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
iVinArrow [24]
3 years ago
5

If f(x) =1/4x+14, then f^-1(x)=

Mathematics
1 answer:
Naddika [18.5K]3 years ago
8 0

Answer: f⁻¹(x)=4x-56

Step-by-step explanation:

f⁻¹(x) is the inverse of f(x). To find the inverse, we replace the y with x, and x with y. Once we do that, we solve for y.

x=\frac{1}{4}y+14                 [subtract 14 on both sides]

x-14=\frac{1}{4}y                 [multiply both sides by 4]

4(x-14)=y               [distribute 4]

4x-56=y

f^-^1(x)=4x-56

You might be interested in
6.<br> HELP W THIS ONE TOO PLS!!
dybincka [34]
This occurs for the input(s) x where the outputs, f(x) and g(x), are equal. So here, f(x) = g(x) when x = 1, because 5 = 5.
5 0
3 years ago
Help please within the next hour
olasank [31]

c. 9

To complete the square, you take half of the coefficient of b and square it. It's important to note that the value being added will always be positive.

{ax}^{2}  +  bx + c

b =  - 6

- 6 \div 2 =  - 3

=  {( - 3)}^{2}

= 9

5 0
3 years ago
The rental car agency has 30 cars on the lot. 10 are in great shape, 16 are in good shape, and 4 are in poor shape. Four cars ar
Korolek [52]

Complete Question:

The rental car agency has 30 cars on the lot. 10 are in great shape, 16 are in good shape, and 4 are in poor shape. Four cars are selected at random to be inspected. Do not simplify your answers. Leave in combinatorics form. What is the probability that:

a. Every car selected is in poor shape

b. At least two cars selected are in good shape.

c. Exactly three cars selected are in great shape.

d. Two cars selected are in great shape and two are in good shape.

e. One car selected is in good shape but the other 3 selected are in poor shape.

Answer:

a

   P_A = \frac{^4 C_4}{^{30}C_{4}}

b

  P_B = \frac{[^{16} C_2 *^{14} C_2 ] +[^{16} C_3 *^{14} C_1 ] + ^{16} C_4}{^{30}C_{4}}

c

  P_C = \frac{^{10} C_3 *^{20} C_1 }{^{30}C_{4}}

d

   P_D = \frac{^{10} C_2 *^{16} C_2 }{^{30}C_{4}}

e

   P_E = \frac{^{16} C_1 *^{4} C_3 }{^{30}C_{4}}

Step-by-step explanation:

From the question we are told that

 The number of car in the parking lot is  n =  30  

  The number of cars in great shape is  k =  10

   The number of cars in good shape is r = 16

    The number of cars in poor shape is q = 4

The number of cars that were selected at random is N= 4

Considering question a

    Generally the number of way of selecting four cars that are in a poor shape from number of cars that are in poor shape is

            ^{q} C_{N}

=>        ^{4} C_{4}

Here C stands for combination.

 Generally the number of way of selecting four cars that are in a poor shape from total number of cars  in the parking lot is

          ^{n} C_{N}

=>      ^{30} C_{4}

Generally the probability that every car selected is in poor shape  is mathematically represented as

       P_A = \frac{^4 C_4}{^{30}C_{4}}

Considering question b

Generally the number of way of selecting 2 cars that are in good shape from number of cars that are in good shape is

            ^{r} C_{2}

=>        ^{16} C_{2}

Here C stands for combination.

 Generally the number of way of selecting the remaining 2 cars  from the remaining number of cars  in the parking lot is

          ^{n-r} C_{2}

=>      ^{30-16} C_{2}

=>      ^{14} C_{2}

Generally the number of way of selecting 3 cars that are in good shape from number of cars that are in good shape is

            ^{r} C_{3}

=>        ^{16} C_{3}

 Generally the number of way of selecting the remaining 1 cars  from the remaining number of cars  in the parking lot is

          ^{n-r} C_{1}

=>      ^{30-16} C_{1}

=>      ^{14} C_{1}

Generally the number of way of selecting 4 cars that are in good shape from number of cars that are in good shape is

