)(x-2)} = \lim_{x\rightarrow -5}\dfrac{1}{(x-2)} = -\dfrac{1}{7}[/tex]
We cancelled out (x+5) from numerator and denominator because x is limiting to -5 but isn't equal to -5.
For discontinuity of x = -5, the limit of f(x) exist (left and right limit both will come as 1/3). But f(-5) is not defined. So we can remove this discontinuity by defining f(-5) = 1/3 and for rest of the values of x, it is same as before.
Thus, the removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).
Learn more about discontinuities here:
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Answer: Option A -5
Step-by-step explanation: Just took the test
help me out on this problem
What is the measure of side opposite to 45 degree if the side opposite to 90 degree is 4
Answer:
[tex]2\sqrt{2}[/tex]
Step-by-step explanation:
if the given figure is triangle, then the required length can be calculated:
[tex]\frac{4}{\sqrt{2} } =2\sqrt{2}.[/tex]
additional info: sin45°=1/√2.
Who ran at a faster constant rate and which equation represents the relationship between Paul's distance and his time
A = Paul ran at a slower constant speed than Melinda, y=1x x being time in hours y being the distance in miles Paul ran
B = Paul ran at a slower constant speed than Melinda, y =3x x being time in hours, y being distance in miles Paul ran
C = Paul ran at a faster constant speed than melinda, y =5x where x is the time in hours and y is the distance in miles Paul ran
D = Paul ran at a faster constant speed than melinda, y =7x x being time in hours and y is the distance in miles Paul ran
Given the proportional relationship representing the speed, Paul ran faster. The equation for Paul is, y = 7x (Option D).
What is the Equation of a Proportional Relationship?Proportional relationship between two variables that has a constant rate or unit rate of m, is given as y = mx.
In a graph, the steeper the slope, the larger the constant rate or unit rate.
The graph for Paul is steeper than that of Melinda. Since Melinda's constant speed is 5, therefore, Paul's constant speed cannot be less than 5. It should be more than 5, i.e. 7.
This means that Paul ran at a faster constant speed than Melinda did.
Paul's equation for distance covered over time can be expressed as, y = 7x. (Option D).
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ends of a diameter: (-11, -9) and (1, -3) whats the radius and center
well, we know the endpoints of its diameter, so hmmm its center will be the midpoint of those endpoints.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-11}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 -11}{2}~~~ ,~~~ \cfrac{ -3 -9}{2} \right)\implies \left( \cfrac{-10}{2}~~,~~\cfrac{-12}{2} \right)\implies \stackrel{center}{(-5~~,~~-6)}[/tex]
well, to get its radius, we can simply get the distance between both points and keeping in mind that the radius is half the diameter, we'll take half of that distance.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-11}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[1 - (-11)]^2 + [-3 - (-9)]^2}\implies d=\sqrt{(1+11)^2+(-3+9)^2} \\\\\\ d=\sqrt{12^2 + 6^2}\implies d=\sqrt{180}\implies d=6\sqrt{5}~\hfill \underset{half~that}{\stackrel{radius}{3\sqrt{5}}}[/tex]
A parallelogram has and area of 37.72 m2 and a height of 4.6 m. How long is the base of the parallelogram?
Answer:
It acually equals 8.2
Step-by-step explanation:
37.72÷4.6=8.2 8.2*4.6=37.72
Hope this helps!
Find the value of csc 0 if cos 0 = -3/5 and 0 is in the second quadrant.
we know that the cos(θ) is -(3/5), however θ is in the II Quadrant, where the cosine is negative whilst the sine is positive, meaning the fraction is really (-3)/5, so
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{5}}\qquad \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{5^2-(-3)^2}=b\implies \pm\sqrt{25-9}=b\implies \pm 4=b\implies \stackrel{II~Quadrant}{+4=b} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}~\hfill[/tex]
What is the measure of ZRST?
R
46
T
O A. 46°
O B. 92°
O .
