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:
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if 5(x-6)=8 then x=?
Step-by-step explanation:
5(x-6)=8
5x - 30 = 8
5x = 8 + 30
5x = 38
X = 38/5
X = 7.6
The value of x is 7.6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
5 (x - 6) = 8
Solve for x.
5x - 30 = 8
5x = 8 + 30
5x = 38
x = 38/5
x = 7.6
Thus,
x is 7.6.
Learn more about expressions here:
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PLZZZZZZZZZZZZZZZZZZZZ HELP
Answer:
1/20
do you need explanation?
Could someone please answer and explain step by step?
[tex]\\ \sf\longmapsto 4\left(\dfrac{7}{8}\right)+7\left(\dfrac{3}{4}+\dfrac{1}{8}\right)-10[/tex]
[tex]\\ \sf\longmapsto \dfrac{4(7)}{8}+7\left(\dfrac{6+1}{8}\right)-10[/tex]
[tex]\\ \sf\longmapsto \dfrac{28}{8}+7\times \dfrac{7}{8}-10[/tex]
[tex]\\ \sf\longmapsto \dfrac{28}{8}+\dfrac{49}{8}-10[/tex]
[tex]\\ \sf\longmapsto \dfrac{28+49-80}{8}[/tex]
[tex]\\ \sf\longmapsto \dfrac{78-80}{8}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-2}{80}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-1}{40}[/tex]
What is the answer to this?
y values = 4 - 1 =3 units . ignore x values
Explain how you know that the sums of 12.6,3.1 and 5.4 is greater than 20
Answer:
2.6+3.1+5.4 =21.1
if you have 20
subtract 21.1-20
then you have 1.1
since the difference is 1.1 then we say
21.1>20
8a-4(-5a-2)=12a solve please!!!
Answer:
A=-1/2
If you search it up, it will show you all the steps
Awnserssss plsssssssssssssssssssssssss 18 points
Answer:
10. f'(x) = (x/14) + (14/9)
11. f'(x) = - x + 2
12. f'(x) = 2x - 8
Step-by-step explanation:
The step to solving inverse is a simple trick. You must invert x and y.
For (10.) let f(x) = y
then y = 9x - 14
x = 9y - 14 (this is inverting x and y)
solving for y: x + 14 = 9y
therefore : y = (x/14) + (14/9)
You can do this for the others as well and using simple "solve for x" methods, you can solve for y which is f'(x).
Figure A maps to figure B with a scale factor of point 8
Answer:
Please you didn't provide the coordinates of figure A and figure B, only the scale factor. If you provide the coordinates,I will be able to solve it.
Thank you.
List all info given by the marks on the diagram.
Which square root is between 4 and 5?
A. √ 10
B. √ 14
C. √24
D. √ 32
A small fly weighs approximately 2.2 • 10^-3 gram and an average sized gnat weighs approximately 9•10^-4
1. find the sum of the weights of the two insects
2. How much heavier is the fly than the gnat?
SOMEONE PLEASE HELP I'LL GIVE YOU 50 POINTS :)
Answer:a because when u start off with a parrell line u have 2 start with the a moves 2 b
Step-by-step explanation:
What are 3 fun facts about Brazil in your own words? Answer ASAP
Due today
Answer:
Brazil is the only country in South America that speaks Portuguese
The name Brazil comes from a tree named brazilwood
Brazil is the largest country in South America
lmk if incorrect
Plz help I am very confused I need help now plz
Answer:
so the second one
4 * (-9) * (-3) * (-1)
Step-by-step explanation:
-2 * (-7) * 12 * 4 = positive
4 * (-9) * (-3) * (-1) = negative
-6 * (-7) * (-8) * 0 = positive
-3 * (-2) * (-4) * (-7) = positive
negative times negative = positive
What is the equation of the quadratic function with a vertex at (2,–25) and an x-intercept at (7,0)?
Let start with some basic theory of quadratics
If f(x)=ax2+bx+c a,b,c ∈R a≠0 f(x)=ax2+bx+c a,b,c ∈R a≠0 has 2 2 roots r1 r1 and r2 r2 than it can take the form f(x)=a(x−r1)(x−r2).f(x)=a(x−r1)(x−r2).
The maximum or minimum value of f(x) f(x) is M=−(b2–4ac)4a M=−(b2–4ac)4a
If a>0 a>0 then M M is the minimum value and if a<0 a<0 then M M is the maximum value.
