Prove whether or not f(x)= 5x - 4 and g(x)= x+4/5 are inverses using composition of functions (PLEASE HELP)
Answers
f(x)= 5x - 4 and g(x)= x+4/5 are inverses by composition of functions
To prove that two functions, f(x) = 5x - 4 and g(x) = (x + 4)/5, are inverses of each other, we need to show that their composition yields the identity function.
First, let's find the composition f(g(x)):
f(g(x)) = f((x + 4)/5)
= 5((x + 4)/5) - 4
= (x + 4) - 4
= x
Now, let's find the composition g(f(x)):
g(f(x)) = g(5x - 4)
= ((5x - 4) + 4)/5
= 5x/5
= x
Since both f(g(x)) and g(f(x)) simplify to x, we can conclude that f(x) = 5x - 4 and g(x) = (x + 4)/5 are indeed inverses of each other based on the composition of functions.
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Is 3x-22=-3x+8 no solution?
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It has one solution which is X=5
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Answer:
220mL
780mL
600mL
480mL
Step-by-step explanation:
500-280=220
500+280=780
280/8=35, so 35 mL is in one L, 35x5=175
875-175=600
750-280=480
Answer:
Step-by-step explanation:
Lucas and Mitchell were asked to add the numbers 3.54 and 12.09.
Lucas stated that he completed the addition problem by using the following method:
First, I broke the numbers apart. I broke 3.54 into 3.00+0.50+0.04 and 12.09 into 12.00+0.09.
Then, I combined 0.04 and 0.09 to get 0.13.
Next, I combined 0.13 and 0.50 to get 0.63.
Then, I combined 3.00+12.00 to get 15.00.
Finally, I added the decimal to get 15.63.
Mitchell stated that he completed the addition problem by using the following method:
First, I added the whole numbers to get 3.00+12.00=15.00.
Next, I added the numbers in the tenths place, 0.50+0.00=0.50.
Then, I added the numbers in the hundredths place, 0.04+0.09=0.013.
I then added 0.50 and 0.013 to get 0.513.
Lastly, I added the decimal to the whole number to get 15.513.
Determine if Lucas and/or Mitchell had a flaw in their method. If they did, correct the flaw(s) so that both the methods used are correct. PLZ ANSWER THE QUESTION!
Answers
Answer:
0.22
Step-by-step explanation:
Select the equivalent expression.
3-5 = ?
Answers
Solve for x.
5/7x + 1/7= 63
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
12/49
Step-by-step explanation:
First write 2 1/3 as a improper fraction, to do that, first multiply the 2 by the denominator, then add it with the 1, which will result in 7/3
when doing division of fraction you have to remember this, KFG
KFG: Keep Flip Change
you keep the first number or fraction, which is 4/7
then you flip the sign, so you change division in to multiplication
after that, you change or write the reciprocal of the second number or fraction, so 7/3 will be 3/7
Now the equation is
4/7 times 3/7, which is 12/49
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AA similarity, SAS similarity, or SSS
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Explanation
Answers
Answer:
The triangles are similar due to AAA
Step-by-step explanation:
'The triangles ABC and DBE are similar because they have a common angle < B, and also angle < E is marked as congruent to angle < A. Then the third angle <C is going to be congruent to angle D as well due to the property of addition of internal angles of a triangle must add to 180 degrees.
Then the triangles are similar due to AAA
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Answer:
ectangles, rhombuses (also called rhombi) and squares are all more specific versions of parallelograms, also called special parallelograms. A quadrilateral is a rectangle if and only if it has four right (congruent) angles.
Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
(4 + x)/2 = 2
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x = 0
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Answer:
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It's urgent, Please answer, Make Sure you Round it
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
460, 451,442
Find the 37th term.
Answers
Answer:
136
Step-by-step explanation:
This is an arithmetic sequence
The formula is an = a1 + f × (n-1)
n= the number we are trying to find = 37
a= the number in any given space on the sequence
a1= 460
f= the common difference between the numbers
f= -9 because you subtract 9 from each to get the number
a37= 460-9(37-1)
a37= 460-9(36)
a37= 460- 324
a37= 136
[tex] \\ [/tex]
The first three terms of a sequence are 460, 451, 442[tex] \\ [/tex]
To Find :[tex] \\ [/tex]
37th term of sequence = ?[tex] \\ [/tex]
Solution :[tex] \\ [/tex]
Clearly these three terms are making an arithmetic sequence, with :
First term, a = 460 Common difference, d = 451 - 460 = - 9[tex] \\ [/tex]
Now, we have to find 37th term of sequence = [tex] \tt a_{37}[/tex]
[tex] \\ [/tex]
Now, we know that :
[tex] \large \underline{\boxed{\bf{a_{n} = a + (n-1)d}}}[/tex]
[tex] \\ [/tex]
[tex] \tt : \implies a_{37} = a + (37-1)d[/tex]
[tex] \tt : \implies a_{37} = a + 36d[/tex]
[tex] \\ [/tex]
Now, by substituting values of a and d :
[tex] \tt : \implies a_{37} = 460 + 36 \times (-9)[/tex]
[tex] \tt : \implies a_{37} = 460 - 324[/tex]
[tex] \tt : \implies a_{37} = 136[/tex]
[tex] \\ [/tex]
Hence, value of 37th term of given sequence is 136.
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Answer:
5. 26
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Step-by-step explanation:
5. Plug in the numbers
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Answer:
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Answers
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
$22,750
Step-by-step explanation:
First, find out how much Pierre is paid per week: $12.50 x 35 -> $437.5/week
Then, multiply to find how much he is paid the whole year: $437.5 x 52 -> $22,750
write the following decimals in the form of p\ q= 0 and p,q are con-primes 1) 15.265
Answers
Given:
The decimal number is 15.265.
To find:
The decimals in the form of [tex]\dfrac{p}{q}[/tex] and p,q are co-primes.
Solution:
Let the decimal number be [tex]x=15.265[/tex].
It can be rewritten as
[tex]x=15.265\times \dfrac{1000}{1000}[/tex]
[tex]x=\dfrac{15265}{1000}[/tex]
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Cancel out the common factors.
[tex]x=\dfrac{3053}{200}[/tex]
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Therefore, the requited fraction form is [tex]\dfrac{3053}{200}[/tex].