3.) rewrite r(x) in expanded form

Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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\(\\ \tt\bull\rightarrowtail h(x)=1/5(x^2-6)-8\)

\(\\ \tt\bull\rightarrowtail h(4)\)

\(\\ \tt\bull\rightarrowtail 1/5(4^2-6)-8\)

\(\\ \tt\bull\rightarrowtail 1/5(16-6)-8\)

\(\\ \tt\bull\rightarrowtail 10/5-8\)

\(\\ \tt\bull\rightarrowtail 2-8\)

\(\\ \tt\bull\rightarrowtail -6\)

The monthly income of the first person is $600.

Given that, the average monthly income of three persons is RS 3,600.

The income of the first is 1/5 of the combined income of the other two.

Here, Let income of the first be A, let income of the second be B and let Income of the third be C.

A+B+C=3600 -----(i)

Income for the first person = 1/5(B+C) -----(ii)

Substitute equation (ii) in equation (i), we get

(B+C)/5 +B+C =3600

B+C+5B+5C=3600×5

6B+6C=18000

6(B+C)=18000

B+C=3000 ------(iii)

Substitute (iii) in equation (i), we get

A=$600

Therefore, the monthly income of the first person is $600.

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Answer:

he will fill 6 pitchers

Step-by-step explanation:

4.8÷0.8=6

Answer:

3x^2-7x-7

Step-by-step explanation:

(x-1)^2= x^2-2x+1

x+10 = 3(x^2-2x+1)

x+10 = 3x^2-6x+3

Then subtract x+10 from both sides which equals:

3x^2-7x-7

Answer:

I think its C

Step-by-step explanation:

The solution of the compound inequality 5x + 7 ≤  - 3 or 3x - 4 ≥ 11 is x ≤ -2 or x ≥ 5. Therefore, the answer is C.

An inequality is an expression containing <, >, ≤ and ≥.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality as follows:

5x + 7 ≤  - 3 or 3x - 4 ≥ 11

5x + 7 ≤  - 3

5x ≤ -3 - 7

5x ≤ - 10

divide both sides by 5

x ≤ - 10 / 5

x ≤ -2

3x - 4 ≥ 11

3x ≥ 11 + 4

3x ≥ 15

x ≥ 15 / 3

x ≥ 5

Therefore,

x ≤ -2 or x ≥ 5

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-1

We can solve in this way,

-3x-5x+8=16

-8x=16-8

-8x=8

x= -8/8

x= -1

Therefore for this equation, x= -1.

Answer

20*19*18 = 6840

UNLESS...............  

he is allowed to ride the same ride again , over and over....  

then it is 20 x 20 x 20 = 8000

Answer: 7 feet

Step 1: Add the values of the sides we know the length of.

9 + 9 + 10 = 28.

Step 2: Subtract the number 28 from 35.

35 - 28 = 7

The answer is 7. Hope this helps!

Answer:

35 - 28 = 7

Step-by-step explanation:

7

Thanks bro...

Answer:

Attached is an example of a circle with a radius of 5 and a diameter of 10.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer:

6x + 12 - (3x - 7)

6x + 12 - 3x + 7

3x + 19

Step-by-step explanation:

Simplifying

6x + 13 + -3x + -7 = 0

Reorder the terms:

13 + -7 + 6x + -3x = 0

Combine like terms: 13 + -7 = 6

6 + 6x + -3x = 0

Combine like terms: 6x + -3x = 3x

6 + 3x = 0

Solving

6 + 3x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + 3x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + 3x = 0 + -6

3x = 0 + -6

Combine like terms: 0 + -6 = -6

3x = -6

Divide each side by '3'.

x = -2

Simplifying

x = -2

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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9514 1404 393

Answer:

  A

Step-by-step explanation:

The correct choice is marked.

The square of the square root is the number being rooted. -2 is not the square root of -4 because it square (-2)² is a positive number, not equal to -4.