Lets go now to the question
Since 2 2 and 7 7 are the roots our function will be f(x)=a(x−2)(x−7), a∈R f(x)=a(x−2)(x−7), a∈R
so f(x)=a(x2
Tina is saving to buy a notebook computer. She has two options. The first option is to put $500 away initially and save $30 every month. The second option is to put $300 away initially and save $50 every month. After how many months would Tina save the same amount using either option? How much would she save with either option?
Answer:
10 months. Each plan will save 800 dollars.
Step-by-step explanation:
500 + 30x = y
300 + 50x = y
You want the months to give the same amount of money. The x has to be the same for both
500 + 30x = 300 + 50x Subtract 300 from both sides
500 - 300 + 30x = 50x Combine
200 + 30x = 50x Subtract 30x from both sides
200 = 50x - 30x Combine
200 = 20x Divide by 20
x = 10
So in 10 months time the amounts will be the same. How much will there be?
500 + 30*10 = 500 + 300 = 800
300 + 50*10 = 300 + 500 = 800
Miranda needs to buy a bottle of honey. She notices that she can pay $4 for a
12 oz bottle, or she can pay $6 for a 24 oz bottle. Which bottle is the better buy?
Hint: Find a unit rate (ounces for each dollar).
Answer:
The better one is $6 for 24 oz bottle
Step-by-step explanation:
If it cost 4 dollars for a 12 oz bottle and that would cost 1 dollar per 3 oz but for the 6 dollar for a 24 oz bottle it would be 1 dollar per 4 oz so 6 dollars for a 24 oz bottle is better!
Write in standard form.
y^2+14y-5x+64=0
[tex] \hookrightarrow \: {y}^{2} + 14y - 5x + 64 = 0[/tex]
[tex] \hookrightarrow \: 5x = {y }^{2} + 14y + 64[/tex]
[tex] \hookrightarrow \: 5x = {y}^{2} + 14y + 49 + 15[/tex]
[tex] \hookrightarrow \: 5x = (y + 7) {}^{2} + 15[/tex]
[tex] \hookrightarrow \: x = \dfrac{(y + 7) {}^{2} + 15 }{5} [/tex]
[tex] \hookrightarrow \: x = \dfrac{1}{5} (y + 7) {}^{2} + 3[/tex]
therefore, the correct option is B
Answer:
x = (1/5)(y + 7)² + 3
Step-by-step explanation:
Given that,
→ y² + 14y - 5x + 64 = 0
Let's find the required solution,
→ y² + 14y - 5x + 64 = 0
→ 5x = y² + 14y + 64
→ 5x = y² +14y +49 + 15
→ 5x = (y + 7)² + 15
→ x = [(y + 7)² + 15]/5
→ [x = (1/5)(y + 7)² + 3]
Hence, it is the correct answer.
Two bacteria are in a dish. The number bacteria triples every hour following this pattern find the number of bacteria in the dish after 10 hours and after n hours 
Answer:
59051
Step-by-step explanation:
Answer:
x=118,095
Step-by-step explanation:
6 = 2[tex]e^{k*1}[/tex]
3 = [tex]e^{k }[/tex]
ln(3) = k ln(e)
k = ln(3)
k = 1.09861
[tex]x = 2e^{1.09861*10}[/tex]
x = 2e^{10.9861}
[tex]x=2e^{10.9861}\quad \left[/tex]
x=118,095
The value of 3 times the quantity of 4 + x is greater than 6 less than x.
Which inequality represents this situation?
A
3(4+x)>6−x
B
3⋅4+x≥x−6
C
3(4+x)>x−6
D
3⋅4+x≥6−x
[tex]\\ \sf\longmapsto 3(4+x)\gt x-6[/tex]
[tex]\\ \sf\longmapsto 12+3x\gt x-6[/tex]
[tex]\\ \sf\longmapsto 12+6\gt x-3x[/tex]
[tex]\\ \sf\longmapsto 18\gt -2x[/tex]
[tex]\\ \sf\longmapsto x\lt\dfrac{18}{-2}[/tex]
[tex]\\ \sf\longmapsto x\lt -9[/tex]
Step-by-step explanation:
[tex]here \: 3(4 + x) > x -6\\ 3 \times 4 + 3x > x-6 \\ 12 + 3x > x-6 \\ 2x >- 6-12 \\ x = \frac{ - 18}{2} \\ x > - 9\\ option \: (c)is \: ur \: answer \\ thank \: you[/tex]
Can someone please help me with this question
Answer:
D: {-1, 0, 1, 4}; R: {-6, 3, 5, 7}D: {-1, 2, 3}; R: {3, 5, 7}D: {-2, -1, 0, 1}; R: {0, 1, 4}Step-by-step explanation:
For relations expressed as (input, output) or (x, y) pairs, the domain is the list of inputs, or x-values. The range is the list of outputs, or y-values. Yes, it is that simple. (We often like to arrange the lists in increasing order.)
