what are the domain and range of F(x)= 2 1 ​ (x+4) 2 −11?​

Each of the function should be evaluated as follows;

In Mathematics, the valid and true solutions to any function are referred to as the domain (input value) and they can be determined by substituting the x-values contained in the table into the function.

When x = 2, the range (output value) for this function is given by:

Function, f(2) = 5^x = 5^2 = 25.

When x = 1, the range (output value) for this function is given by:

Function, f(1) = 5^x = 5^1 = 5.

When x = 0, the range (output value) for this function is given by:

Function, f(0) = 5^x = 5^0 = 1.

When x = -1, the range (output value) for this function is given by:

Function, f(x) = 5^x = 5^-1 = 1/5.

Read more on function here: brainly.com/question/3632175

#SPJ1

The length of the rectangle is 20 and the width is 13.

The perimeter of a rectangle = 2(length + width)

Width = w

Length = 2w - 6

90 =  2(w + 2w - 6)

In order to determine the value of w, take the following steps:

Divide both sides of the equation by 2

90/2 = w + 2w - 6

45 = w + 2w - 6

Combine and add similar terms:

45- 6 = w + 2w

39 = 3w

Divide both sides of the equation by 3

w = 39/3

w = 13

In order to determine the length, substitute for w in the equation that represents the length.

Length = 2(13) - 6

= 26 - 6

= 20

To learn more about the perimeter of a rectangle, please check: https://brainly.com/question/3205029

#SPJ1

If the frame has 2 inches of width and its area is 208 inches of square. The dimensions of square without frame is 6.75 and 13.50.

Let the width of rectangle without frame is b.

Let the height of rectangle without frame is h.

Since the base of a square without frame is the double of its height. So

b = 2h...............(1)

The frame has 2 inches of width, so;

The width of rectangle with frame = b + 4

The height of rectangle with frame = h + 4

The area of the rectangle with frame = 208  inches of square

The formula of area of rectangle

A = Height × Width

(h + 4) × (b + 4) = 208

Putting the value of b from the equation 1

(h + 4) × (2h + 4) = 208

Simplify

h(2h + 4) + 4(2h + 4) = 208

2h^2 + 4h + 8h + 16 = 208

2h^2 + 12h + 16 = 208

Subtract 208 on both side, we get

2h^2 + 12h - 192 = 0

Taking common 2 from the equation, we get

h^2 + 6h - 86 = 0

After factoring the equation we get

h = (−3+√95, −3−√95)

h = 6.75, -12.75

The height can't be negative so we use the positive value of h.

Now putting the value of h in the equation 1.

b = 2×6.75

b = 13.50

To learn more about area of rectangle link is here

brainly.com/question/20693059

#SPJ4

The complete question is:

The base of a square without frame is the double of its height, if the frame has 2 inches of width and its area is 208 inches of square. Find the dimensions of the square without frame.

The equation of a quadratic equation with a vertex and a point is

y = 1/4 (x - 11)² + 2

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 6 is an equation.

We have,

Vertex = (11, 2)

Point = (9, 3)

The equation of a quadratic equation with a vertex and a point is

y = a (x - h)² + k

Where (h, k) is the vertex and (x, y) is the point.

Now,

(11, 2) = (h, k)

(9, 3) = (x, y)

Substitute.

y = a (x - h)² + k

3 = a (9 - 11)² + 2

3 = a x 4 + 2

3 = 4a + 2

3 - 2 = 4a

a = 1/4

Now,

The equation of a quadratic equation is y = 1/4 (x - 11)² + 2.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The probability of a sample mean more than 65 is given as follows:

0.1587 = 15.87%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 63, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2[/tex]

The probability of a sample mean above 65 is one subtracted by the p-value of Z when X = 65, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (65 - 63)/2

Z = 1

Z = 1 has a p-value of 0.8413

1 - 0.8413 = 0.1587 = 15.87%.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

From the Number in the graph , the inequality that describes the relationship between points A and B on number line is (c) B > A .

