Here we have a problem of composition of functions.
Remember that:
(f ° g)(x) = f( g(x) )
Now we have the table:
x | 1 2 3 4 5 6
f(x) | 6 4 4 1 6 4
g(x) | 5 5 2 1 4 3
Using the table, we want to find:
To read the table, for example for f(5) first you go to the "x" part of the table and find the 5.
Now you go to the f(x) table and see which is the value of f(5), in this case, we can see that f(5) = 6.
a) f(g(1))
First, looking at the table, we can see that:
g(1) = 5
Then:
f(g(1)) = f(5)
Again, looking at the table we can see that f(5) = 6
Then we have:
f(g(1)) = 6
b) g(f(1))
Same approach as before:
f(1) = 6
then g(f(1)) = g(6)
And looking at the table, g(6) = 3
Then: g(f(1)) = 3
c) f(f(1))
f(1) = 6
f(f(1)) = f(6) = 4
f(f(1)) = 4
d) g(g(1))
g(1) = 5
then:
g(g(1)) = g(5) = 4
g(g(1)) = 4
e) (gof)(3)
This is equal to:
(gof)(3) = g(f(3))
we know that f(3) = 4
then:
g(f(3)) = g(4) = 1
(gof)(3) = 1
f) (fog)(6) = f(g(6))
We can see that:
g(6) = 3
then:
f(g(6)) = f(3) = 4
Concluding:
(fog)(6) = 4
If you want to learn more, you can read:
https://brainly.com/question/8308119
please help i’m abt to break down
Answer:
4= -5v-1
5= 3x
6= 9y-6
7= h-20
8= 29w-17z
9= 8mn-2n+5m
Step-by-step explanation:
first three that you did were correct! Hope it helps!
WILL GIVE BRAINLEST
Slove f(-4) if f(x) = -4x -2
Give Step by Step pls.
Answer:
Use the given functions to set up and simplify f(−4).
14
Step-by-step explanation:
Plug x + h into the function f and simplify to find f(x + h). Now that you have f(x + h), find f(x + h) - f(x) by plugging in f(x + h) and f(x) and simplifying. Plug your result from step 2 in for the numerator in the difference quotient and simplify.
https://study.com/academy/lesson/how-to-solve-the-difference-quotient.html
please help me, if you help then thanks!
9514 1404 393
Answer:
k = 3
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
__
Using these rules, we can simplify the left-side expression, then equate exponents of the same base.
[tex](3)^2(3^2)^k=3^8\\\\(3^2)(3^{2k})=3^8\\\\3^{2k+2}=3^8\\\\2k+2=8\qquad\text{equate exponents}\\\\k+1=4\qquad\text{divide by 2}\\\\\boxed{k=3}\qquad\text{subtract 1}[/tex]
Andre settles his debt of RM4980 by paying RM50 at the end of the first month. And for the following months, he pays RM8 more than the previous month. Find
(a) the number of months he takes to settle his debt.
(5 marks]
(b) the amount of the last payment.
[2 marks]
Answer:
A) 30 months
B) RM282
Step-by-step explanation:
a1=50+(1-1)8
a1=50+(0)8
a1=50
a2=50+(2-1)8
a2=50+(1)8
a2=58
So this is true.
The formula is an=50(n-1)8
Hope this helps
If p=(3,1) and Q=(-3,-7) find the distance PQ
Answer: The answer is 10.
Compute the mean of the discrete probability distribution below:
X P(X)
2 0.20
3 0.25
4 0.45
5 0.10
Answer:
Step-b2
0.20
3
0.25
4
0.45
5
0.10
y-step explanation:
Which expression is equivalent to 7 2/3 ⋅ 7 1/4?
Answer:
B
Step-by-step explanation:
Recall that [tex]7^a\cdot 7^b = 7^{a+b}[/tex]
So now
[tex]7^{2/3} \cdot 7^{1/3}\\= 7^{\frac{2}{3}+\frac{1}{4}}\\=7^{\frac{8}{12}+\frac{3}{12}}\\=7^{11/12}[/tex]
The equivalent value of the expression is A = 7^ ( 11/12 )
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Let the first number be p = 7 ^ ( 2/3 )
Let the second number be q = 7 ^ ( 1/4 )
And , A = pq
On simplifying , we get
A = 7 ^ ( 2/3 ) . 7 ^ ( 1/4 )
From the laws of exponents , we get
mᵃ×mᵇ = mᵃ⁺ᵇ
So , A = 7 ^ ( 2/3 + 1/4 )
A = 7 ^ ( 11/12 )
Hence , the equation is 7^ ( 11/12 )
To learn more about exponents click :
https://brainly.com/question/28966438
#SPJ2
Given the list of numbers, 3, 2, 6, 3, 9, 5, 12, 7, if the pattern continues, what is the sum of the ninth and tenth numbers?
