Answer:
6x - 1 = 9
Step-by-step explanation:
1. first you have to divide every term in the equation by 2
12x/2 + 4/2 = 20/2
2. simplify
6x + 2 = 10
3. next you have to subtract one from both sides
6x + (2-1) = (10-2)
4. simplify
6x + 1 = 9
solve this problem show work. -5/6 + 1/3
Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet$ $f(x) 2$ is divisible by $(x 1)^3$. Write your answer in expanded form (that is, do not factor $f(x)$).
There seems to be one character missing. But I gather that f(x) needs to satisfy
• [tex]x^3[/tex] divides [tex]f(x)[/tex]
• [tex](x-1)^3[/tex] divides [tex]f(x)^2[/tex]
I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or
[tex]f(x) = x^5 + \cdots[/tex]
Since [tex]x^3[/tex] divides [tex]f(x)[/tex], and
[tex]f(x) = x^3 p(x)[/tex]
where [tex]p(x)[/tex] is degree-2, and we can write it as
[tex]f(x)=x^3 (x^2+ax+b)[/tex]
Now, we have
[tex]f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2[/tex]
so if [tex](x - 1)^3[/tex] divides [tex]f(x)^2[/tex], then [tex]p(x)[/tex] is degree-2, so [tex]p(x)^2[/tex] is degree-4, and we can write
[tex]p(x)^2 = (x-1)^3 q(x)[/tex]
where [tex]q(x)[/tex] is degree-1.
Expanding the left side gives
[tex]p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2[/tex]
and dividing by [tex](x-1)^3[/tex] leaves no remainder. If we actually compute the quotient, we wind up with
[tex]\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}[/tex]
If the remainder is supposed to be zero, then
[tex]\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}[/tex]
Adding these equations together and grouping terms, we get
[tex](a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1[/tex]
Then [tex]b=-1-a[/tex], and you can solve for a and b by substituting this into any of the three equations above. For instance,
[tex]2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1[/tex]
So, we end up with
[tex]p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}[/tex]
What is the distance between points (6,-5) and (2,-2)
Answer:
ans is 5.
hope it will help you.
Find the distance of the line, then find the slope of the line using the following coordinates (-7,2) and (-4,6)?
Answer:
Distance = 5 units
Slope = [tex]\displaystyle\frac{4}{3}[/tex]
Step-by-step explanation:
Hi there!
1) Finding the distance of the line
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two endpoints of a line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the points (-7,2) and (-4,6):
[tex]d=\sqrt{(-4-(-7))^2+(6-2)^2}\\d=\sqrt{(-4+7)^2+(6-2)^2}\\d=\sqrt{(3)^2+(4)^2}\\d=\sqrt{9+16}\\d=\sqrt{25}\\d=5[/tex]
Therefore, the length of the line/distance of the line is 5 units.
2) Finding the slope of the line
[tex]m=\displaystyle\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 points (-7,2) and (-4,6):
[tex]m=\displaystyle\frac{6-2}{-4-(-7)}\\\\m=\displaystyle\frac{6-2}{-4+7}\\\\m=\displaystyle\frac{4}{3}[/tex]
Therefore, the slope of the line is [tex]\displaystyle\frac{4}{3}[/tex].
I hope this helps!
A train is going at 200/KM per hour
The train tracks is 8482 Miles wide
How long will it take for the train to reach the end
Answer:
It moved for 152.7 seconds
Step-by-step explanation:
Time taken/ period, T :
[tex]{ \sf{T = \frac{distance}{speed} }}[/tex]
substitute the variables:
[tex]{ \sf{T = \frac{8482}{(200 \times 1000)} }} \\ \\ { \sf{T =0.042 \: hours }}[/tex]
In seconds:
[tex]{ \sf{T = (0.042 \times 3600) \: s}} \\ { \sf{T = 152.7 \: seconds}}[/tex]
Answer: 68.25 hrs.
Step-by-step explanation:
200 Km. to miles = 124.274 miles
8482 mi/124.274 mi =
68.25 hours
What type of triangle has side lengths 2, 712, and 19?
Answer:
OPTION B
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
How many of the 320 million Americans would you predict wear contacts lenses?