__
1. Domain: {-1, 0, 1, 4}
Range: {-6, 3, 5, 7}
__
2. Domain: {-1, 2, 3}
Range: {3, 5, 7}
__
3. Domain: {-2, -1, 0, 1}
Range: {0, 1, 4}
Add 6 5/6 + ( -6 1/5 )
Answer:
0.63
Step-by-step explanation:
Which of the following is the best measure central tendency for a quantitative data with extreme values? A. All of those
b. Median
c. Mode
d. Mean
Answer:
in this question, the mean would be the best measure for central tendency....
Step-by-step explanation:
because it is the measure that includes all the values in the data set for its calculation, and any change in any of the scores will affect the value of the mean. This is not the case with the median or mode.
So in conclusion your answer will be D.mean
The assositive property works with expressions that use
Answer:
lol
Step-by-step explanation:
Answer:
The associative property can be used with multiplication and addition.
Examples:
2+(3+2) -> (2+3)+2 (Associative Addition)
2*(3*2) -> (2*3)*2 (Associative Mult.)
It does not work with division or subtraction.
2-(3-2) does not equal (2-3)-2
Please help again, sorry for asking…
[tex]\text{BC}=6\text{x}+4\\\\\text{AC}=52\\\\\text{AB}=4\text{x}+8\\\\\text{AB}+\text{BC}=\text{AC}\\\\4\text{x}+8+6\text{x}+4=52\\\\10\text{x}+12=52 \ \ /-12\\\\10\text{x}=40 \ \ /:10\\\\\text{x}=4\\\\\text{BC}=6\cdot4+4=24+4=\boxed{28}[/tex]
Find the greatest 4-digit number which
is a common multiple of 12, 40, and 45.
Answer:
the least common multiple is 240 of the following
Step-by-step explanation:
Answer:
9720
Step-by-step explanation:
because I looked it up and saw three different websites tell me it's 9720
Ricky, Nathan, and Henry collect comic books. Ricky owns twice as many comic books as Nathan. Henry owns as many comic book
Ricky. If Nathan owns 129 comic books, how many does Henry own
Answer:
258 i think
Step-by-step explanation:
Which one is smaller 5/12 or 5/11?
Hi! I'm happy to help!
Fractions are wholes that are split up. When you split the whole into more pieces, the pieces are smaller.
Due to the fact that 5/12 is split into more pieces than 5/11, and they have the same amount of pieces, 5/11 would be larger because of bigger pieces.
5/11 is bigger because it has bigger pieces.
I hope this was helpful, keep learning! :D
Given the formula:
A = Pe^r.t
Using your scientific calculator, find the money accumulated if you invested $65,000 at 7.3% interest for 10 years compounded continuously.
a. $134,880.24.
b. $96,219,495.29.
c. $69,922.48.
d. None of the above.
9514 1404 393
Answer:
a. $134,880.24
Step-by-step explanation:
Put the numbers into the formula and do the arithmetic.
A = $65,000×e^(0.073×10) ≈ $134,880.24
_____
Additional comment
The doubling time for continuously compounded interest is 69.3 years divided by the interest rate in %. Here, that is 69.3/7.3 = 9.49 years. That means an investment of 10 years will be slightly more than double the original amount. 2×65,000 = 130,000, so choice A is in the right ballpark. The other numerical choices are not.
A bicycle is traveling at 16 miles per hour.
How many feet will it cover in 55 seconds?
Round your answer to the nearest tenth of a foot.
Answer:
1,290.7ft
Step-by-step explanation:
d = rate x time
d = 16mi/hr x 1hr/3600s x 55s x 5280ft/mi
d = 1290.7ft (cancel mi, hr, s)
