How to algebraically find the inverse of a function?

The problem can be represented by two inequalities: one to ensure earning at least $50 per week (5x + 10y >= 50) and another to restrict working to no more than 10 hours per week (x + y <= 10), alongside x >= 0 and y >= 0 to indicate non-negative hours worked for each job.

To determine the system of inequalities to solve the problem, we need to define variables for the number of hours spent on each job. Let's use x to represent the number of hours working as a cashier at the grocery store, and y to represent the number of hours mowing lawns. The student earns $5 per hour at the grocery store and $10 per hour mowing lawns. They want to earn at least $50 per week and work no more than 10 hours in total.

From this information, we can establish the following inequalities:

5x + 10y >= 50 (To ensure earning at least $50 per week)

x + y = 10 (To ensure working no more than 10 hours per week)

Additionally, we include y >= 0 and x >= 0 to represent that the number of hours worked at either job cannot be negative.

Answer: 12

Step-by-step explanation:

Shade 0.08 3 times

In total that's 24 hundreths to shade

all im doing is trying to get points Lol

the simplified expression is 25xy^4 + 65xy^3 + 22xy + 12xy^2 + 18y + 12y^2 + 5y^3 + 12

To simplify the given expression, we first need to combine like terms. Like terms are those that have the same variables raised to the same powers. In this case, we have terms with x and y raised to different powers.

The expression is:

25xy^4 + 60xy^3 + 5xy^3 + 5xy + 12xy^2 + 5y^2 + 12 + 5xy + 12y + 5y^3 + 12y^2

Now, let's combine the like terms:

Combine the terms with xy^4: 25xy^4

Combine the terms with xy^3: 60xy^3 + 5xy^3 = 65xy^3

Combine the terms with xy^2: 12xy^2

Combine the terms with xy: 5xy + 5xy + 12xy = 22xy

Combine the terms with y^2: 5y^2 + 12

Combine the terms with y: 12y + 5y + 12y^2 = 18y + 12y^2

Combine the terms with y^3: 5y^3 + 5y^3 = 10y^3

Now, let's put all the combined like terms together:

25xy^4 + 65xy^3 + 22xy + 12xy^2 + 18y + 12y^2 + 5y^3 + 12

This is the simplified expression.

The probable question maybe:

simplify the given expression [tex]\(25xy^4 + 60xy^3 + 5xy + 5xy^3 + 12xy^2 + 5y^2 + 12 + 5xy + 12y + 5y^3 + 12y^2\)[/tex]

Answer:

10.4 cm

Step-by-step explanation:

Looking at the triangle in the attached pic, we can see that the right, smaller triangle is a right triangle on which we can apply the pythagorean theorem to solve for the height, h.

Pythagorean theorem tells us [tex]c^2=a^2+b^2[/tex] where c is the hypotenuse (12 in our case) and a & b are the two legs (6 and h are the respective lengths).

So let's solve for h:

[tex]c^2=a^2+b^2\\12^2=6^2+h^2\\144=36+h^2\\144-35=h^2\\108=h^2\\h=\sqrt{108} \\h=10.4[/tex]

Final answer:

The algebraic expression for the problem is '8n - 20 = 3n + 80', which simplifies to 'n = 20'. Therefore, the number in question is 20.

Explanation:

The question presents a classic algebra problem where we have to find the value of a variable that satisfies a given condition. Specifically, this problem states:

"If 8 times a number is decreased by 20, the result is the same as 3 times the number increased by 80."

To solve this, we'll convert the words into an algebraic equation and solve for the number. Let's use 'n' to represent the number:

This equation tells us that when you multiply the number by 8 and subtract 20, it's equal to the result of multiplying the number by 3 and adding 80. To find 'n', we combine like terms and solve:

Thus, the number we're looking for is 20.

Hii!

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[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

72

[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]

To find the next term in the arithmetic sequence, we should first find the common difference.

The common difference is the amount we add or subtract to obtain the next term. In the given sequence we add 7.

So, let's find the next term.

[tex]\twoheadrightarrow\sf65+7[/tex]

[tex]\bullet[/tex] Add 7

[tex]\twoheadrightarrow\sf72[/tex]

[tex]\bullet[/tex] Great job! We found the next term

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

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Answer:

The equation of the parabola which opens left or right is [tex]x=ay^2+by+c[/tex].

Step-by-step explanation:

We know that,

If in the equation of the parabola,

1. If x is squared, then the parabola opens upwards or downwards.

2. If y is squared, then the parabola opens towards left or right.

Since, we want the equation of the parabola which opens left or right.

So, we get that,

The variable 'y' is being squared in the equation of the given parabola (from 1).

Answer:

x = ay^2 + by + c

Step-by-step explanation:

it was correct for me

An irrational number is something that cant be expressed as a ratio.  For ex:the square root of 2.  Hope this helps.

You sold 36 tickets and your friend sold 22 tickets.

Let's represent the number of tickets you sell as x and the number of tickets your friend sells as y.

We know that you sell 14 more tickets than your friend, so we have the equation:

x = y + 14

We also know that together you and your friend sell 58 tickets, so the equation becomes:

x + y = 58

Now we can solve these two equations simultaneously to find the values of x and y.

