Answer:
A third-degree polynomial can be written as:
f(x) = a*x^3 + b*x^2 + c*x + d
Where the leading coefficient is a, and all the coefficients are real.
If we know that the leading coefficient is 1, then the equation becomes:
f(x) = x^3 + b*x^2 + c*x + d
Now, we also know that:
(6 + i) and 5 are zeros.
This means that:
(6 + i)^3 + b*(6 + i)^2 + c*(6 + i) + d = 0
remember that:
i^2 = - 1
This is equal to:
(6 + i)*(36 + 2*6*i + i^2) + b*(36 + 2*6*i + i^2) + c*(6 + i) + d = 0
(6 + i)*(35 + 12i) + b*(35 + 12i) + c*(6 + i) + d =0
(210 + 35i + 72i - 12) + b*(35 + 12i) + c*(6 + i) + d = 0
198 + 107i + b*(35 + 12i) + c*(6 + i) + d = 0
sparating in real and imaginary part, we get:
(198 + b*35 + c*6 + d) + (107 + b*12 + c)*i = 0
Then each parentheses needs to be zero, this means that:
198 + b*35 + c*6 + d = 0
107 + b*12 + c = 0
Knowing that 5 is another zero, we have:
5^3 + b*5^2 + c*5 + d = 0
125 + b*25 + c*5 + d = 0
Then we have a system of 3 equations and 3 variables:
198 + b*35 + c*6 + d = 0
107 + b*12 + c = 0
125 + b*25 + c*5 + d = 0
To solve this, we first need to isolate one of the variables in one of the equations.
Let's isolate d in the last one, so we get:
d = -125 - b*25 - c*5
now we can replace this in the first equation to get:
198 + b*35 + c*6 + d = 0
198 + b*35 + c*6 + ( -125 - b*25 - c*5) = 0
70 + b*10 + c = 0
So now we have two equations:
70 + b*10 + c = 0
107 + b*12 + c = 0
Again, now we can isolate the one variable in one of the equations, this time let's isolate c in the first one.
c = -70 - b*10
now we can replace this in the other equation:
107 + b*12 + c = 0
107 + b*12 + (-70 - b*10) = 0
38 + b*2 = 0
now we can solve this for b
b*2 = -38
b = -38/2 = -19
Now, with the equation c = -70 - b*10 we can find the value of c.
c = -70 - b*10 = c = -70 - (-19)*10 = 120
And with the equation d = -125 - b*25 - c*5
we can find the value of d:
d = -125 - b*25 - c*5 = -125 - (-19)*25 - (120)*5 = -250
Then we have:
a = 1
b = -19
c = 120
d = -250
The eqation is:
f(x) = 1*x^3 - 19*x^2 + 120*x - 250
1. Choose the correct algebraic equation to represent: the amount decreased by $9 is $42.
9-m=42
9-m
m-9=42
m-9
Answer:
m-9=42
Step-by-step explanation:
An amount subtracted by $9 is $42.
(an amount is unknown, so it is represented with variable, m)
m-9=42
What is the area of this triangle?
Answer:
the answer of the question is D
a see-saw has length 5.2 m. when one end is resting on the ground it makes an angle of 23 degrees with the ground. find the height of the other end above ground level.
answer: I did it in the picture above I hope it's clear and helpful
Shree travels a distance of 12 km from her house to school by a bus at 20 km/hr and returns home at 16 km/hr.
i Calculate the time required to reach school from home .
ii find out the time required to reach home from school .
iii Determine the average distance of entire journey .
Answer:
Step-by-step explanation:
1 t= S/V1= 12/20=0.6 hours
2 t =S/V2 = 12/16= 0.75 hours
3 12km
i guess they wanna determine the average V
Sally collected 22 pounds of cans to recycle
and plans to collect 1.8 more pounds each
week. In this situation, what is the value of
the y-intercept?
Step-by-step explanation:
this is an example u can see and write it yourself...