Answer:
Step-by-step explanation:
Every other one beginning with the first 3 adds 3 to the preceding number that has an odd position.
So the odd positions go up 3 6 9 12
And the next odd position is 15 which is the nineth term.
It's hard to tell what the even ones are doing. It could be anything just about. I'm guessing its a 9. So the tenth term is 9.
The sum of 9 and 15 = 24
If someone gives you a more consistent answer, take it.
Name the angle in three different ways
Answer:
angle WVU
angle UVW
angle VUW
Step-by-step explanation:
PEASE HELP ME 70 POINTS
Answer:
x: -2
f(x): 1.5
x: 0
f(x): 0.5
x: 3
f(x): -1
Step-by-step explanation:
Answer:
3/2, 1/2, - 1
Step-by-step explanation:
x + 2y = 1 --> this is 'f(x)'. Sub in the each x-value to the equations.
First part:
x = -2
x + 2y = 1
-2 + 2y = 1
2y = 3
y = 3/2
Second part:
x = 0
x + 2y = 1
0 + 2y = 1
2y = 1
y = 1/2
Third part:
x = 3
x + 2y = 1
3 + 2y = 1
2y = -2
y = -2/2
y = - 1
HELP!!! LOTS OF POINTS AND I GIVE BRIANLEST NO FAKE ANSWERS
Choose the missing step in the given solution to the inequality −x − 10 > 14 + 2x.
−x − 10 > 14 + 2x
−3x − 10 > 14
_____________
x x < −8
a)−3x > 24
b)−3x > 4
c)−3x > −4
d)−3x < 24
-x - 10 > 14 + 2x
-x - 2x > 14 + 10
-3x > 24
Answer: A
Hey there! Here's your answer:
The missing steps are : -3x > 24
Here's why:
The inequality is: -x - 10 > 14 + 2x
Now, we need to find the solution of the given inequality:
= x - 10 > 14 + 2x
Subtracting 2x from both the sides:
= -x - 10 - 2x > 14 + 2x - 2x
= -3x - 10 > 14
Adding 10 on both the sides:
= -3x - 10 + 10 > 14 + 10
= -3x > 24
Now, dividing both the sides by -3:
= x < -8
Therefore, the missing steps are: -3x > 24
Hope this helps!
simplify 3√578 - √162 + 4√32
[tex]3\sqrt{578}-\sqrt{162}+4\sqrt{32}=\\\\=3\sqrt{289\cdot2}-\sqrt{81\cdot2}+4\sqrt{16\cdot2}=\\\\=3\sqrt{17^2\cdot2}-\sqrt{9^2\cdot2}+4\sqrt{4^2\cdot2}=\\\\=3\cdot17\sqrt2-9\sqrt2+4\cdot4\sqrt2=\\\\=51\sqrt2-9\sqrt2+16\sqrt2=51\sqrt2+7\sqrt2=\boxed{58\sqrt2}[/tex]
how to write 8/15 as a decimal?
Answer:
0.53
Step-by-step explanation:
Basically just go to your calculator and put in 8 divded by 15
Which of the following is a solution to the inequality?5x-10<20
Answer:
x < 6
Step-by-step explanation:
5x - 10 < 20
5x < 30
x <6
hope that helps
Is the value of the two in 23,406 10 times as great as the value of the three?
Answer:
yes, it is 10 times as great
Easy question:
Two ends of a line have coordinates (-6,10) and (2,2). What are the coordinates of the midpoint of the line?
Answer:
midpoint = (-2 , 6)
Step-by-step explanation:
The midpoint can be found with the formula {(x1 + x2 )/2, (y1 + y2.) P1( x1 , y1 ), and P2 (x2 , y2 ) are the coordinates of two points, and the midpoint is a point lying equidistant and between these two points.
Multiply. (2x+5)(3x^2+2x+1)
a. 6x^3+19x^2+12x+5
b. 6x^3+15x^2+12x+6
c. 6x^3+19x^2+8x+6
d. 6x^3+18x^2+20x+5
Solution is in attachment !!
[tex] \boxed{ \boxed{6 {x}^{3} + 19x + 2x + 5 }}[/tex]
Answer:
a. [tex]6x^{3}+19x^{2}+12x+5[/tex]
Step-by-step explanation:
[tex](2x+5)(3x^{2} +2x+1)\\\\6x^{3}+4x^{2}+2x+15x^{2}+10x+5=\\\\6x^{3}+19x^{2}+12x+5[/tex]
A regular hexagon is a six sided figure with all sides equal and all six angles equal. Find the length of the sides if the perimeter of the regular hexagon is 396 yd.