            ^{r} C_{4}

=>        ^{16} C_{4}

Generally the probability that at least two cars selected are in good shape

       P_B = \frac{[^{16} C_2 *^{14} C_2 ] +[^{16} C_3 *^{14} C_1 ] + ^{16} C_4}{^{30}C_{4}}

Considering question c

Generally the number of way of selecting 3 cars that are in great shape from number of cars that are in great shape is      

            ^{k} C_{3}

=>        ^{10} C_{3}

 Generally the number of way of selecting the remaining 1 cars  from the remaining number of cars  in the parking lot is

          ^{n-k} C_{1}

=>      ^{30-10} C_{1}

=>      ^{20} C_{1}

Generally the probability of selecting exactly three cars selected are in great shape is

        P_C = \frac{^{10} C_3 *^{20} C_1 }{^{30}C_{4}}

Considering question d

Generally the number of way of selecting 2 cars that are in good shape from number of cars that are in good shape is

            ^{r} C_{2}

=>        ^{16} C_{2}

Generally the number of way of selecting 2 cars that are in great shape from number of cars that are in great shape is      

            ^{k} C_{2}

=>        ^{10} C_{2}

Generally the probability that two cars selected are in great shape and two are in good shape.

              P_D = \frac{^{10} C_2 *^{16} C_2 }{^{30}C_{4}}

Considering question e

Generally the number of way of selecting 1 cars that is in good shape from number of cars that are in good shape is

            ^{r} C_{1}

=>        ^{16} C_{1}

    Generally the number of way of selecting 3 cars that are in a poor shape from number of cars that are in poor shape is

            ^{q} C_{3}

=>        ^{4} C_{3}

Generally the probability that one car selected is in good shape but the other 3 selected are in poor shape is

         P_E = \frac{^{16} C_1 *^{4} C_3 }{^{30}C_{4}}

4 0
3 years ago
Use the given information to find the lengths of the other two sides of the right triangle if side a is opposite angle A, side b
sveta [45]

SOH CAH TOA tells you

... cos(B) = a/c

... 4/5 = 8/c

... c = 10 . . . . . multiply by 5c/4

By the Pythagorean theorem,

... b = √c² -a²) = √(10² -8²) = √36 = 6

The lengths of the other two sides are: b = 6, c = 10.

_____

You can tell from the value of the cosine that this is a 3-4-5 right triangle. You can tell from the value of "a" that the scale factor is 2. That means the other two sides are 6 and 10.

4 0
3 years ago
Solve the equation 2x+8=12+10x
kari74 [83]

Solve the equation. Isolate the variable, x.

Note the equal sign, what you do to one side, you do to the other.

First, subtract 8 and 10x from both sides:

2x (-10x) + 8 (-8) = 12 (-8) + 10x (-10x)

2x - 10x = 12 - 8

Simplify. Combine like terms:

(2x - 10x) = (12 - 8)

-8x = 4

Isolate the variable, x. Divide -8 from both sides:

(-8x)/-8 = (4)/-8

x = -(4/8)

Simplify:

x = -1/2

-1/2 is your answer for x.

~

6 0
3 years ago
Read 2 more answers
Other questions:
  • For the right triangle shown, which expression represents the length of CA?
    10·1 answer
  • mukul has $2.25 in nickerl,dimes and quarters. he has 6 more times than quarters and 9 more nickels than quarters. How manyof ea
    9·1 answer
  • A stack of one hundred twenty cards is placed next to a ruler, and the height of stack is measured to be
    10·1 answer
  • Which expression is equivalent to (3x + 6) + 4x?
    12·1 answer
  • Rise is the change between the y-coordinates of any two points along a line in the xy-plane
    6·2 answers
  • Enter an algebraic expression for the word expression.<br><br> The quotient of −8 and y
    5·1 answer
  • Identify solutions to each inequality- pls someone help me
    13·1 answer
  • SOMEONE HELP ME PLEASE
    10·2 answers
  • For what value k the pair of linear equations 4x-3y=9 and 2x+ky=11 has no solution
    10·1 answer
  • ‏The result of a division problem is the a ) divisor . b ) quotient . c ) factor . d ) remainder .
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!