The lines below are perpendicular. If the slope of the green line is ž, what is
the slope of the red line?
-5
5
m =
Answer:
B or (-2/3)
Step-by-step explanation:
Perpendicuar lines have negative inverse slopes SO
3/2 ---> -2/3
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Angle MNO measures 112°. What is the measure of angle LMN?
Answer:
hope this help
Step-by-step explanation:
Answer:
90
51
10
Step-by-step explanation:
(3[tex]\sqrt{7} \\[/tex]+7[tex]\sqrt{3}[/tex])/[tex]\sqrt{21}[/tex]
Answer:
sqrt(3) + sqrt(7)
Step-by-step explanation:
3*sqrt(7) / sqrt(21) = 3/sqrt(3)
If you rationalize the denominator, you get 3*sqrt(3)/3. The threes cancel
You are left with sqrt(3)
7sqrt(3)/sqrt(21) = 7 / sqrt(7)
If you rationalize the denominator, you get
7 sqrt(7)/ 7 = sqrt(7)
The 7s have been canceled out
The answer is
sqrt(3) + sqrt(7)
can someone please help me out marking brainliest
rút gọn M=[ căn x -2/x-1- căn x +2/x+2 căn x+ 1] nhân x bình-2x+1/2 với x>0 x khác 1
Answer:
Step-by-step explanation:
40 POINTS I’ll give brainlist
Answer:
I don't understand the equation, please state it differently
Says i need at least 20 characters in order to get this up.. you know i really should know this stuff but oh well
Answer:
C
-1/5, -1/3,-7
Step-by-step explanation:
I NEED HELP BUT THE ANSWER MUST WORK ON KHAN ACADEMY
Answer:
x=55
Step-by-step explanation:
Since 2 sides are the same length, their base angles much be the same. The unmarked angle muse also be x
x+x+70 = 180 since the sum of the angles of a triangle must be 180
2x+70 = 180
2x = 180-70
2x = 110
Divide by 2
2x/2 =110/2
x=55
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{x + x + 70 = 180}^\circ[/tex]
[tex]\underline{\large\text{COMBINE the LIKE TERMS}}[/tex]
[tex]\large\textsf{(x + x) + 70 = 180}^\circ[/tex]
[tex]\large\textsf{x + x = \bf 2x}[/tex]
[tex]\large\textsf{2x + 70 = 180}^\circ[/tex]
[tex]\underline{\large\text{SUBTRACT 70 to BOTH SIDES}}[/tex]
[tex]\large\textsf{2x + 70 - 70 = 180 - 70}[/tex]
[tex]\large\text{CANCEL out: 70 - 70 because that gives you 0}[/tex]
[tex]\large\text{KEEP: 180 - 70 because helps solve for the x-value}[/tex]
[tex]\large\textsf{180 - 70 = \bf 110}[/tex]
[tex]\underline{\underline{\large\text{New equation: 2x = 110}}}[/tex]
[tex]\underline{\large\text{DIVIDE 2 to BOTH SIDES}}[/tex]
[tex]\large{\mathsf{\dfrac{2x}{2}=\dfrac{110}{2}}[/tex]
[tex]\large\text{CANCEL out: } \mathsf{\dfrac{2}{2}} \large\text{ because that gives you 1}[/tex]
[tex]\large\text{KEEP: }\mathsf{\dfrac{110}{2}}\large\text{ because that gives you the answer of the x-value}[/tex]
[tex]\mathsf{x = \dfrac{110}{2}}\\\\\large\textsf{x = 110}\div\large\textsf{2}\\\\\large\textsf{x = \bf 55}^\circ[/tex]
[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = \bf 55}}^\circ}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The graph shows the function f(x) = 2*
What is the value of x when f(x) = 8?
