Consider functions fand g.
f(x) = (x + 1)^3
g(x) = 3 x+ 1
Evaluate the function composition.
(fog)(-64) =
Answers
Answer:
-8
Step-by-step explanation:
plz watch all steps in picture
The value of the composition function (f·g)(-64) is 1750329.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are f(x)=(x+1)³ and g(x)=∛x+1.
We need to find (f·g)(-64).
We know that, (f·g)(x)=f(x)×g(x)
Here, f(-64)=(-64+1)³
= -63³
= -250047
g(x)=∛(-64)+1
= -8+1
= -7
Now, (f·g)(-64)=f(-64)×g(-64)
= -250047×(-7)
= 1750329
Therefore, the value of (f·g)(-64) is 1750329.
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Related Questions
Please help me out solve it and tell me how you got that answer so I can understand please!
Answers
The solution for s in the given equation is [tex]s = C-nD[/tex]
The question seems to be incomplete
Here is the complete question:
Solve for s in this equation [tex]D= \frac{C-s}{n}[/tex] Depreciation.
To solve for s, that means we should make s the subject of the equation
From the given equation,
[tex]D= \frac{C-s}{n}[/tex]
To solve for s, first multiply both sides by n to clear the fraction
We get
[tex]n\times D= n \times \frac{C-s}{n}[/tex]
Then,
[tex]nD = C - s[/tex]
Now, add s to both sides
[tex]nD + s= C - s+s[/tex]
[tex]nD+s = C[/tex]
Then, subtract nD from both sides
[tex]nD-nD+s = C-nD[/tex]
∴ [tex]s = C-nD[/tex]
Hence, the solution for s in the given equation is [tex]s = C-nD[/tex]
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Christine received a $15.00 gift card or a photo center. She used it to buy prints that cost 7 cents each. The remaining balance, B ( in dollars), on the card after buying x prints is given by the following function. B (x) = 15.00-0.07x. what is the remaining balance of the card if Christine bought 40 prints
Answers
Answer:
Remaining balance is $12.2
Step-by-step explanation:
see all steps in picture.
Express as a trinomial.
(x + 6)(2x + 4)
Answers
Answer:
2x²+16x + 24
Step-by-step explanation:
(x + 6) ( 2x + 4)
x ( 2x + 4) + 6 ( 2x + 4)
2x² + 4x + 12x + 24
2x² + 16x + 24
Hope this helps
The polynomial function [tex](x + 6)(2x + 4)[/tex] expressed as a trinomial is [tex]2x^2 + 16x + 24[/tex].
Given data:
The polynomial function is represented as A.
Now, the value of [tex]A=(x + 6)(2x + 4)[/tex].
On simplifying the equation:
From distributive property to multiply the terms:
[tex]A=x * 2x + x * 4 + 6 * 2x + 6 * 4[/tex]
[tex]A=2x^2 + 4x + 12x + 24[/tex]
On simplifying the equation:
[tex]A=2x^2 + 16x + 24[/tex]
Hence, the trinomial is [tex]2x^2 + 16x + 24[/tex].
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If
f(x) = x^2 + 2x – 4
and
g(x) = 3x + 1
Find
f(g(x)) = 9x^2 + [ ? ]x+ [?]
Answers
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)
what is seven over four as a mixed number?
Answers
Answer:1 3/4
Step-by-step explanation:
Answer:7/4=1 3/4
Step-by-step explanation:
it is like this,7,we can think of 8,which would 2,but it is 7,so we drop down to 1 whole.Then we have 3 remaining,which makes 1 and 3/4
The factorization of a (x + y + z) + b(x + y + z) + c(x + y + z) is
pls answer maheshsinghmeenu sister
Answers
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
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 $f(x)$).
Answers
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]
there are initially 1000 bacteria in a culture. The number of bacteria double each hour. the number of bacteria N present after t hours is given by N=1000 (2)t. how long will it take the culture to increase to 30,000 bacteria.
Answers
Answer:
FREEEEEEE POINTSSSSSSS
Step-by-step explanation:
Distance between (-2,-2) and (8,-6)
Answers
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]
What is the vertex of the parabola with the equation y=15x2+2x−8?
Answers
Answer:
a =15, b=2
Axis of Symmetry = [tex]\frac{-b}{2a}[/tex]
[tex]=\frac{-2}{2 * 15}[/tex]
= [tex]-\frac{1}{15}[/tex]
To find the y-value for the vertex sub in the axis of symmetry for x
[tex]y=15(-\frac{1}{15} )^{2}+2(-\frac{1}{15} )-8\\\\=-\frac{121}{15}[/tex]
∴ Vertex [tex](-\frac{1}{15}, -\frac{121}{15} )[/tex]
Step-by-step explanation:
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4(x- 8). What
is the slope-intercept form of the equation for this line?
0 y= 1/4x-12
y= 1/4x-4
y= =1/4x+2
y= 1/4x+6
Answers
Hi! I'm happy to help!
Point slope form states that y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]). m represents your slope (rise/run) and [tex]y_{1}[/tex] and [tex]x_{1}[/tex] represent your first y and x points, and y and x represent your second y and x points. We already have our equation here:
y - 4 = 1/4(x- 8)
Now, let's dive into what slope-intercept form is. Slope intercept form states that y=mx+b. m represents our slope, b represents our y intercept, y represents a y point, and x represents the corresponding x point.
Since we know our m, we can solve for b, by using our other numbers. Let's use our first set of coordinates.
4=1/4(8)+b
4=2+b
2=b
Now our second set to double check:
2=1/4(0)+b
2=0+b
2=b
We know that b must equal 2, so our equation must be y=1/4x+2, which is option 3.