(y + 14) + y = 58

2y + 14 = 58

2y = 44

y = 22

x = 22 + 14

x = 36

Therefore, you sold 36 tickets and your friend sold 22 tickets.

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The system of equations representing the problem is y = x + 14 and x + y = 58. Solving this system we get x = 22 (friend's sold tickets) and y = 36 (your sold tickets).

We'll use a system of linear equations to model this situation. Let's define x as the number of tickets your friend sells, and y as the number of tickets you sell. From the problem, we know two things:

1. You sell 14 more tickets than your friend: y = x + 14.

2. Together, you and your friend sell 58 tickets: x + y = 58.

To solve this system, we can substitute y in the second equation with x + 14 from the first equation. This gives us:

x + (x + 14) = 58.

Solving this we get x = 22 and substituting x into the first equation gives: y = 22 + 14 = 36.

So, your friend sold 22 tickets, and you sold 36 tickets.

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Answer:

The object would travel 7 meters.

Step-by-step explanation:

The distance the object would travel is 7 meters if applying 6 newtons of force to an object results in 42 joules of work.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

If applying 6 newtons of force to an object results in 42 joules of work

We know,

Work = Force x Distance

42 = 6xDistance

Distance = 7 meters

Thus, the distance the object would travel is 7 meters if applying 6 newtons of force to an object results in 42 joules of work.

Learn more about the distance here:

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Answer: 1/4

Step-by-step explanation:

Answer:

The correct option is 2. The value of n is 3.

Step-by-step explanation:

Circumcenter is the point, where the perpendicular bisectors of a triangle intersect each other.

Circumcenter is also known as the center of the triangle. The distance from circumcenter to each vertex are same.

In triangle DEF, if A is the circumcenter.

[tex]AE=AD[/tex]

[tex]10=2n+4[/tex]

Subtract 4 from both sides.

[tex]10-4=2n[/tex]

[tex]6=2n[/tex]

Divide both sides by 2.

[tex]3=n[/tex]

Therefore the value of n is 3 and option 2 is correct.

Answer:

Option 2 is true

Step-by-step explanation:

We have to find the value of n for which point A becomes circumcenter.

Circumcenter: It is that point where perpendicular bisectors of triangle intersects.

The circumcenter  is also knows as center of triangle.

Circumcenter is at equal distance from each vertex of triangle.

If point A is circumcenter then

AE=AD

We have AE=10 units

AD=2n+4

Substitute the value

10=2n+4

[tex]2n=10-4[/tex]

By subtraction property of equality

[tex]2n=6[/tex]

[tex]n=\frac{6}{2}=3[/tex]

Hence, the value of n is 3 would make point A the circumcenter.

Answer:

Option B. Graph B

Step-by-step explanation:

The given system of the inequalities are 6x + y > -3 and 2x + y ≤ 4

If we take the first inequality which represents the area below the line 6x + y = -3 or y = -6x - 3 (Slope of the line -6 and y-intercept is -3)

Second graph is represented by 2x + y ≤ 4 which represents the area below  the line y = 4 - 2x ( slope = -2 and y intercept = 4)

Option B shows the shaded area which the common area representing the solution set of these systems.

The volume of the wedge is 50π/3 - 25√3.

To find the volume of the wedge, we need to calculate the volume of the cylindrical segment between the two intersecting planes. The formula for the volume of a cylindrical segment is V = h((R^2θ)/2 - (R^2sinθ)/2), where h is the height of the segment, R is the radius of the cylinder, and θ is the angle of the intersection between the planes. In this case, h is 10 and θ is 30°, so the formula becomes V = 10((10^2 * π/6)/2 - (10^2 * sin(π/6))/2). Simplifying the equation gives V = 50π/3 - 25√3.

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Answer: system 2 (5,0)        and                        system 3   (-1 2)

             2x-6y=10                                                      3x-y=-5

                x+8y=5                                                      x+4y=7

Step-by-step explanation:

Solve each system. Then drag each one to the column headed by a point which could be its solution. (5,y) or (x,2)

system 1

2x - 2y =12          

-2x-3y = -22

solve simultaneous equation

2x - 2y =12          

-2x-3y = -22

add the equations gives

2x +(-2x) =0

-2y+(-3y) =-5y

12+ (-22) = -10

-5y =-10

y =2

2x -2(2) =12

2x-4 =12

2x = 12+4

x= 16/2 =8 x=8 and y =2 = (8,2)

system 2

2x-6y=10  *(-1) = -2x + 6y =-10

x+8y=5 *(2)    = 2x + 16y =10 add the equations

22y =0 y =0

x : 2x - 6(0) =10

x = 10/2 = 5

(5, 0)

 system 3

  3x-y=-5  *(-1) = -3x + y =5

  x+4y=7 * (3) = 3x + 12y = 21

add the equations = 13y = 26  y = 2

3x -2 =-5 = 3x = -3 =x =-1

(-1 2) answer

system 4

x+y=2   *(-2) = -2x -2y = -4

2x+y=13 *(1) = 2x +y = 13

add the two equations = -y =9

y = -9

substitute 2x-9= 13= 2x =22 x =11

(11 -9)