Ay
10-
A. 3
B. 2
C. 0
D. 1
Answer:
A
Step-by-step explanation:
Equate f(x) to 8 , that is
[tex]2^{x}[/tex] = 8 = 2³
Since bases on both sides are equal, both 2, then equate exponents
x = 3
The value of the x when the exponential function shown in the graph f(x) = 2ˣ is 8 is when x = 3, which is option A.
Here, given the graph of the function,
f(x) = 2ˣ
We have to find the value of x when f(x) = 8.
In order to find the value of x, when f(x) = 8, we have to write as,
f(x) = 8
2ˣ = 8
Now write 8 as an exponent with base 2.
2ˣ = 2³
Hence the value of x = 3
Learn more about Exponential Functions here :
https://brainly.com/question/9919887
#SPJ7
Please help me solve this problem
Answer:
-4
they wanted you to compute using x as 3
-2*3 + 2 = -4
Step-by-step explanation:
help please I'm doing some math homework
Answer:
Slope is 5/2
Step-by-step explanation:
[tex]{ \boxed{ \bf{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1}} }}}[/tex]
Substitute the terms:
[tex]{ \tt{slope = \frac{7 - ( - 3)}{4 - 0} }} \\ = \frac{5}{2} [/tex]
HElp ASAP
A cement truck mixes 1 part cement
with 4 parts sand. If 2.5 cubic yards of
cement are used, how much sand is
needed for the mixture?
a. 6.25 cubic yards
b. 7.5 cubic yards
c. 10 cubic yards
d. 12.5 cubic yards
Answer: The answer is already there
Step-by-step explanation:
Which graph shows the solution set
Answer:
D
Step-by-step explanation:
Answer:
It's D on there
Step-by-step explanation:
⁴⁄₇ × ²⁄₃
Click the picture so that you can see the whole question
Answer:
8/21
Step-by-step explanation:
just multiply the numerator and denominator
what must be subtracted from 61 to get 5
Answer: 56
Step-by-step explanation:
Let x be the number that is supposed to be subtracted from 61.
Given
61 - x = 5
Add both sides by x
61 - x + x = 5 + x
61 = 5 + x
Subtract 5 on both sides
61 - 5 = 5 + x - 5
x = 56
Hope this helps!! :)
Please let me know if you have any questions
anyone know collage level algebra 2? I need help
Evaluate the series: image Question 1 options: A) 392 B) 249 C) 420 D) 406
Answer:
The required sum is 392
Step-by-step explanation:
Given the sum as shown;
[tex]\sum \left \77} \atop {a=1}} \right. (3a^2-4)[/tex]
When n = 1
f(1) = 3(1)²-4
f(1) = 3 - 4
f(1) = - 1
When n = 2
f(2) = 3(2)²-4
f(2) = 12 - 4
f(2) = 8
When n = 3
f(3) = 3(3)²-4
f(3) = 27 - 4
f(3) = 23
When n = 4
f(4) = 3(4)²-4
f(4) = 48 - 4
f(4) = 44
When n = 5
f(5) = 3(5)²-4
f(5) = 75 - 4
f(5) = 71
When n = 6
f(6) = 3(6)²-4
f(6) = 108 - 4
f(6) = 104
When n = 7
f(7) = 3(7)²-4
f(7) = 147 - 4
f(7) = 143
Taking their sum
Sum = f(1)+f(2)+(3)+f(4)+f(5)+f(6)+f(7)
Sum = -1 + 8 + 23 + 44 + 71 + 104 + 143
Sum = 392
Hence the required sum is 392
the width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer: 80, 40
Step-by-step explanation: I just made an equation which went something along the lines Of 3.1x=248 , then you get 80, then 40.
PLEASE HELP!!!!!!!!
