I need help simplifying #6

Answer: [tex]f^{-1}(4)=\frac{8}{5}[/tex]

Step-by-step explanation:

1. You need to find the Inverse function [tex]f^{-1}(x)[/tex]:

- Given the function f(x):

[tex]f(x) = 3x - \frac{4}{ 5}[/tex]

- Rewrite it with [tex]f(x)=y[/tex]:

[tex]y= 3x - \frac{4}{ 5}[/tex]

- Now you must solve for "x":

[tex]y+\frac{4}{ 5} = 3x\\\\(y+\frac{4}{ 5})(3)=x\\\\x=\frac{y}{3}+\frac{4}{15}[/tex]

- Now you must exchange the variables:

[tex]y=\frac{x}{3}+\frac{4}{15}[/tex]

- Then:

[tex]f^{-1}(x)=\frac{x}{3}+\frac{4}{15}[/tex]

2. Substitute [tex]x=4[/tex] into the Inverse function and then evaluate:

[tex]f^{-1}(4)=\frac{(4)}{3}+\frac{4}{15}\\\\f^{-1}(4)=\frac{8}{5}[/tex]

Answer:

y = 7 and x = 6

Step-by-step explanation:

15x-4y=62 ---------------------------(i)

5x+8y=86-----------------------------(ii) X 3

15x+24y=258---------------------------(iii)

(iii)-(i)

28y = 196

y = 7

Sub. for y in (I) to get x

x = 6

Final answer:

The system of equations 15x - 4y = 62 and 5x + 8y = 86 is solved using the method of elimination, yielding the solution x = 6 and y = 7.

Explanation:

We are asked to solve a system of equations:

We will use the method of elimination to solve this system, which involves manipulating the equations so that adding or subtracting them will eliminate one of the variables, allowing us to solve for the other.

Therefore, the solution to the system of equations is x = 6 and y = 7.

Answer:

n ≥ -17

Step-by-step explanation:

Writing a symbolic inequality, we get:

10 - 3n ≤ 61

Solve this for 3n by adding 3n to both sides of this equation:

10 ≤ 61 + 3n

Solve for n by subtracting 61 from both sides and then dividing all of the resulting terms by 3:

-51 ≤ 3n (divide both sides by 3):

-17 ≤ n, or

n ≥ -17

Answer:-42

Step-by-step explanation:

-12*7/2

Is also represented like this

-12/1*7/2 proper fraction

Multiple -12*7 and divide by 2

-84/2= -42

Answer:

Using BIDMAS the answer equates to -42.

Step-by-step explanation:

Answer:

[tex]\large\boxed{6x^3-33x^2+45x-6}[/tex]

Step-by-step explanation:

[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3x-6)(2x^2-7x+1)\\\\=(3x)(2x^2)+(3x)(-7x)+(3x)(1)+(-6)(2x^2)+(-6)(-7x)+(-6)(1)\\\\=6x^3-21x^2+3x-12x^2+42x-6\qquad\text{combine like terms}\\\\=6x^3+(-21x^2-12x^2)+(3x+42x)-6\\\\=6x^3-33x^2+45x-6[/tex]

Answer:

sodium chloride

Step-by-step explanation:

sea salt is basically sodium chloride

Answer:

Sodium chloride is the most abundant salt

Step-by-step explanation:

Answer:

55%

Step-by-step explanation:

its honestly just a guess

Answer:

n = 2

Explanation:

Simplify both sides of the equation

4n − 2n = 4

4n + −2n = 4

(4n + −2n) = 4 (Combine Like Terms)

2n = 4

2n = 4

Divide both sides by 2

2n / 2 = 4 / 2

n = 2

4n-2n=4

4n-2n= 2n

2n=4

÷2

n=2

Answer:

The number of balloons Raj could buy is 8.

Step-by-step explanation:

Given:

Raj has a $25 budget to spend on decorations for a party.

He has already spent $18.60.

He wants to get some helium balloons that’s cost $0.80 each.

Now, to write and solve an inequality to show the number of balloons Raj could buy.

Let the number of balloons be [tex]x.[/tex]

Cost of each balloons = $0.80.

So, the total cost of balloons = [tex]0.80x.[/tex]

He already spent = $18.60.

Total budget Raj has = $25.

Now, to solve an inequality to show the number of balloons:

[tex]0.80x+18.60\leq 25[/tex]

Subtracting both sides by 18.60 we get:

[tex]0.80x\leq 6.40[/tex]

Dividing both sides by 0.80 we get:

[tex]x\leq 8.[/tex]

Therefore, the number of balloons Raj could buy is 8.

5 is bigger because its right of your number line and it isn’t -8 because it below 0 and left of the number

The endpoints C and D has no midpoint M.

