Using the factor theorem, the equation for q is:
[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, ..., x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2)...(x - x_n)[/tex]
In which a is the leading coefficient.
In this problem:
Passes through the origin, so x = 0 is a zero, that is [tex]x_1 = 0[/tex].x = i is a zero, and thus, it's conjugate also is, that is, x = -i, hence [tex]x_2 = i, x_3 = -i[/tex]x = 7 - i is a zero, and thus, it's conjugate also is, that is, x = 7 + i, hence [tex]x_4 = 7 - i, x_3 = 7 + i[/tex]Then, the equation is:
[tex]q(x) = a(x - 0)(x - i)(x + i)(x - 7 + i)(x - 7 - i)[/tex]
[tex]q(x) = ax(x^2 - i^2)((x-7)^2 - i^2)[/tex]
Considering that [tex]i^2 = -1[/tex]
[tex]q(x) = ax(x^2 + 1)(x^2 - 14x + 50)[/tex]
[tex]q(x) = ax(x^4 - 14x^3 + 51x^2 - 14x + 50)[/tex]
[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
q(-1) = -520 means that when [tex]x = -1, q = -520[/tex], and this is used to find a.
[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
[tex]-520 = a(-1 - 14 - 51 - 14 - 50)[/tex]
[tex]130a = 520[/tex]
[tex]a = \frac{520}{130}[/tex]
[tex]a = 4[/tex]
Hence, the equation is:
[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
A similar problem is given at https://brainly.com/question/24380382
Is the table a linear function?
Yes or no
abc is a right angled triangle.
ac=14cm
angle c=90 degrees.
size of angle b:size of angle a=3:2
work out the length of ab
Answer:
67
Step-by-step explanation:
Mamadou has a points card for a movie theater.
He receives 55 rewards points just for signing up.
He earns 7.5 points for each visit to the movie theater.
He needs at least 100 points for a free movie ticket.
Write and solve an inequality which can be used to determine
v
v, the number of visits Mamadou can make to earn his first free movie ticket.
Answer:
Inequality: 7.5v+55≥100
Answer: v≥6
Step-by-step explanation:
Have a good day :)
The inequality for the given situation is 7.5v+55≤100.
Given that, Mamadou receives 55 rewards points just for signing up. He earns 7.5 points for each visit to the movie theater. He needs at least 100 points for a free movie ticket.
What is an inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The number of visits Mamadou can make to earn his first free movie ticket is v.
The inequality for the given situation is 7.5v+55≤100
Subtract 55 on both the sides of inequality.
That is, 7.5v+55-55≤100-55
⇒ 7.5v≤45
⇒ v=45/7.5
⇒ v=6
Therefore, the inequality for the given situation is 7.5v+55≤100.
To learn more about the inequality visit:
https://brainly.com/question/20383699.
#SPJ5
Find the value of y that will make these two triangles congruent:
Answer:
7
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
first you'd make 4y+12=32
get rid of 12 -12 =-12
4y=20
divide 4 =4
y=5
How do I find the variables here? ;-;
Answer:
y = 116
w = 116
x = 4
Step-by-step explanation:
a // b and t is transversal.
y + 64 = 180 {co-interior angles are supplementary}
y = 180- 64
y = 116
w = y {Alternate interior angles are equal}
w = 116
4x² = 64 {Alternate interior angles are equal}
x² = 64/4
x² = 16
x² = 4²
x = √(4*4)
x = 4
Write an equation in point-slope form for the line.
Hello there!
y-y1=m(x-x1)
y-3=4(x-1)
And that's our equation in point-slope form. Hope it helps!
~Just a joyful teen
[tex]SilentNature\\(GraceRosalia)[/tex]
Express 0.1345345... using bar notation
Answer:
0.1345
Step-by-step explanation:
The bolded numbers are what is barred
345 is constantly repeated so that is what would be barred as that repeats for ever
Answer:
3/1345
Step-by-step explanation:
easy one - giving brainly!
Answer:
6:9,2:3
Step-by-step explanation:
sorry I Only knew this much
Answer:
well to make life easier
You can always just simplify the given ratio
12:18 is basically 2:3 and we can use that as a base line
so we got
2:3
6:9
12:18
24:36
48: 72
It goes on you can just multiply by 2
Fill in the [?]:
11,562 um = [?]m
Give your answer in standard form.
Enter
cheryis softball batting average in 0.340 and karins is 0.304 kartin says they have the same avarge what error did she make explain
I need the answer to this picture below
Answer:
-4,1,7,15
Step-by-step explanation:
Please help me solve this ASAP please !
This is a Reflection :) Have a great day !
which aglae has a lager mass at 3 hours in kilograms
Answer:
A) The blue algae has 12 kg more mass at 3 hours.
B) The green algae has 12 kg more mass at 3 hours.
C) The blue algae has 36 kg more mass at 3 hours.