In the Number Line we can see that , Both the points A and B are between 0 and 1 on the number line ,

We know that , On a number line , the further right we move the higher numerical values we get ;

On the number line the point B is further to the right , as well as closer to 1 than A , So , we can conclude that B is greater than A .

Therefore , The point B is greater than point A .

The given question is incomplete , the complete question is

Which inequality describes the relationship between points A and B on the number line ?

(a) A > B

(b) B ≤ A

(c) B > A

(d) B = A

Learn more about Inequality here

https://brainly.com/question/26046494

#SPJ4

Answer:

27

Step-by-step explanation:

First do the () part which is (7-3) equal 4×4 equal 16 so then u will add 16+11 getting 27

Answer:

x ≥ -6

Step-by-step explanation:

Answer: x ≥-6

explanation: im pretty good at math

At two theaters Paige would be willing to buy a ticket and popcorn.

Consider the following table that shows ticket and popcorn prices at five movie theater chains.

Here, the inequality d < 4. 75 represents the prices d in dollars that Paige is willing to pay for popcorn.

And the inequality d < 8. 00 represents the prices d in dollars that Paige is willing to pay for a movie ticket.

To find: the number of theaters that would Paige be willing to buy a ticket and popcorn

We can observe that the number of theaters that has the movie ticket price less than 8 dollars are two.

The number of theaters that has the popcorn price less than 4.75 dollars are three.

And the number of theaters that has the popcorn price less than 4.75 dollars as well as the movie ticket price less than 8 dollars are two.

Learn more about an inequality here:

https://brainly.com/question/30238995

#SPJ4

Answer:  A=2 B=4 C=5

Step-by-step explanation:

I disagree with Brie.

Only the bean plant has a proportional relationship. The sunflower does not have a proportional relationship.

In a proportional relationship, the ratio of the dependent variable (height) to the independent variable (number of days) is constant. In this case, the ratio of height to number of days is not constant for both plants.

For the bean plant, the ratio of height to number of days is 0.25, which is constant. This means that the bean plant grows by 0.25 inches per day.

For the sunflower, the ratio of height to number of days changes as the number of days increases, it starts with 10 and increases by 0.02 each day. This means that the growth rate of the sunflower is not constant, it starts with 10 and increases by 0.02 inches per day.

Thus, I disagree with Brie.

Learn more about proportional relationship on:

brainly.com/question/12242745

#SPJ1

To find out how many bicycles John can assemble in 1 hour, you can use the formula:

rate = work/time

where rate is the number of bicycles John can assemble in 1 hour, work is the total number of bicycles he assembled, and time is the total time it took him to assemble the bicycles.

In this case, the work is 10 bicycles and the time is 8 hours. So, we can substitute these values into the formula:

rate = 10 bicycles / 8 hours

rate = 1.25 bicycles/hour

So John can assemble 1.25 bicycles in 1 hour, assuming he works at a consistent pace.

x = 4,  y = 3 for the given equation 2x - 3 y = -1 , y = x - 1 .

Given data :

2x - 3 y = -1

y = x - 1

In a system of equations, there are multiple equations present. We actually look for the point at which these equations are identical when we attempt to solve a system of equations problem. In order to solve such an issue, we typically employ the substitution method, which involves inserting the values of one variable into the initial expression in order to determine the value of the second variable.

3y=2x+1

y= (2/3)x + 1/3 = x-1

x/3 =4/3

x = 4,  y=3

Learn more about equations refer to :

https://brainly.com/question/2228446

#SPJ1

Charlie must buy 7/3 yards long brown thread to weave a bracelet.

Based on number of pieces of brown thread and length of each piece, the formula that will be formed is -

Length of thread required = number of threads × length of each piece

Keep the values in formula to the length of piece required to weave a bracelet

Length of thread required = 7 × 1/3

Performing multiplication on Right Hand Side of the equation

Length of thread required = 7/3 yards

Thus, 7/3 yards of length is required to weave the bracelet.