C. 23°
D. 44°
s
Answer:
ОА. 449
ОВ. 23°
Ос. 92°
OD. 46°
Step-by-step explanation:
The measure of the angle RST is 23 degrees, option C is correct.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that an arc is 46∘
We need to find the measure of the subtending angle inscribed in the circle.
The measure of the angle inscribed in a circle is one-half the measure of the arc it subtends.
The measure of the arc is twice the measure of the subtending inscribed angles.
measure of the angle RST= 1/2 measure of the arc
∠RST=1/2(46)
=23 degrees.
Hence, the measure of the angle RST is 23 degrees, option C is correct.
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A line passes through the point (-10, -8) and has a slope of -1/2. Write an equation in slope intercept form for this line
What number when multiplied by itself is 11 greater.
Answer:
6
Step-by-step explanation:
True or false? If you took a true "il then statement and revered the clauses,
the new statement would also be true
O A True
O B. False
the answer to ur question is false
If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?
1/5
4/5
5
16
Answer:
Step-by-step explanation:
y = k*x This is the formula for a direct variation.
y = 20x = 4 Substitute these values into the direct variation20 = 4 * k Divide by 4
20/4 = 4k/4
k = 5
Answer: the constant of variation is 5
A train traveling at 40 mph can go 15 more miles in the same amount of time that a car can traveling at 30 mph can go. How far does the train go in the same amount of time?
Answer:
60
Step-by-step explanation:
After 1.5 hour the train travel 60 mille (1.5 × 40) and the car travel 45 (1.5 × 30) which make the train travel 15 more than the car at the same amount of time.
determine the sum by suitable arrangement
i)157+376+413+524 thank you
Answer:
the answer is 1470
Step-by-step explanation:
157+376+413+524
=1470
how many terms are in each factor of this expression?
5(6 + 4x)
Answer:
2 terms
Explanation:
[tex]\dashrightarrow \ \ \sf 5(6 + 4x)[/tex]
[tex]\dashrightarrow \ \ \sf 5(6) + 5(4x)[/tex]
[tex]\dashrightarrow \ \ \sf 30 + 20x[/tex]
"x" is one term and "30" which is a constant is another term.→ There are total two terms in this factor.
Answer:
2 Terms
Step-by-step explanation:
There will be two terms ..
=> 5(6 + 4x)
=> 30 + 20x
Daniel used 4 strawberries and 12 blueberries to make a parfait. What was the ratio of the number of strawberries to the number of blueberries in the parfait?
A- 1:2
B- 1:3
C- 1:4
D- 1:6
Answer:
C- 1:3
Step-by-step explanation:
You have to simply 4 and 12, which becomes 1 and 3 (by dividing both numbers by 4). Then I guess you just keep a colon symbol in between 1 and 3.
Josh has a rewards card for a movie theater.
• He receives 15 points for becoming a rewards card holder.
• He earns 3.5 points for each visit to the movie theater.
• He needs at least 55 points to earn a free movie ticket.
Which inequality can Josh use to determine x, the minimum number of visits he needs
to earn his first free movie ticket?
PLSS HELPPPP =((( plss
Answer:
55 ≤ 3.5x + 15
Step-by-step explanation:
Missing Inequality.
Given that:
Josh has a reward card for movie theater.
He receives 15 points for becoming a rewards card holder.
He earns 3.5 points for each visit to the movie theater.
He needs at least 55 points to earn a free movie ticket.
To Find:
Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket?
Solution:
From the given we know that:
Points Josh received for becoming a member = 15
Points Josh received for visiting the moving theater = 3.5
Total points needed for a free movie ticket = 55
Note that:
< = Less than
> = Greater than
≤ = Less than or equal to
≥ = Greater than or equal to
Thus, We know that Josh need to get less than or equal to 55.
Therefore, we use this sign ≤
Since we know that we need to get less than or equal to 55 then
we get
55 ≤ 3.5x + 15.
Hence, the inequality that Josh can use to determine x, the minimum number of visits he needs to earn his first free movie tickets is:
55 ≤ 3.5x + 15
Kavinsky