Step-by-step explanation:

step 1: The given endpoints of C and D are (-4,10) and (-4,10)

step 2: Midpoint formula = ((x1+x2)/2 , (y1+y2)/2)

step 3: Here, C(-4,10) = (x1,y1)

                      D(-4,10) = (x2,y2)

step 4: The midpoint represents the half distance of the line CD. Since C and D are same points, they cannot form a line. Therefore, the endpoints CD have no midpoint.

Answer:

ok so im going give the equation to fiqure this along with the awnser,

the basic equation is A=P (1+R/N)N(T)

P= Principle (Starting amount)

R= Interest rate

N= Amount of time compounded PER YEAR  

T= amount of years

Step-by-step explanation:

so this would be A=$7500 (1+ 0.055/12)12(3)

which come to A=$7500 (1.178948602)

which comes to a total of $8842.11

hope this helps

Final answer:

The balance of a savings account with an initial deposit of $7500 and an annual interest rate of 5.5%, compounded monthly, will be approximately $8863.52 after 3 years.

Explanation:

The question involves the concept of compound interest, more specifically how much the balance of a savings account with an initial deposit of $7500 and an annual interest rate of 5.5%, compounded monthly, will be in 3 years. To calculate this, we use the compound interest formula: A = P(1 + r/n)^(nt), where:

For the given problem:

We can substitute the values into the formula:

A = 7500(1 + 0.055/12)^(12*3)

Calculating this out, we find:

A = 7500(1 + 0.0045833)³⁶

A = 7500(1.0045833)³⁶

A = 7500(1.1811360235)

A = $8863.52 (approximately)

Therefore, the approximate balance of the savings account after 3 years will be $8863.52.

Answer:

y=-4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3y+14−2=0

3y+14+(−2)=0

(3y)+(14+(−2))=0 (Combine Like Terms)

3y+12=0

3y+12=0

Step 2: Subtract 12 from both sides.

3y+12−12=0−12

3y=−12

Step 3: Divide both sides by 3.

3y/3= −12/3

y=−4

Answer:

y=−4

Answer: B is the answer

Step-by-step explanation:

Answer:

20% of 600 is 120

Step-by-step explanation:

We shall use X as the variable

20% of x is 120

To find 20 percent of something, divide by 5.

Alternatively, you can find 10% of it then multiply by two.

600÷5 is 120

We see that 20% of 600 is 120

Answer:

x≥1500

Step-by-step explanation:

Answer:

There would be 11 books in each stack, to have the same number.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Books in stack 1 = 15

Books in stack 2 = 9

Books in stack 3 = 9

2.  If the books were rearranged so that the stack had the same number of books how many books would be even?​

Total books = Books in stack 1 + Books in stack 2 + Books in stack 3

Total books = 15 + 9 + 9

Total books = 33

Total books/Number of stacks = Number of books per stack to be the same

33/3 = Number of books per stack to be the same

Number of books per stack to be the same = 11

Answer:

1.50$

Step-by-step explanation:

2 hamburgers would equal 3$ and if the hot dogs are 1$ each it woul make the equation true

To find the price of a hamburger, set up a system of equations and solve for the price using the given information. So, the price of a hamburger is $2.50

To find the price of a hamburger, we can set up a system of equations based on the given information.

Let x be the price of a hamburger.

From the first scenario, we have 2x + 5(0.50) = 8.00.

From the second scenario, we have 5x + 2(0.50) = 9.50.

Simplifying these equations gives us 2x + 2.50 = 8.00 and 5x + 1.00 = 9.50.

Solving these equations, we find that x = $2.50.

Therefore, the price of a hamburger is $2.50.

https://brainly.com/question/28948054

#SPJ2

Answer:

B) -6

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(2-(-4))/(-1-0)

m=(2+4)/(-1)

m=6/-1

m=-6

the answer is B, -6, because if you graph it the line goes down and it rises up 6

Answer:

the slope of the ski run is 9

Answer:

(3, 5 )

Step-by-step explanation:

when x = 3, that is x ≥ 3, thus

y = 2x - 1 = 2(3) - 1 = 6 - 1 = 5 ⇒ (3, 5 ) is the point on the graph

Answer:

Table and graph attached

Step-by-step explanation:

Graph of a Function

Given a real function f(x), we can construct its graph by taking random values for x, computing f(x) for each selected value, and plotting the pairs (x,f(x)) in a rectangular grid. By joining the points we get an approximate graph.

It's not always easy to find an appropriate set of values for x which makes the important part of the graph be clearly shown in the graph. We select the range for x between -30 and +70. The results are shown in the table below.  

The graph is also shown in the second image provided.