Learn more about multiplication -

https://brainly.com/question/10873737

#SPJ4

The solution of the inequality |x + 1| ≥ 3 is:

x ≥ 2 or x  ≤ -4

Here we want to solve the absolute value inequality:

|x + 1| ≥ 3

The absolute value can be decomposed into two inequalities, these are:

(x + 1) ≥ 3

(x + 1) ≤ -3

Now we can solve these two inequalities to get:

x ≥ 3 - 1 = 2

x  ≤ -3 - 1 = -4

Then the solution is:

x ≥ 2 or x  ≤ -4

Laern more about inequalities at:

https://brainly.com/question/24372553

#SPJ1

Answer: Its D

Step-by-step explanation:

I looked up the answer

Point T becomes (18, 2), which equals T', when we transform STUV using the technique above.

Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.

The movement of two-dimensional figures about a plane or coordinate system is described by mathematical transformations. A preimage, also known as an inverse image, is a two-dimensional shape that exists without any change. After transformation, the figure is shown in the image.

If we pay attention to the transformation, it is obvious that every point in the rectangle JKLM is changed to a point that is 13 units to the right and 3 units to the bottom.

The T in STUV is currently at (5, 5).

When we transform STUV using the formula above, point T becomes (5 + 13, 5 - 3) (18, 2), which equals T'.

Therefore, the correct answer is option b. (18, 2).

The complete question is:

Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied to trapezoid STUV.

What will be the location of T' in the image trapezoid S'T'U'V'?

a. (18, −2)

b. (18, 2)

c. (15, −2)

d. (15, 2)

To learn more about transformation refer to:

https://brainly.com/question/28025572

#SPJ1

The area of a circle is given by the formula:

A = πr^2

Where A is the area of the circle, π is approximately 3.14 and r is the radius of the circle.

Given the radius, r = 7.27m, we can substitute this into the formula and calculate the area of the circle.

A = π * 7.27^2 = π * 52.5129

A = 165.9 m^2

The area of the circle is 165.9 m^2. Rounded to 2 decimal places, the area of the circle is 165.90 m^2

Answer:

The graph would look like this

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

[tex]k + 7 = 16\\k = 9\\8k - 72\\8(9) - 72 = 0[/tex]

Answer:

see below

Step-by-step explanation:

v=πr² (h/3)

h=3v/πr²

original equation measures v using bottom circle area multiply the height.

the equation for the height reverses the multiplication using volume divided by the area, so the result is a linear measurement.

The equation of the translated function for this problem is given as follows:

y = ln(x + 8) + 12.

The four translation rules are defined as follows:

The parent function in this problem is given as follows:

y = ln(x).

The translations in this problem, and their effects, are given as follows:

Hence the translated function is defined as follows:

y = ln(x + 8) + 12.

More can be learned about translations at brainly.com/question/28174785

#SPJ1

The inequality is y ≥ 1/2x.

We must first identify the linear equation that describes the line in the graph in order to determine the inequality it reflects.

So, using the two points (0, 0) and (2, 1), we first get the slope of the line:

m = y2 - y1 /x2 - x1 = 1-0 / 2-0 = 1/2

Now, we can determine the linear expression using one point, the slope, and the slope-point formula.

y - y1 = m( x - x1)

y - 0 = 1/2(x - 0 )

y = 1/2 x

Then, to evaluate the linear equation, we only need to select a test point from the shaded region, which will be (0,1):

y = 1/2 x

1 = 1 / 2 (0)

1 = 0

Because 1 is greater than 0 and the line is solid, we can infer that the inequality sign is in the proper position.

Therefore, the inequality is y ≥ 1/2x.

The Complete Question is inequality.

To Learn more About inequality Refer To:

https://brainly.com/question/24372553

#SPJ1

The angles b and d have 80° degrees.

Trigonometry is the branch of mathematics that studies and defines the relations between the side lengths and angles of a triangle.

One key fact to know in all trigonometry problems is that all angles within a normal triangle = 180 degrees.

By creating algebraic equations based on the information given in the question, we can find missing values using this key fact.

Given:

Angle a = 20 deg

Angle b = Angle d = x

x = ?

