Let f(x)=2x+2. Solve f^-1(x) when x=4

Answers

Answer 1

Answer: f⁻¹(x) stands for the invers of function f(x). The inverse of f(x) is equal to x. We need to solve for x.

solve for x
f(x) = 2x + 2
2x + 2 = f(x)
2x = f(x) - 2
x = $(f(x)-2)/(2)$
f⁻¹(x) = $(x-2)/(2)$

Determine the value of f⁻¹(x) when x = 4
f⁻¹(x) = $(x-2)/(2)$
f⁻¹(4) = $(4-2)/(2)$
f⁻¹(4) = $(2)/(2)$
f⁻¹(4) = 1
When x = 4, the value of f⁻¹(x) is equal to 1

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Answers

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(3-7n^2+3n^3)-(6n^3-1-5n^2). Simplify.

Answers

Simplify

3 - 7n^2 + 3n^3 - (6n^3 - 1 - 5n^2)

Simplify brackets

3 - 7n^2 + 3n^3 - 6n^3 + 1 + 5n^2

Collect like terms

(3 + 10) + (-7n^2 + 5n^2) + (3n^3 - 6n^3)

Simplify

4 - 2n^2 - 3n^3

Answer:

-3n^3 - 2n^2 + 4.

Step-by-step explanation:

(3-7n^2+3n^3)-(6n^3-1-5n^2)

First distribute the negative over the second parentheses:

= 3 - 7n^2 + 3n^3 - 6n^3 + 1 + 5n^2

Now simplify like terms:

= -3n^3 - 2n^2 + 4 (answer).

Solve by substitution {x-4y=22} and {4x-5y=22}

Answers

x - 4y = 22
Add 4y to each side
x = 22 + 4y

Now replace x with 22 + 4y in the second equation.
4(22 + 4y) - 5y = 22
Distribute.
88 + 16y - 5y = 22
Simplify.
88 + 11y = 22
Subtract 88 from each side.
11y = -66
Divide by 11.
y = -6

Plug in -6 for y in an earlier equation and solve for x.
x-4(-6)=22
Negative 4 times negative 6 = 24 (the negatives cancel)
x+24=22
Subtract 24 from each side.
x = -2

An X-ray machine for animals costs$125,000. If the loan is for 10 years, an the interest paid is $65,625, what is the interest rate on the loan

Answers

The answer is 5.25%.

$65,625/10yrs=$6,562.50 per a year.

6,562.5/125000= .0525 which translates to 5.25%.

There are 13 chickens and pigs in the barn. There are 40 legsin all (each chicken has two legs and each pig has four legs).
Use substitution to solve the linear system of equations and
determine how many chickens, x, and pigs, y there are.
Express the solution as an ordered pair (x,y).

Answers

Answer:

(6, 7)

Step-by-step explanation:

x+y= 13

2x+4y= 40 ⇒ x+2y = 20 ⇒ 13-y +2y= 20 ⇒ y= 20-13= 7

x= 13-y= 13-7= 6

chickens= 6

pigs= 7

Final answer:

To solve the problem, set up a system of equations using the given information. Solve one equation for a variable and substitute it into the other equation to find the values of the variables. Determine the number of chickens and pigs in the barn. The solution is (6, 7).

Explanation:

To solve this problem, we can set up a system of equations based on the given information. Let x represent the number of chickens and y represent the number of pigs. From the information given, we can write two equations: x + y = 13 (equation 1) and 2x + 4y = 40 (equation 2).
Using substitution, we can solve equation 1 for x and substitute it into equation 2:

Equation 1:

x + y = 13

x = 13 - y

Equation 2:

2(13 - y) + 4y = 40

26 - 2y + 4y = 40

2y = 14

y = 7

Now, substitute the value of y back into equation 1 to find x:

x + 7 = 13

x = 6

Therefore, there are 6 chickens and 7 pigs in the barn, which can be expressed as the ordered pair (6, 7).