Answer:

58 chickens, 42 goats

Step-by-step explanation:

there are a total of 100 chickens and goats

c + g = 100....c = 100 - g

there are 284 feet....chickens have 2 feet and goats have 4 feet

2c + 4g = 284

2(100 - g) + 4g = 284

200 - 2g + 4g = 284

-2g + 4g = 284 - 200

2g = 84

g = 84/2

g = 42 <===== goats

c + g = 100

c + 42 = 100

c = 100 - 42

c = 58 <==== chickens

Final answer:

To solve the problem, set up equations based on the number of feet each animal has, then use substitution to find there are 58 chickens and 42 goats in the barnyard.

Explanation:

How to Solve Problems Involving Numbers of Chickens and Goats

Old McDonald has 100 chickens and goats in the barnyard, and altogether, there are 284 feet. To find out how many chickens and how many goats are there, we can set up a system of equations based on the information given. A chicken has 2 feet and a goat has 4 feet. Let's assign the variable C to represent the number of chickens and G to represent the number of goats.

We are given two pieces of information which we will translate into two equations:

Equation 1: C + G = 100 (since there are 100 chickens and goats in total)

Equation 2: 2C + 4G = 284 (since chickens have 2 feet and goats have 4 feet)

To solve for C and G, we can multiply Equation 1 by 2 to align it with the coefficients of Equation 2:

2C + 2G = 200

Now, subtract this new equation from Equation 2 to solve for G:

(2C + 4G) - (2C + 2G) = 284 - 200

2G = 84

G = 42

With G known, we can substitute it back into Equation 1 to find C:

C + 42 = 100

C = 58

Therefore, there are 58 chickens and 42 goats in the barnyard.

Answer:

The true statement is Line h has points on planes R, P, and T

Step-by-step explanation:

The rest of the question is the attached figure

According to the graph, we will check which option is true.

a. Line h intersects line f at two points, A and B   (Wrong)

Because: h intersects line f at B only.

b. Line h is the intersection of planes R and T      (Wrong)

Because: g is the intersection of planes R and T

c. Line h intersects plane P at point C                   (Wrong)

Because: h intersects plane P at point B

d. Line h has points on planes R, P, and T             (True)        

Because h has the point B on the plane P, h has the point A on the plane T

and the points of h on the plane R

Answer:

Line h has points on planes R, P, and T

Step-by-step explanation:

did the test

Final answer:

5 minus 0.671 equals 4.329.

Explanation:

The student is asking for the number that, when subtracted from 5, equals 4.329. To find this number, you subtract 4.329 from 5:

5 - x = 4.329

Solving for x, you subtract 4.329 from 5:

x = 5 - 4.329

x = 0.671

Therefore, 5 minus 0.671 equals 4.329. When dealing with subtraction, it's important to round the result correctly, just as with other operations such as addition, multiplication, and division.

Answer:

a. 53

Step-by-step explanation:

The side with length 15 is opposite the right angle, so it is the hypotenuse of the right triangle.

For angle x, the side measuring 12 is the opposite leg.

Our 3 items of interest are: angle, opposite leg, hypotenuse.

The trig ratio that relates the opposite leg to the hypotenuse is the sine ratio.

sin x = opp/hyp

sin x = 12/15

sin x = 0.8

Now we take the inverse sine of 0.8 to find the measure of the angle.

x = sin^(-1) 0.8 = 53 deg

Answer:

x=9(student cost)

y=3(adult cost)

12=4x+8y

60=4x+8y

Answer:

x=9(student cost)

y=3(adult cost)

12=4x+8y

60=4x+8y

Step-by-step explanation:

Answer:

W = -9/8

Step-by-step explanation:

for two perpendicular lines

W*V = -1

W = 9/8*(-1)

W= -9/8

Final answer:

The slope of line W, which is perpendicular to line V with a slope of 8/9, is -9/8.

Explanation:

The slope of a line perpendicular to another in a two-dimensional plane is the negative reciprocal of the original line’s slope. Given that line V has a slope of 8/9, the slope of the perpendicular line W would be -9/8. This is because the product of the slopes of two perpendicular lines is -1 (negative one). Therefore, the slope of the line W, which is perpendicular to V, is -9/8.

Answer:

f(1) = - 1.8

f(n) = f(1) x 9ⁿ⁻¹

Step-by-step explanation:

f(1) = - 1.8

f(n) = f(1) x 9ⁿ⁻¹

f(1) = - 1.8 x 9⁰ = -1.8

f(2) = - 1.8 x 9¹

f(3) = - 1.8 x 9²

check:

f(1)=−1.8

f(n)=f(n−1)⋅9

f(2) = f(1) x 9 = -1.8 x 9¹

f(3) = f(2) x 9 = (- 1.8 x 9) x 9 = -1.8 x 9²

Answer: f(n)= -1.8*9^n-1

Step-by-step explanation: