inverse function of f(x)= \frac{5}{x} +4

To convert 31,750 feet to miles, divide the number of feet by the number of feet per mile:

31,750 feet / 5,280 feet/mile = 6 miles

Answer: look at the image for the answer and explanation

Step-by-step explanation:

The rule A(x,y) ⇒  (-y,x) describes a transformation. The correct option is D.

The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x, and y, making y negative.

The transformation is described by the rule A(x,y) (-y,x). The right answer is D.

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A rectangle that has been divided into equal parts is referred to as a rectangular fraction. Depending on how many equal pieces you divide the whole into, the equal parts may be divided into halves, thirds, fourths, and so on.

1/2 of 2/3 is equal to 1/3

What is the equation?

The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.

To represent the multiplication of 1/2 and 2/3, we can draw a rectangle and divide it into equal parts.

1) First, we draw a rectangle.

2) Then, we divide it into 2 equal parts horizontally.

3) Next, we divide each half vertically into 3 equal parts.

4) Now we can see that each small rectangle represents 1/6 of the whole rectangle.

So, 1/2 of 2/3 is equal to 1/2 of 1/3.

Therefore, 1/2 of 2/3 is equal to 1/3.

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The length of side f is 12.0 inches

From the question, we have the following parameters that can be used in our computation:

In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°

The sum of angles in a triangle is 180 degrees

Using the above as a guide, we have the following:

E = 180 - 72 - 61

E = 47

Using the law of sines, we have

f/sin(F) = e/sin(E)

substitute the known values in the above equation, so, we have the following representation

f/sin(72) = 9.2/sin(47)

So, we have

f = sin(72) * 9.2/sin(47)

Evaluate

f = 12.0

Hence, the length is 12.0 inches

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Answer:

x = 5, y = 1

Step-by-step explanation:

For x :

Substitute y into the equation : 5x + 3 ( -1/5x + 2 ) = 28

Simplify : 22/5x + 6 = 28

Isolate x : x = 5

For y :

Substitute x for 5 : y = -1/5 * 5 + 2

Solve: y = 1

Step-by-step explanation:

Here is it. I hope it will help

Answer:

Step-by-step explanation:

6(x+5) = 6x+30

-2(x-3)=-2x+6

6x+30=-2x+6

8x+30=6

8x=-24

x=-3

Answer: x = -3

Step-by-step explanation:

6(x + 5) = -2(x-3)

1. Distribute: 6x + 30 = -2x + 6

2. Add 2 to both sides: 8x + 30 = 6

3. Subtract 30 on both sides: 8x = -24

4. Divide by 8 on both sides: x = -3

The parameters for the home mortgage, and the monthly payment, PMT,  for the mortgage are as follows;

Part 1;

P = $175,000, APR = 7%, n = 12, Y = 30

Part 2;

The monthly payment for the mortgage, PMT ≈ $1,164.28

A mortgage is a loan agreement, with the possession of the collateral presented for the loan such as a house being bought with the loan amount, being relinquished by the debtor, upon default

Part 1

The value of the mortgage  = $175,000

The fixed Annual Percentage Rate, APR = 7%

The duration of the payment = 30 years

Part 2; The monthly payment PMT loan formula can be presented in the following format;

Therefore;

[tex]PMT = \frac{175000\times \frac{0.07}{12} }{1-\left(1+\frac{0.07}{12}\right)^{(-12\times 30)} } \approx 1164.28[/tex]

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Answer:

A.

Step-by-step explanation:

Since [tex]5[/tex] can rewritten as [tex]\sqrt{25}[/tex] and [tex]6[/tex] rewritten as [tex]\sqrt{36},[/tex] we can see which options go between [tex]\sqrt{25}[/tex] and [tex]\sqrt{36}.[/tex] The only square root that goes between is [tex]\sqrt{29}.[/tex] Therefore the answer is [tex]\boxed{A.}[/tex] (or [tex]\sqrt{29}.[/tex])

The dimensions of the sticker are 11 millimeters and 3 millimeters.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Given is a sticker which is rectangular in shape.

Area of the sticker = 33 millimeters²

Perimeter of the sticker = 28 millimeters

Area of a rectangle = Length × Width

Perimeter of a rectangle = 2(Length + Width)

Let x be the length and y be the width of the rectangle.

x y = 33

2(x + y) = 28 ⇒ 2x + 2y = 28 ⇒ 2y = 28 - 2x ⇒ y = 14 - x

Substituting y = 14 - x in x y = 33,

x(14 - x) = 33

14x - x² = 33

-x² + 14x - 33 = 0

x² - 14x + 33 = 0

Factorizing the quadratic equation,

(x - 11) (x - 3) = 0

x - 11 = 0 or x - 3 = 0

x = 11 or x = 3

If x = 11, then y = 33/11 = 3

If x = 3, y = 33/3 = 11

Hence the dimensions are 11 millimeters and 3 millimeters.

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The function can be used to calculate his earnings, 15d + 0.25r + 2h

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

The function that the student can use to calculate his earnings is:

Earnings = 15d + 0.25r + 2h

where:

d = number of days worked

r = number of raffle tickets sold

h = number of hours worked at the game

The first term, 15d, represents the base pay of $15 per day worked.

The second term, 0.25r, represents the additional earnings of $0.25 per raffle ticket sold.

The third term, 2h, represents the additional earnings of $2 per hour worked at the game.

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Answer:

x=9

Step-by-step explanation:

Since y=5x, you plug it into the other equation's y and it'd look like this 5x=4x+9. Then you subtract 4x on both sides and that would leave you with an x=9.

In the vertex form the equation can be rewritten as x = 1×(y - 2)² + 5

The equation is given in the standard form y²-4y-x+9 = 0 and we have to convert it into vertex form

So basically, the general vertex form of any equation is x = a(y - k)² + h

⇒ y²-4y-x+9 = 0

Shifting the x to RHS,

⇒ x = y²- 4y + 9

Writing y²- 4y in the form of (a-b)²,

⇒ x = y²- 4y + 4 + 5

⇒ x = 1×(y - 2)² + 5,

Hence the equation is now converted to vertex form

⇒ where a = 1, k = 2 and h = 5

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The value of the equation for x is 32

PEDMAS is described as a mathematical acronym that represents the important operations during calculations.

The alphabets represents;

From the information given, we have;

-(-2)+√(-2)²-4(1)(-8)

expand the brackets

2 + -2 -4(-8)

multiply the values

2 -2 + 32

Add the values

32

Hence, the value is 32

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Step-by-step explanation:

please see the attached picture

Step-by-step explanation:

you draw a circle ⭕ then you do lines inside the circle the you write the numbers aside

Following are the values of the functions -

1) f(a) = 8a - 4

2) f(a+h) = 8a+ 8h - 4

3)[tex]\frac{f (a+h)-(a) }{h}= 8[/tex]

An expression or relationship with one or more variables is called a function. Both its inputs and outputs are numerous. There is just one output per input. The function explains how the inputs and outputs are related.

To evaluate f(a), we simply substitute the value of "a" into the function:

1) f(a) = 8a - 4

To evaluate f(a+h), we substitute the value of "a+h" into the function:

2) f(a+h) = 8(a+h) - 4

f(a+h) = 8a+ 8h-4

To find the expression for [tex]\frac{f (a+h)-(a) }{h}[/tex], we divide the result by h: L(a+h)-f(a) h we can subtract f(a) from f(a+h) and then

3) [tex]\frac{f (a+h)-(a) }{h}[/tex]

[tex]= \frac{ (8a+8h-4-(8a-4)}{h} \\= \frac{8h}{h}= 8[/tex]

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Answer:

The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got [tex]0y[/tex]. Instead of subtracting, they should have added it.

Step-by-step explanation:

Given:

[tex]8x+2y=44\\5x+2y=35[/tex]

We can combine the system of equations into a single equation:

[tex]13x+4y=79[/tex]

From this step, we can conclude that the answer for part b is incorrect. The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got 0y. Instead of subtracting, they should have added it.

We can continue solving the system of equations by writing y in terms of x.

[tex]8x+2y=44\\2y=44-8x\\y=22-4x[/tex]

now substitute this into the single equation:

[tex]13x+4y=79\\13x+4(22-4x)=79\\13x+88-16x=79\\-3x+88=79\\-3x=-9\\x=3[/tex]

Since we now know that [tex]x=3\\[/tex], we can substitute this into the equation we made for y.

[tex]y=22-4x\\y=22-4(3)\\y=22-12\\y=10[/tex]

The solution for the system of equations is [tex]x=3[/tex] and [tex]y=10\\[/tex].

Vertex A: (90°, 3) and Vertex B: (90°, -1) of the sine function.

The vertex A of the curve y = sin x + 2 is obtained by shifting the vertex of y = sin x upward by 2 units. Since the vertex of y = sin x is (90°, 1), the vertex of y = sin x + 2 will be:

A = (90°, 1 + 2) = (90°, 3)

Therefore, the coordinates of the vertex A of the curve y = sin x + 2 are (90°, 3).

b) The curve y = -sin x is obtained by reflecting the curve y = sin x about the x-axis. Since the vertex of y = sin x is (90°, 1), the vertex of y = -sin x will be:

A = (90°, -1)

Therefore, the coordinates of the vertex A of the curve y = -sin x are

(90°, -1).

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A and C are equivalent expressions for a given expression.

What does an expression mean?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is -4y+8.

Given options are:

A. -4(y-2)

By simplifying it we will get -4(y-2) = -4y+8

So, both are equivalent.

B. -4(-2+4y)

By simplifying it we will get -4(-2+4y) = 8-16y

So, both are not equivalent.

C. (2-y)4

By simplifying it we will get (2-y)4 = 8-4y

So, both are equivalent.

D. 4(-y+8)

By simplifying it we will get 4(y-8) = 4y-32.

So, both are not equivalent.

A, and C are equivalent expressions for a given expression.

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Answer:

3ab2+1 = -23

3a^2b-1 =-25

Step-by-step explanation:

The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.

The transformation applied to f(x) to obtain q(x) is divided into several steps:

Reflection: The negative sign in front of 1/x reflects the graph of f(x) across the x-axis, causing the y-values to change sign.

Vertical shift: Adding "+1" to -1/x raises the graph of f(x) by one unit.

Horizontal shift: Although there is no explicit horizontal shift in q(x), we can see that the graph of q(x) has a vertical asymptote at x=0, whereas the graph of f(x) does not. This means that the graph of q(x) has been shifted to the right by one unit.

The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.

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The symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.

The solution has been obtained by using concept of relational symbols.

What are relational symbols?

Relational symbols are used in mathematics to represent mathematical relations, which combine with one or more other mathematical objects to construct complete mathematical statements. These are the relational symbols for equality and comparison in arithmetic and common mathematics.

We are given 2 numbers as 364 and 225.

It is clearly visible that both the numbers are not same so, the symbol '≠' depicts the relationship between the two numbers.

Also, we know that the number 364 is greater than 225. So the another symbol depicting relation between the numbers is '>'.

Hence, the symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.

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Question: Which of the symbols correctly relates the two numbers below? Check all that apply.

364? 225

A. =

B. >

C. ≥

D. <

E. ≤

F. ≠

Answer:

Step-by-step explanation:

To determine whether an ordered pair is a solution to a system of equations or inequalities, we need to substitute the values for x and y into each equation or inequality and see if the resulting expression is true. If it is true for all of the equations or inequalities, then the ordered pair is a solution to the system.

Here's the step-by-step process for each ordered pair:

(1,3):

Substitute x = 1 and y = 3 into y < 4x - 1: 3 < 4(1) - 1 = 3 < 3, which is true.

Substitute x = 1 and y = 3 into y > x: 3 > 1, which is true.

Since both inequalities are true, the ordered pair (1,3) is a solution to the system y < 4x - 1 and y > x.

(0,0):

Substitute x = 0 and y = 0 into y < 4x - 1: 0 < 4(0) - 1 = -1, which is false.

Substitute x = 0 and y = 0 into y > x: 0 > 0, which is false.

Since at least one inequality is false, the ordered pair (0,0) is not a solution to the system y < 4x - 1 and y > x.

Answer:

---------------------------

According to picture we observe:

The segment connecting the midpoints is the midsegment.

As per property of the midsegment, it is parallel to opposite side and is half of its measure.

It tells us that WB is parallel to AE and:

Answer:

the perimeter of the polygon is 36 feet.

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of all its sides. In this case, you have three sides with lengths of 14 ft, 15 ft, and 7 ft. To find the perimeter, simply add these lengths together:

Perimeter = 14 ft + 15 ft + 7 ft

Perimeter = 36 ft

So the perimeter of the polygon is 36 feet.