Answer:
40,640,000
Step-by-step explanation:
The way I solved this equation was by dividing 320,000,000 by 1,000 (to make smaller numbers). Then, I got 320,000. From here, I was able to multiply 320,000 by 127 (the number found in this specific study group) to get 40,640,000. Or, you could just multiply 320,000,000 by 0.127 (the decimal equivalent to 127/1000) to get the same answer. Please mark Brainliest if this helped :)
Answer:
40,640,000
Step-by-step explanation:
The sample size is 1000 and 127 wear contacts so
127/1000 = x/320000000
(127 * 320000000)/1000 = x
40,640,000 = x
(1.2E-3) x (4.6E-1) =
Answer:
0.0012*x*0.46
Step-by-step explanation:
explain what a ratio is in the easiest way possible
Step-by-step explanation:
A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.
If f(x) = -6x and g(x) = -6x + 5, find (fog)
Answer:
Step-by-step explanation:
(f o g) is the same as f(g(x))
f(x) = -6x, substitute x with g(x) = -6x+5
f(g(x)) = -6g(x) = -6(-6x+5) = 36x -30
(f o g) = 36x -30
10. Multiple Choice Use points A(5, 1),
B(5, 6), C(1,4) and D(4, -2) to determine which of the following is true.
AB = BC AB = CD
AB = BD AC = AB
BC = CD
9514 1404 393
Answer:
AC = AB
Step-by-step explanation:
The attached diagram shows the only segments that are the same length are ...
AC = AB
__
A and B lie on the same vertical line, 5 units apart. A and C are separated by 3 units vertically and 4 units horizontally, so AC is the hypotenuse of a 3-4-5 right triangle.
i need help i need answered assap no bs
Steps:-
First put the vertices on graph and find Triangle ABC .
Then Transact it the give amount i.e 5units and get A'B'C'
Plz urgent
inequalities
Answer:
X>-4
Y>-18
X>-7
I hope this helps
Help me pls ?? 1. Suppose there is a raffle with numbered tickets 1 - 150. One ticket is randomly
drawn from a hat. Find the following probabilities:
A. Drawing an even number
B. Drawing a number greater than 100
C. Drawing an even prime number
D. Drawing a negative number
A segment has endpoints (14,-8) and (4, 12). What are the coordinates of
its midpoint?
Answer:
(9,2)
Step-by-step explanation:
To find the x coordinate of the midpoint, average the x coordinates of the endpoints
(14+4)/2 = 18/2 = 9
To find the y coordinate of the midpoint, average the y coordinates of the endpoints
(-8+12)/2 = 4/2 = 2
find the highest common factor of 36 and 48
Answer:
12
Step-by-step explanation:
36/12=3
48/12=4
Answer:
highest common factor of 36 and 48 is 12
A skateboard costs $60 and its got a discount
of 30% and then a sales tax of 10% was
added. What is the final price?
Answer:
$46.20
Step-by-step explanation:
The discount of 30% brings the price down to $42, and then the sales tax would be $4.20, making the answer $46.20
The factorization of a (x + y + z) + b(x + y + z) + c(x + y + z) is
pls answer maheshsinghmeenu sister
Answer:
(a+b+c) (x+y+z)
Step-by-step explanation:
hope this helps to uh
Step-by-step explanation:
x+y+z+bx+by+bz+cx+cy+cz
Take Like terms
x+bx+cx+y+by+cy+z+bz+cz
x(b+c)+y(b+c)+z(b+c)
(x+y+z)(b+c)
hope it helps
If
f(x) = x^2 + 2x – 4
and
g(x) = 3x + 1
Find
f(g(x)) = 9x^2 + [ ? ]x+ [?]
Step-by-step explanation:
f(g(x))=(3x+1)^2 +2(3x+1) -4
=9x^2 +6x +1 +6x +2 -4
=9x^2 +12x +(-1)
H. Pete wants a new truck. The sale price is 15% lower than the original price. The sale price is $20,000. Write and evaluate an expression for the original price. Uses for sale price and p for original price.
100-15=85%=SP
[tex]\\ \sf\longmapsto 85\%\times x=20000[/tex]
[tex]\\ \sf\longmapsto \dfrac{85}{100}x=20000[/tex]
[tex]\\ \sf\longmapsto x=20000\times \dfrac{100}{85}[/tex]
[tex]\\ \sf\longmapsto x=235.2(100)[/tex]
[tex]\\ \sf\longmapsto CP=23520[/tex]
Please Help!! I am really stuck on this assignment and i need it done
Answer:
Step-by-step explanation:
11-B
Uhhhh sorry about everything else I’ll come back when I figure it out
6-D
7-C? Maybe
Answer:
Step-by-step explanation:
The correct answer is b.