Answer: 3
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol{} We \ have \ a \ square\ function \\\\ f(x)=ax^2+bx+c \\\\And \ we \ know \\\\ \left[\left \[ {{f(0)=a\cdot 0+b\cdot0+c=0} \atop {f(-4)=a(-4)^2+-4b+c=-24}} \right.=>[/tex] [tex]\displaystyle\ \Large \boldsymbol{} \left[ \ {{c=0} \atop {16a-4b=-24}} \right. =>\boxed{4a-b=-6} \\\\\\ and \ x_0 =-\frac{b}{2a}=1 =>\boxed{ b=-2a} \\\\\\ \left \{ {{4a-b=-6} \atop {b=-2a}} \right. =>4a+2a=-6=> a=-1 \ ; \ b=2 \\\\\\then \ b-a=2-(-1)=\boxed{3}[/tex]
Debt is a result of spending more than you make.
True
False
I am really bad at algebra please help!!
I need it now please with explanation ☺️
Answer:
E. 7x
Step-by-step explanation:
3x plus 4x is equal to 7x because they both have the same terms and when added cannot the X of 3x and 4x cannot be joined together .
So they remain the same.
(e) 12x
(f) 12x²
(g) 12x²
(h) 1x
(I) 2x²
(J) 2x²
(K) -10x
(L) -20x
(M) 6x²
(N) 20x²
(O) -15x²
(P) -12x³
Your answers were wrong so i did all of them
Quick tip the power comes only when you multiply and not when you add
For example x + x = 2x
x × x = x²
All the answers
Must click thanks and mark brainliest
Cho tứ diện ABCD . Trên cạnh AB lấy điểm M , AC lấy N , trong tam giác BCD lấy điểm P tìm giao điểm
a, MP và (ACD)
b, AD và ( MNP)
c , BD và ( MNP)
Answer:
a. Trong mp (BCD), nối BP cắt CD tại E
Trong mp (ABP), nối MP cắt AE kéo dài tại F (trong trường hợp MP không song song AE)
⇒F=MP∩(ACD)⇒F=MP∩(ACD)
b. Nếu MN cắt BC, kéo dài MN cắt BC tại G
Nối GP cắt BD tại H
Trong mặt phẳng (ABD), nối MH cắt AD tại K (trong trường howph MH ko song song AD)
⇒K=AD∩(MNP)⇒K=AD∩(MNP)
c. H=BD∩(MNP)
Step-by-step explanation:
tìm x biết
x/7=6/-21
Answer:
x = - 2
Step-by-step explanation:
Given
[tex]\frac{x}{7}[/tex] = [tex]\frac{6}{-21}[/tex] ( cross- multiply )
- 21x = 42 ( divide both sides by - 21 )
x = - 2
Based only on the given information, it is guaranteed that LN I MO.
L
Given: ALON
LM: NM
LO = NO
MO #MO
M
0
N
Answer:
true
Step-by-step explanation:
We are given that sides LM and NM, LO and NO, MO and MO are congruent. Since this describes 3 sides of the triangle, you can say ΔMNO is congruent to ΔMLO. From this, you can say ∠OMN is congruent to ∠OML. The two angles (∠OMN and ∠OML) form a straight line, meaning they add up to 180 degrees. We can write:
∠OMN + ∠OML = 180
And since ∠OMN = ∠OML, we can substitute and solve:
∠OMN + ∠OMN = 180
2∠OMN = 180
∠OML =∠OMN = 90
Since both these angles are 90 degrees, LN is perpendicular to MO by definition.
Three adults are picked at random from those with a mass of 70 kg or less.
Calculate the probability that one of them has a mass of 35 kg or less and the other two each have a
mass greater than 35 kg.
A car covers a distance of 132 km. If each tire’s diameter is 42 cm, how many rotations does each tire make in covering this distance?
Answer:
Step-by-step explanation:
Diameter (D)= 42cm
Circumference = (pie)D= (22/7)*D=(22/7)*42 = 132cm
1 circumference = 1 revolution
1 revolution = 132cm = 1.32m
for covering 5.28km no. of revolution = 5.28*1000/1.32 = 4000
Hope this answer helps you :)
Have a great day
Mark brainliest