Answer:

169

Step-by-step explanation:

Perimeter of a rectangle= 2(length+breath)

2(18 + 8)

2(26)

52.

A square has four equal sides.

The length will be determined by dividing 52 by 4

\(52 \div 4 = 13\)

The length is 13.

Since the area of a square is

\( {l}^{2} = {13}^{2} \)

L is length.

The answer is

\( {169}^{2} \)

Answer:If A is at point (x,y), then A' would be at point (-x,-y). Same goes for points B and C.

Step-by-step explanation:

In the case above, the value of the overhead rate for the second quarter is $17,640.

Note that:

In the case above, for one to be able to calculate the predetermined overhead rate, a person need to divide the value of the  estimated overhead costs which is $52,500 by that of the estimated direct labor hours .

Predetermined overhead rate=Estimated overhead costs/ estimated direct labor hours

Predetermined overhead rate=$52,500/  12,500

Predetermined overhead rate=$4.20/DLH overhead rate

Hence:  $52,500/ 12,500 =   $4.20/DLH overhead rate.

Since the Overhead that was applied at standard hours was said to be allowed, then:

= $4.2 x 2,400 x 1.75

= $17,640.

Therefore, In the case above, the value of the overhead rate for the second quarter is $17,640.

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Answer:

its 1

Step-by-step explanation:

Answer: The solution is the point (-14, -54)

Step-by-step explanation:

When we have a system of linear equations like:

y = a*x + b

y = c*x + d

The solution of this system is the point (x, y) that is a solution for both equations, if we graph the lines, this point would be the point where the lines intersect.

To start with this, we need to find the equations of the lines, we will use the following:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Now, for the first table, we can use the points: (-3, -10) and (0, 2)

The slope of this line is:

a = (2 - (-10))/(0 - (-3)) = 12/3 = 4

then we have:

y = 4*x + b

To find the value of b, we can just replace one of the points in the equation, for example, we can use the point (0, 2), this means that we need to replace x by 0, and y by 2.

2 = 4*0 + b

2 = b

Then the equation for the first table is y = 4*x + 2

For the second table, we can use the points (0, -12) and (3, - 3)

Then the slope is:

a = (-3 - (-12))/(3 - 0) = 9/3 = 3

Then we have:

y = 3*x + c

And to find the value of c, we can do the same as before, now we use the point (0, -12) then:

-12 = 3*0 + c

-12 = c

Then the equation for this line is:

y = 3*x - 12

The system of linear equations is then:

y = 4*x + 2

y = 3*x - 12

To find the solution of the system, we must have that y = y, then we can write:

4*x + 2 = y = 3*x - 12

4*x + 2 = 3*x - 12

Now we can solve this for x.

4*x - 3*x = -12 - 2

x = -14

x = -14

Now we can replace this in one of the equations to find the value of y.

y = 3*(-14) - 12 = -54

Then the solution is the point (-14, -54)

Answer: f=32+9/5c,c=r

Step-by-step explanation:

Answer:

Step-by-step explanation:

To compare the minimum y-values of the given functions, we need to find the minimum point of each function and compare their respective y-values.

For the function f(x) = 4 sin(2x-1) - 11, we know that the sine function oscillates between -1 and 1, and is multiplied by a factor of 4, which will change the amplitude of the function. We can find the minimum point of the function by setting its derivative equal to zero:

f'(x) = 8 cos(2x-1) = 0

cos(2x-1) = 0

2x-1 = (2n+1/2)π, where n is an integer

x = (2n+1/4)π + 1/2, where n is an integer

The minimum point will occur at x = (2n+1/4)π + 1/2, and the corresponding y-value can be found by substituting this value of x into the original function:

f(x) = 4 sin(2x-1) - 11

f((2n+1/4)π + 1/2) = 4 sin(2[(2n+1/4)π + 1/2]-1) - 11

f((2n+1/4)π + 1/2) = 4 sin(2nπ + π/2) - 11

f((2n+1/4)π + 1/2) = 4 (-1)^n - 11

We can see that the y-value of the minimum point alternates between -15 and -7 as n changes. Therefore, the smallest minimum y-value for the function f(x) is -15.