27h + 16 = 178 Subtract 16
27h = 178 -16 Combine
27h = 162 Divide by 27
h = 162 / 27
h = 6
Question 6
No they are not the same. They have the same terminal point but they are going in different directions. The answer is D Direction matters.
Question 7
The vectors add if as in arithmetic if they are going in the same direction.
answer C
You were looking at your power bill for the month, you pay 12 cents per kilowatt-hour. Your power bill came out to $99.89 how many KWH of energy were used in your house this month?
Answer:
832.4 KWH of energy
Step-by-step explanation:
Find how many KWH of energy were used by dividing the total cost by 0.12:
99.89/0.12
= 832.4
So, approximately 832.4 KWH of energy were used that month.
Common difference of the arithmetic sequence -6,-13,-20
Answer:
-7
Step-by-step explanation:
-13 - (-6)
=> -13 + 6
=> -7
So Common Difference = -7
Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are labeled in alphabetical order going clockwise around the figure. If AB = 3 units and AD = 5 units, what is the length of B'C'? A. 5 units B. 9 units C. 11 units D. 3 units
Answer:5 units
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Find all values of $x$ such that
\[\frac{2x}{x + 2} = -\frac{6}{x + 4}.\]
Answer:x_1= -1 or x_2= -6
Step-by-step explanation:
In the pictures
By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number.
These numbers are broken down into factors or divisors.
For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number and these composing integers are called factors of that considered integers.
Given
[tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex]
Cross multiplication;
2x(x + 4) = 6(x + 2)
[tex]2x^{2} + 8x = 6x + 12\\\\2x^{2} + 8x - 6x - 12 = 0\\\\2x^{2} + 2x - 12 = 0\\\\x^{2} + x - 6 = 0[/tex]
Divide above equation by 2, we get
[tex]x^{2} + x - 6 = 0[/tex]
(x +2) (x-3)
x = -2, 3
Therefore, By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.
Find out more information about factorization here;
brainly.com/question/1863222
#SPJ2
What is A= 2/h (a+b) for h?
Answer:
h= 2A/a+b
Step-by-step explanation:
you know the gig
A researcher stands outside a restaurant and asks the youngsters leaving the restaurant if they enjoyed the food there. What type of sampling technique has the researcher employed
My question is in the picture attached below, thank you.
Ps: I need full explanations of the answers as said by the instructions. Thanks
The volume of a rectangular prism is the product of the prism's dimension (i.e. length, width and height). The dimension of the rectangular prism are:
[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]
Given that:
[tex]Volume = (18x^4 + 15x^3 - 12x^2)[/tex]
First, we factor out [tex]3x^2[/tex]
[tex]Volume = 3x^2 \times (6x^2 + 5x - 4)[/tex]
Expand
[tex]Volume = 3x^2 \times (6x^2 + 8x-3x - 4)[/tex]
Factorize
[tex]Volume = 3x^2 \times (2x(3x + 4) -1(3x + 4))[/tex]
Factor out [tex]3x + 4[/tex]
[tex]Volume = 3x^2 \times ((2x -1) (3x + 4))[/tex]
Rewrite as:
[tex]Volume = 3x^2 \times (2x -1) \times (3x + 4)[/tex]
The volume of a rectangular prism is:
[tex]Volume = Length \times Width \times Height[/tex]
So; by comparison:
[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]
Read more about polynomials and volumes at:
https://brainly.com/question/2141804
Distance between (-2,-2) and (8,-6)
Answer:
Distance btw (-2, -2) and (8, -6) is (10, -4)
Step-by-step explanation:
I. Give (-2, -2) is A and (8, -6) is B
B - A = 8 - (-2) in x
= -6 - (-2) in y
So B - A = 10, -4
II. You can prove the answer by A.value + (10, -4) = B.value
Hope that help :D
Hi ;-)
[tex]\text{A}=(-2,-2) \ \text{and} \ \text{B}=(8,-6)\\\\|AB|=\sqrt{(8-(-2))^2+(-6-(-2))^2}\\\\|AB|=\sqrt{(8+2)^2+(-6+2)^2}\\\\|AB|=\sqrt{10^2+(-4)^2}\\\\|AB|=\sqrt{100+16}\\\\|AB|=\sqrt{116}\rightarrow\boxed{|AB|=2\sqrt{29}} \ (\text{because} \ 116=4\cdot29)[/tex]
a point, ray, line, segment or plane which divides a segment into 2 congruent parts
Answer:
This is called a bisector.