AIR 2021) Four functions are shown.
Which function is linear?

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.

Answer: look at the image for the answer and explanation

Step-by-step explanation:

Step-by-step explanation:

please see the attached picture

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).

To know more about Sine Function, click here,

https://brainly.com/question/11881676

#SPJ1

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.

To know more about Functions check:

https://brainly.com/question/5975436

#SPJ9

Answer:425

Step-by-step explanation:

993-43=950

950/2=425

Answer:

$475

Step-by-step explanation:

Let's call the cost of the dryer x. That means the cost of the washer is x + $43. The combined cost of the two is $993, so we can write the equation:

x + (x + $43) = $993

Expanding the right side:

2x + $43 = $993

Subtracting $43 from both sides:

2x = $950

Dividing both sides by 2:

x = $475

So the cost of the dryer is $475.

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

[tex]b = \bar y - m\bar x[/tex]An equation that models that population growth of the small town is y = 2,453.75x + 88,499.37 .

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

The given table is:

Year (x)                          0,              1,           2,              3

Population (y)            88,000,    90,640,  93,359,    96,160

We can use the least squares method to estimate the slope and y-intercept.

The formula for the slope (m) is:

[tex]m = \dfrac{\sum(x - \bar x)(y - \bar y)}{ \sum(x - \bar x)^2}[/tex]

The formula for the y-intercept (b) is:

[tex]b = \bar y -m \bar x[/tex]

Using the data from the table, we can calculate the mean of x and y:

[tex]\bar x[/tex] = (0 + 1 + 2 + 3) / 4

  = 1.5

[tex]\bar y[/tex] = (88,000 + 90,640 + 93,359 + 96,160) / 4

  = 92,180

Next, we can calculate the slope (m) and y-intercept (b):

m = (0 - 1.5)(88,000 - 92,180) + (1 - 1.5)(90,640 - 92,180) + (2 - 1.5)(93,359 - 92,180) + (3 - 1.5)(96,160 - 92,180)² / (0 - 1.5) + (1 - 1.5)² + (2 - 1.5)² + (3 - 1.5)²

= (-2.25)(-4,180) + (-0.5)(-1,540) + (0.5)(1,179) + (2.25)(4,980) / 2.25² + 0.5²+ 0.5² + 2.25²

= 2,453.75

b = 92,180 - (2,453.75 x 1.5)

  = 92,180 - 3,680.63

  = 88,499.37

So, the equation that models the growth of the population is:

y = 2,453.75x + 88,499.37

To know more about Equation check:

https://brainly.com/question/1529522

#SPJ1

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

Read more about triangles at

https://brainly.com/question/14285697

#SPJ1

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.

To know more about Graph visit:-

https://brainly.com/question/17267403

#SPJ1

Step-by-step explanation:

Here is it. I hope it will help

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:

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

Learn about PEDMAS at: https://brainly.com/question/345677

#SPJ1

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:

its c

Step-by-step explanation:

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

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.

To learn more about equivalent expressions, refer to the link below:

https://brainly.com/question/24734894
#SPJ1

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.

Learn more about Area and Perimeter of Rectangles here :

https://brainly.com/question/16572231

#SPJ9

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 '≠'.

Learn more about relational symbols from the given link

https://brainly.com/question/30139516

#SPJ1

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

364? 225

A. =

B. >

C. ≥

D. <

E. ≤

F. ≠

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.

The average rate of change of the function f(x) over the interval (-1, 2) is; 3.

As evident in the task content; the given function is as represented by the graph of f(x).

Hence, the average rate of change of the function over the given interval; (-1, 2) is;

= ( f (2) - f (-1) ) / (2 - (-1))

where; f (2) = 5 and f (-1) = -4.

Therefore, the average rate of change is;

= (5 - (-4)) / (2 - (-1))

= 9 / 3.

= 3.

Ultimately, the difference quotient of f (x) over the given interval is; 3.

Read more on difference quotient;

https://brainly.com/question/28490181

#SPJ1

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].

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.

Step-by-step explanation:

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

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.

To know more about multiplication equation visit,

https://brainly.com/question/30315410

#SPJ1

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

To learn more about vertex form

https://brainly.com/question/30339547

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])