1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tju [1.3M]
3 years ago
6

For f(x) = 5x + 2:

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
4 0

A)\\f(x)=5x+2\\\\f(7):\ \text{Put x = 7 to the equation of the function:}\\\\f(7)=5(7)+2=35+2=37\\\\\boxed{f(7)=37}

B)\\f(x)=5x+2\to y=5x+2\\\\\text{exchange x to y}\\\\x=5y+2\\\\\text{solve for y}\\\\5y+2=x\qquad\text{subtract 2 from both sides}\\\\5y=x-2\qquad\text{divide both sides by 5}\\\\y=\dfrac{1}{5}x-\dfrac{2}{5}\\\\\boxed{f^{-1}(x)=\dfrac{1}{5}x-\dfrac{2}{5}}

C)\\f^{-1}(x)=\dfrac{1}{5}x-\dfrac{2}{5}\\\\f^{-1}(7):\ \text{Put x = 7 to the equation of the function}\ f^{-1}(x):\\\\f^{-1}(7)=\dfrac{1}{5}(7)-\dfrac{2}{5}=\dfrac{7}{5}-\dfrac{2}{5}=\dfrac{7-2}{5}=\dfrac{5}{5}=1\\\\\boxed{f^{-1}(7)=1}

D)\\f(f^{-1}(7))\\\\f^{-1}(7)=1,\ \text{Therefore put x = 1 to the equation of the function}\ f(x):\\\\f(1)=5(1)+2=5+2=7\\\\\boxed{f(f^{-1}(7))=7}

You might be interested in
Antonina needs to have worked at least 909090 volunteer hours to graduate. She has already volunteered with a housing organizati
Veseljchak [2.6K]
An inequality can be formed by simply translating the problem statement to numerical expressions.

From the problem we know that 3w added with 52 hours should be equal or greater than 90 (helpful insight from the keyword "at least"). Therefore, it's inequality would look like:

3w+52>=90 (>= is used instead of ≥ for constraints in formatting)

The inequality above best models the situation.
8 0
3 years ago
Read 2 more answers
Duncan takes a break from studying and goes to the gym to swim laps. If swimming burns 9.05×105 cal per hour, how many kilojoule
fgiga [73]

For this case we have to by definition:

1 kilojoule equals 0.239006 kilocalorie.

1 kilocalorie equals 1000 calories

Then, if we have:9.05 * 10 ^ 5 \frac {calories} {hour} *\frac {1} {1000} \frac {kilocaloria} {calorie} = 9.05 * 10 ^ 2 \frac {kilocaloria} {hour}

Now:

9.05 * 10 ^ 2 \frac {kilocaloria} {hour} * \frac {1} {0.239006} \frac {kilojoule} {kilocaloria} = 3786.52 \frac {kilojoule} {hour}

Answer:

3786.52 \frac {kilojoule} {hour}

3 0
3 years ago
What's the solution for y+1/2=3/4
creativ13 [48]
\frac{y+1}{2} = \frac{3}{4}

2(y+1) = 3        LCD is 4

2*y + 2*1 = 3

2y + 2 = 3

2y = 3 - 2

2y = 1

y = 1 / 2


6 0
3 years ago
Which postulate or theorem, if any, could be used to prove the triangles congruent? If not
inysia [295]
Question 11a)

We are given side BC equals to side CE and angle CBA equals to angle CED
We also know that angle ACB equals to angle ECD are equal (opposite angles properties)

We have enough information to deduce that triangle ABC and triangle CDE are equal by postulate Angle-Side-Angle (ASA)

---------------------------------------------------------------------------------------------------------------

Question 11b)

We are given side AB equal to side ED, side BC equals to side EF, and side AC equals to side DF
We have enough information to deduce that triangle ABC and triangle DEF congruent by postulate Side-Side-Side (SSS)

----------------------------------------------------------------------------------------------------------------

Question 11c)

We are given side AC equals to side DF, angle ABC equals to angle DEF, and angle BAC equals to angle EDF

We have enough information to deduce that triangle ABC congruent to triangle DEF by postulate Angle-Side-Angle (ASA)

-----------------------------------------------------------------------------------------------------------------

Question 11d)

We do not have enough information to tell whether this shape congruent or not
7 0
3 years ago
Read 2 more answers
23 POINTS HERE PEOPLE
SOVA2 [1]

Hello!  

<h2>Answer: </h2>

23. 138 people voted for Nyemi, 69 people voted for Luke, and 23 people voted for Natalie.

24. Reina did not ride 11/16 of the rides.

<h2>Explanation:</h2>

23:

3 ÷ 5 = 0.6

230 × 0.6 = 138

230 × 0.3 = 69

230 × 0.1 = 23

24:

We know that Alberto rode 5/8 of the rides at the park, and Reina rode half of this.

5/8 × 1/2 = 5/16

16 - 5 = 11

8 0
3 years ago
Read 2 more answers
Other questions:
  • Complete the steps to find 3.18x10
    14·2 answers
  • Sixty one thousandths written in decimal notation
    12·2 answers
  • The Storm roller coaster climbs to a height of 180 feet. The Snake roller coaster climbs to a height of 105 feet. How much highe
    14·2 answers
  • Solve for w. | – w|≥2 Write a compound inequality like 1 &lt; x &lt; 3 or like x &lt; 1 or x &gt; 3. Use integers, proper fracti
    7·1 answer
  • Apply the associative property of multiplication to rewrite the expression and simplify -4(9b)
    10·1 answer
  • The bill in a restaurant is $102.25. A tip of 20% is added to the bill. What id tyhe final amount paid?
    14·1 answer
  • The dot plot shows how many swimmers are in each line at a waterpark:
    6·2 answers
  • In training, Kayden does
    10·1 answer
  • In 2008, the number of tourists visiting France was 7.94 x 10^7. The number of tourists visiting Italy was 4.27 x 10^7. Find the
    8·1 answer
  • guys is this answer is 44.8 or is it 21. It’s square roots and cube roots can someone please help mees
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!