Answer:
sides = 61.5 yd
Step-by-step explanation:
hopefully the picture I have attached us clear and understandable
:)
3p squared + 6p + 18 divided by p - 6
9514 1404 393
Answer:
3p +24 +162/(p-6)
Step-by-step explanation:
The result of the division can be found using polynomial long division, or using synthetic division. The latter requires less writing and gives the same answer:
[tex]\dfrac{3p^2+6p+18}{p-6}=3p+24+\dfrac{162}{p-6}[/tex]
1000000000000 = 4*10?
Answer:
No
Step-by-step explanation:
if your asking is 10 to the power of 4 is 1000000000000, it is not. 10 to the power of 4 is 10000
12. Negative twelve is four less than twice a number, p.
Answer:
tyrr
Step-by-step explanation:
g
The equation to represent the given phrase is 2p-4=-12.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given phrase is "Negative twelve is four less than twice a number, p."
Here, four less than twice a number, p is
2p-4
The difference is equal to -12.
Now, 2p-4=-12
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, transpose -4 to the other side of an equation, we get
2p=-12+4
2p=-8
p=-2
Therefore, the value of p is -2.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
Evaluate πr² when r = 4.5. Use 3.14 for π.
1) 63.585
2) 199.6569
3) 14.13
4) 28.26
Answer:
A
Step-by-step explanation:
In the diagram below, A8 is parallel to CD. What is the value of y? Help me
Answer:
C. 108
Step-by-step explanation:
The angles are known as same-side interior angles. They are supplementary angles so their sum is 180°.
[tex]y+72=180\\y+72-72=180-72\\y=108[/tex]
The sum of 4 times a number and - 7, added to 9 times the number
Answer:
13x – 7
Step-by-step explanation:
If "a number represents x", then:
The sum of 4 times a number and - 7, added to 9 times the number = (4x + -7) + 9x.
(4x + -7) + 9x →
(4x + 9x) + -7 →
(13x) + -7 →
(13x) – 7 →
13x – 7.
The unknown number will be equal to 4.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the sum of 4 times a number and - 7, added to 9 times the number is 45. The value of the unknown number will be calculated as below:-
The sum of 4 times a number and - 7, added to 9 times the number = (4x + -7) + 9x.
(4x + -7) + 9x = 45
(4x + 9x) + -7 = 45
(13x) + -7 = 45
(13x) – 7 = 45
13x – 7 = 45
13x = 45 + 7
13x = 52
x = 4
Therefore, the unknown number will be equal to 4.
The complete question is given below:-
The sum of 4 times a number and - 7, added to 9 times the number is 45. Calculate the value of an unknown number.
To know more about an expression follow
https://brainly.com/question/723406
#SPJ2
GIVING BRAINLIST
Solve one sixth ÷ 6 = ___.
one thirty sixth
alt=one thirty eighth
one fourtieth
one fiftieth
[tex]\dfrac{1}{6}:6=\dfrac{1}{6}\cdot\dfrac{1}{6}=\dfrac{1\cdot1}{6\cdot6}=\dfrac{1}{36}[/tex]
Plz help I am confused
Give the slope and the y-intercept of the line y=9x+7 . Make sure the y-intercept is written as a coordinate.
Answer:
The slope is 9
The y intercept is (0,7)
Step-by-step explanation:
y=9x+7
The equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 9
The y intercept is (0,7)
Seven friends share the cost of a gift. Each friend pays $4.45. The gift costs $37.50. Can the friends buy the gift? Use estimation to justify your answer.
A. Yes; round 7 to 10, $4.45 to $4, and $37.50 to $38.
10 × $4 = $40, and $40 > $38.
B. Yes; round $4.45 to $5 and $37.50 to $35.
7 × $5 = $35, and $35 = $35.
C. No; round $4.45 to $5 and $37.50 to $40.
7 × $5 = $35, and $35 < $40.
D. No; round $4.45 to $4 and $37.50 to $38.
7 × $4 = $28, and $28 < $38.
Answer:
d
Step-by-step explanation:
round $4.45 to $4 and $37.50 to $38.
7 × $4 = $28, and $28 < $38.
Answer:
No , Option D is correct
Step-by-step explanation:
Their paid money is less that the cost of the gift ..
When there is -2^2, how come the answer is negative and not positive.
Answer:
the negative cancels out the positive
Can anyone help me with this
Answer and Step-by-step explanation:
This graph is a One to One Function.
For a function to be one-to-one, each x value must have its own y-value, which is the case for this graph.
The y value of a point where a vertical line intersects a graph represents an output for that input x value. If you draw a vertical line on the graph, and it intersects more than once, then the graph does not define as a function because that x value has more than one output (y).
#teamtrees #PAW (Plant And Water)
I hope this helps!