We know that since two angles are equal, it is an isosceles triangle.

Using algebra and the given information, we create an equation:

20+2x=180

2x=180-20

2x=160

x=80

Therefore, we know that angles b and d are 80° degrees.

To know more about the isosceles triangle:

https://brainly.com/question/1475130

#SPJ4

The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.

What happens when a function is shifted vertically?

Because this transformation involves adding a positive or negative constant to the function, a vertical shift, which moves the graph up or down, is the simplest shift. In other words, regardless of the input, the output result of the function receives the same constant.

The y-value adjusts when a function shifts vertically. While the y-value modifies the shift's magnitude, the x-value remains constant.

We add the value to the y-term if it changes upward. We shall deduct that amount from the y-term if it shifts downward.

The simplest transformation is a vertical shift, which entails moving the graph up or down. This is because this transformation only requires changing the function's sign from positive to negative.

The only variable that alters in vertical shifts of the fundamental linear equation y = mx + b is the b value, or the y-intercept.

The graph shown above is the graph of the parent function y=x after a vertical shift up 1 unit.

Hence, The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.

To learn more about vertical shift visit,

brainly.com/question/26246140

#SPJ1

The inequality equations is

a) The point ( -9 , 4 ) lies on the inequality relation

b) The point ( 6 , -2 ) lies on the inequality relation

c) The point ( 0 , -4 ) does not lie on the relation

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

a)

Now , let the first point be represented as P ( -9 , 4 )

The shaded region is below 4 in the y axis and less than -4 in the x axis

So , the point ( -9 , 4 ) does lies on the inequality equation graph

b)

Now , let the first point be represented as Q ( 6 , -2 )

The shaded region is below -8 in the y axis and less than 8 and more than 4  in the x axis

So , the point ( 6 , -2 ) does lies on the inequality equation graph

c)

Now , let the first point be represented as R ( 0 , -4 )

The shaded region is above -8 in the y axis and more than -4 in the x axis and less than -1

So , the point ( 0 , -4 ) does not lie on the inequality equation graph

Hence , the inequality equations is solved

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Answer:  it takes 7.5 seconds for the object to reach the ground.

Step-by-step explanation:

The equation for the height of the object is h=-16t^2+900. To find the time when the object reaches the ground, we need to find the value of t when h=0.

Therefore, we can set h=-16t^2+900 = 0 and solve for t:

-16t^2+900 = 0

-16t^2 = -900

t^2 = 56.25

t = sqrt(56.25)

t = 7.5

So, it takes 7.5 seconds for the object to reach the ground.

Answer:

[tex]\boxed{n = - 5}[/tex]

Step-by-step explanation:

[tex]\textrm{We have the following equation:}\\\\\dfrac{n}{5}+\dfrac{\left(n-3\right)}{2}=n\\\\\textrm{ and we are asked to solve for n}[/tex]

Solution Steps

Multiply throughout by 10 which is the LCM of the denominators,  5 and 2

[tex]\dfrac{n}{5}\cdot \:10+\dfrac{n-3}{2}\cdot \:10=n\cdot \:10\\\\2n + 5(n-3) = 10n\\[/tex]

Expand the brackets: [tex]5(n-3) = 5n - 15\\\\[/tex]

The equation becomes:

2n + 5n - 15 = 10n

Add similar terms:

7n - 15 = 10n

Move 15 to the right side:

7n = 10n + 15

Move 10 to the left side

7n - 10n = 15

- 3n = 15

n = -15/3

[tex]\boxed{n = - 5}[/tex]

The graph of the inequality 0 > x ≥ 5 can be seen on the image at the end.

Here we want to graph the following inequality:

0 > x ≥ 5

So, x is strictly larger than 0 and smaller than or equal to 5.

Because x = 0 is not a solution, we will draw an open circle at x = 0.

Then a line that goes to the right until x = 5, where we will draw a closed circle, because that value belongs to the solution set, then the inequality is the one you can see below.

Learn more about inequalities at:

https://brainly.com/question/24372553

#SPJ1