For the function h(x) = (x-2)² + 4, we know that it is a quadratic function with a minimum point at x=2. The y-value of the minimum point can be found by substituting x=2 into the function:

h(2) = (2-2)² + 4

h(2) = 4

Therefore, the smallest minimum y-value among the two given functions is 4, which is the minimum y-value of the function h(x) = (x-2)² + 4.

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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With compound interest of 6% paid semiannually, a deposit of $900 would result in $1,191.02 after 5 years, while simple interest would earn $270, resulting in a total of $1,170.

To calculate the future value of an investment with compound interest, we can use the following formula:

FV =\(PV * (1 + r/n)^{(n*t)}\)

where FV, PV, r, n and t is the future value, present value, annual interest rate, number of compounding periods per year and number of years respectively.

In this case, the present value (PV) is $900, the annual interest rate (r) is 6%, and the interest is compounded semiannually, so there are 2 compounding periods per year (n=2). The period (t) of investment  is 5 years.

Using these values, we can calculate the future value (FV) as follows:

FV = \(\$900 * (1 + 0.06/2)^{(2*5)\)

= \(\$900 * (1.03)^{10\)

= $1,191.02

Therefore, the future value of the investment after 5 years with compound interest would be $1,191.02.

If the interest were simple interest instead of compound interest, the calculation would be simpler. Simple interest is calculated as follows:

I = P x r x t

where I is the interest, P is the principal or present value, r is the interest rate, and t is the time period.

In this case, the interest rate is still 6% and the investment period is still 5 years, but the interest is calculated only on the principal amount of $900. Therefore, the interest earned would be:

I = $900 x 0.06 x 5

= $270

Therefore, the total amount after 5 years with simple interest would be the sum of the principal and the interest earned, which is:

Total = $900 + $270

= $1,170

Therefore, if the interest were simple interest instead of compound interest, the total amount after 5 years would be $1,170, and the interest earned would be $270.

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Answer:

A is incorrect because points are: (length [x], height [y])

B is correct because a point is not a size, it is a position, and they have no dimensions, as they are a dot.

C is incorrect, as I explained above.

D is incorrect, also as I explained above.

Select the bolded answers, as the question asks which are false

Imma get that brainliest ;)

Answer:

It's has to be D) because it says it depends on their dimensions.

Step-by-step explanation:

a) says they have no length or high which is almost the same thing as B).

Cuz B) they have no size or dimension

which that means that if you have to check if they all apply they all have to be the same thing in different words.

C) says their size variety which variety means it could be different types it could be without dimension it could be tall or etc

And D) says their size depends on their dimension all the others say don't have size or dimension. I hope this helps you

Answer:

-4

Solution:

72 = 2 + 5(-2 - 4x)

Distribute right side

72 = 2 - 10 - 20x

Combine like terms

72 = -8 - 20x

Add 8 to both sides

80 = -20x

Divide -20 to both sides

-4 = x

Best of Luck!

Answer:

\(5x+11\)

Step-by-step explanation:

Step 1: Distribute

\(3x+6+2x+5\)

Step 2: Add like terms

\(5x+11\) < your answer

Answer:

d

Step-by-step explanation:

Answer:

This is very confusing.

Can you try and make this a shorter question for me to answer?

Step-by-step explanation:

The labelled diagram of the triangle is shown below

From the diagram,

BC is common to triangles ABC and BCD.

AC is the hypotenuse of triangle ABC and BC is the hypotenuse of triangle BCD. CD and BC are corresponding legs of triangles ABC and BCD

Thus,

CD/BC = BC/AC

5/m = m/(15 + 5)

5/m = m/20

By crossmultiplying,

m * m = 5 * 20

m^2 = 100

m = square root of 100

m = 10