You should pick option 3.
(y-intercept is where the line hits the y-axis(when x=0). We could've used our second coordinates (0,2), where x equals 0 to know that 2 is the y-intercept (b). This shortcut only works on specific problems though.)
I hope this was helpful, keep learning! :D
i need help i need answered assap no bs
Answers
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'
Round to the nearest hundred 16,537
Answers
Answer:
16,500
Step-by-step explanation:
thats it
Show that 3x^2 -2x + 1 is always greater than 0.
( This is an Additional Math Question )
Answers
Answer:
3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3
(x-1/3)^2 is greater or equal to zero
3(x-1/3)^2 is greater or equal to zero
and 2/3 is greater than zero
So there sum is greater than zero
Proved
Step-by-step explanation:
3x^2 -2x + 1 =3(x^2-2/3x+1/3)
Consider x^2-2/3x+1/3
Remember that (a-b)^2 =a^2-2ab+b^2
x^2=a^2
a=x
-2/3x= -2*x*b
b=1/3
S0 (x-1/3)^2= x^2-2/3x+1/9
x^2-2/3x+1/3= x^2-2/3x+1/9+1/3-1/9= (x-1/3)^2+2/9
3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3
(x-1/3)^2 is greater or equal to zero
3(x-1/3)^2 is greater or equal to zero
and 2/3 is greater than zero
So there sum is greater than zero
Proved
If f(x) = -6x and g(x) = -6x + 5, find (fog)
Answers
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
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
Answers
Answer:5 units
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
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
Answers
Explanation: He is taking people young and old,tall and short, and asking them if they like the food or not so he doesn’t get biased opinions based on that persons age or any other trait.
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
Answers
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.
Help plsssssssssssssssssss
Answers
2. 7/5 More than
3. 2/3Less than
If the number is less than a 1, it’s going to be less. If the number is greater than 1 it will be more. I’m this case, you can just look at what’s being multiple and apply that rule- so just excuse the 7/75.
My question is in the picture attached below, thank you.
Ps: I need full explanations of the answers as said by the instructions. Thanks
Answers
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:
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B is the midpoint of AC. If AB = x + 5 and AC = 3x - 6, find BC.
Answers
Hey there! I'm happy to help!
We see that at AB is halfway across our line. We see that AC is the total line.
So, to find the other half, we have to subtract AB from AC, which will give us the value of BC.
We first will subtract our x values.
3x-x=2x
And then we subtract our numbers.
-6-5=-11
So, BC is 2x-11.
Have a wonderful day and keep on learning! :D
Answer:
21 unitsStep-by-step explanation:
Since B is the midpoint, we have:
AB = BC = AC/2Substitute and solve for x:
x + 5 = (3x - 6)/23x - 6 = 2x + 103x - 2x = 10 + 6x = 16Find BC:
BC = AB = 16 + 5 = 21What type of triangle has side lengths 2, 712, and 19?
Answers
Answer:
OPTION B
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
a point, ray, line, segment or plane which divides a segment into 2 congruent parts
Answers
Answer:
This is called a bisector.
explain what a ratio is in the easiest way possible
Answers
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.
Plz urgent
inequalities
Answers
Answer:
X>-4
Y>-18
X>-7
I hope this helps
will mark brainliest if correct
Answers
Answer:
Distributive property
Step-by-step explanation:
The 2 shares a product/multiplies with both the 5 and 7.
solve this problem show work. -5/6 + 1/3
Answers
-5/6 + 1/3 = -5/6 + 2/6
To add fractions, add the numerators:
-5 + 2 = -3
So, -5/6 + 2/6 = -3/6
This can reduce, since 3 and 6 are divisible by 3.
-3/6 = -1/2
Find the coordinates of the point 7/10 of the way from A to B.
Answers
Answer:
The coordinates are (6.5, 1.7).
Step-by-step explanation:
The difference between A and B's x-coordinate is 15. 7/10 of this is 10.5, which added to -4 gives us an x-coordinate of 6.5.
The difference between A and B's y-coordinate is 11. 7/10 of this is 7.7, which added to -6 gives us a y-coordinate of 1.7.
Therefore, the coordinates are (6.5, 1.7).
One-sixth of the smallest of three consecutive even
integers is three less than one-tenth the sum of the
other even integers. Find the integers. this
#49 with work pleasee
Answers
Answer:
The three even, consecutive integers are 72, 74, and 76.
Step-by-step explanation:
Let a be the first even integer.
Then the other two consecutive integers, b and c, will be represented by:
[tex]\displaystyle b = a + 2 \text{ and } \\ \\ c = b + 2 = (a + 2) + 2 = a + 4[/tex]
One-sixth of the smallest (that is, a) is three less than one-tenth the sum of the other two even integers (that is, b and c).
Therefore:
[tex]\displaystyle \frac{1}{6} a = \frac{1}{10}\left( b +c\right) - 3[/tex]
Solve for a. Substitute:
[tex]\displaystyle \frac{1}{6} a =\frac{1}{10}\left((a+2)+(a+4)\right) - 3[/tex]
Simplify and solve for a:
[tex]\displaystyle \begin{aligned} \frac{1}{6} a &= \frac{1}{10}(2a + 6) - 3 \\ \\ \frac{1}{6} a &= \frac{1}{5} a + \frac{3}{5} - 3\\ \\ -\frac{1}{30} a &= -\frac{12}{5} \\ \\ a &= 72\end{aligned}[/tex]
Hence, the first even integer is 72.
Therefore, the two other consecutive even integers must be 74, and 76.
In conclusion, the three even, consecutive integers are 72, 74, and 76.
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?
Answers
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