D) The green algae has 36 kg more mass at 3 hours
a red die is tosses and then a green die is tossed. what is the probability that the red die shows a six and the green die shows six?
limθ→π/4 (cosθ−sinθ)/(θ– π/4)
Answer:
-√2
Step-by-step explanation:
For the typing purpose I replaced θ with n in the calculation
[tex]\lim_{n \to \frac{\pi }{4}} \frac{cos n-sin n}{\frac{\pi }{4} } ...limits L'Hopital's Rule\\= \lim_{n \to \frac{\pi }{4}} \frac{-sin n-cos n}{1 } ... plug. in . \frac{\pi }{4} \\= - sin \frac{\pi }{4} - cos \frac{\pi }{4}\\= - \frac{\sqrt{2} }{2} - \frac{\sqrt{2} }{2}\\= \frac{- 2\sqrt{2}}{2} \\= - \sqrt{2}[/tex]
Dont get this, please help
Answer:
1. Enlarge, Shrink
2. Smaller
3. Bigger
Step-by-step explanation:
Dilation is something expanding or shrinking, like how your eyes dilate.
Simply think of the scale factor as what you are multiplying the entire figure by. If you are multiplying it by let's say 2, it would double in size, thus getting larger. If you were to multiply it by 1/2, then it would decrease, or shrink, to half its original size.
Answer:
1: enlarge, shrink
2: smaller
3: bigger
Hope this helps! SO sorry if incorrect!!!!!!
HELP ME PLEASE IM CRYING
An ant moves at 14 cm a min. How many minutes will it take him to travel 10 points
364 cm? What is the time ? (Write your answer in "t=" form)
Answer:
26 minutes/ t=26
Step-by-step explanation:
F) c=14t
S) 364=14t
E) t=26
7 find the missing length
Answer:
8km
Step-by-step explanation:
it is 8km because it is not that much bigger than 6km
Answer:
C) 8 km
Step-by-step explanation:
x is another leg next to 6.
10 is the hypotenuse.
a^2 + b^2 = c^2
a & b are legs and c is the hypotenuse.
x^2 + 6^2 = 10^2
x^2 + 36 = 100
x^2 = 100 - 36
x^2 = 64
√x^2 = √64
x = 8
P.S It may look just slightly different, but your teacher or the program did not make it up to scale.
Hope This Helps! •v•
Any help please? Don’t understand
Find the 9th term of the geometric sequence 9, -27, 81, ...
Answer:
59049
Step-by-step explanation:
nine times negative 3 8 times
Answer:
a₉ = 59049
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 9 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-27}{9}[/tex] = - 3 , then
a₉ = 9 × [tex](-3)^{8}[/tex] = 9 × 6561 = 59049
please help asap, this is for a math project! (ill give brainliest)
Write 7/571 as a mixed number!
Answer:
7
Step-by-step explanation:
jh
Answer:
7+32/77
Step-by-step explanation:
The johnsons's back yard is 3/8 of am arce.They planted a vegtable garden on 1/3 of the yard.How big is the garden?
Pls help;
Answer:
1/8 of an acre
Step-by-step explanation:
Mike has 7 friends. Each friend has 109 baseball cards. How many cards do they have in all?
They have _______ baseball cards.
Answer:
They have 763 baseball cards in total
Step-by-step explanation:
7×109=763
Answer:
They have 763 baseball cards in total (BRANILIST PLEASE!!!!)
Step-by-step explanation:
You just multiply the number of friends with the number of cards each person has.
help a friend out?
Solve and graph the absolute value inequality: 12x +41 > 8.
Answer:
Answer is C
The inequality is x
<−6 or x>2
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
| 2x + 4 | > 8
Case I Case II
2x + 4 > 8 -(2x +4) > 8
-4 -4 -2x - 4 > 8
2x > 4 +4 +4
x > 4/2 -2x > 12
x > 2 -x > 12/2
-x > 6
x < - 6 Multiply by -1 will change the inequality sign.
x > 2 and x< - 6
x > 2 open circle at 2 and shade to the right.
x < -6 open circle at -6 and shade to the left
21
Determine which equations are in standard form.
A 6x-7y=8
B y = 2x + 6
1
с
52 + 2y = 3
=
D
4x - 11y =-7
E - 3x + 5y = 12
-
Multiply (x + 1)^3
(x + 1)^3 = (x + 1)(x + 1)^2
= (x + 1)(x^2 + 2x + 1)
= x^3 +_____ x^2 +_____ x + _____
Step-by-step explanation:
by factoring out the GCF what is 12r-4?
Answer:
4(3r-1)
Step-by-step explanation:
GCF is the highest number that divides exactly into two or more numbers. In this case, it would be 4 because it's the largest number that both 12 and 4 divide into.
What is 43.982 rounded to the nearest hundredth
Answer:
The answer is 42.98
Step-by-step explanation:
you can search up rounding charts online and that would help you a lot! After the decimal, it goes by tens, hundreds, thousand, and so on.
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
State if the triangle are similar amd if they are, give the reasons AA SSS SAS
which triangles?
i see no triangles
try again bro