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A domain restriction placed on a non-invertible function affect its inverse.

Using inverse function concepts, it is found that:

The inverse of the function is [tex]y = \sqrt{x+3}-1[/tex], and the domain of the inverse function is [tex]\left[-3,\infty ][/tex]

   A function will have an inverse if for each output, there is only one respective input.

   The domain of the inverse is the range of the original function.

The function given is:

[tex]f(x) = (x+1)^{2} -3[/tex]

   It's range is [tex]\left[-3, \infty][/tex], which will be the domain of the inverse.

To find the inverse, we exchange x and y, and isolate y, then:

[tex]y = (x+1)^{2} - 3\\ \\x = (y+1)^{2} - 3\\\\(y+1)^{2} = x+3\\ \\\sqrt{((y+1)^{2}} = \sqrt{x+3} \\\\y+1 = \sqrt{x+3}\\\\y = \sqrt{x+3} -1[/tex]

The inverse of the function is [tex]y = \sqrt{x+3} -1[/tex], and the domain of the inverse function is [tex]\left[-3, \infty][/tex].

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Answer: the rate change in this problem would be by 1.50

Step-by-step explanation:

The rate of change in this word problem will be 2.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A local ice cream shop has a special deal on Thursdays. buy a waffle cone for $3 and get each scoop for $1.50.

Now,

The rate of change will be find as;

The rate of change = $3 / $1.50

                              = 2

Thus, The rate of change in this word problem will be 2.

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The commission on the sale of 31000 worth of furances when the rate of commission is 4% is given by 1240.

Given that, a salesperson's commission rate is 4%.

Sale of person is 31000.

So the commission of the that sales is = 31000*4% = 31000*(4/100) = 310*4 = 1240

Hence the commission of the sale is 1240.

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The statement that two of the team members must have personal records that are within four inches of each other it is not true for three high jumpers, and true for four high jumpers.

1 foot =  12 inches

So, for three high jumpers the statement is not true. A counterexample,

First player = 6 feet

Second player = 6 feet 6 inches

Third player = 6 feet 11 inches

Thus, personal record each player have interval more than 4 inches of each other.

For four high jumpers the statement is true. Since there are 4 jumpers and 3 intervals by the pigeonhole principle, at least two of the four jumpers have intervals within four inches. For example, in the image, the new jumpers should be placed in areas A, B, C and this makes at least two of the four jumpers have an interval of four inches.

Thus, the statement is not true for three jumpers and true for four jumpers.

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Answer: n-20

Step-by-step explanation: just multiply 5 and 4.

hope this helps!

please give brainliest!

The equation of the line is y=x-6 when the points are (-3,-9) and (4,-2).

Given that,

The points are (-3,-9) and (4,-2).

We have to find the linear equation.

We know the formula of the equation of the line is,

y=mx+b

The slope of the line is m that is rise by run.

m=-2+9/4+3

m=7/7
m=1

The slope of the line is 1.

Now, b is intercept.

-9=1(-3)+b

-9=-3+b

b=-9+3

b=-6

The equation of the line is y=x-6.

Therefore, The equation of the line is y=x-6 when the points are (-3,-9) and (4,-2).

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Answer:

[tex]x=7[/tex]

Step-by-step explanation:

The interior angles of a triangle add up to 180 degrees.

So we have  [tex]108+47+(2x+11)=180[/tex]

Solve for x.

[tex]47+(2x+11)=72[/tex]

[tex]2x+11=25[/tex]

[tex]2x=14[/tex]

[tex]x=7[/tex]

Answer:

7

Step-by-step explanation:

108+47=155

180-155=25

25-11=14

14/2=7

By using the rectangle, we proved that area of triangle is half the area of rectangle that is 1/2 (base×height).

To Prove:- Area of a triangle= 1/2 (base×height)

Diagonals of the rectangle divide it into two parts of equal areas.

Let  ABCD  be a rectangle.

In ΔABC and ΔADC,

                                         AC=AC

By Alternate Interior Angles:

                                    ∠BAC=∠CAD

                                    ∠BCA=∠CDA

Hence, ΔABC≅ΔACD

                               ∴ar(ΔABC) =ar(ΔACD)

Let ΔABC,

We draw a line AD perpendicular to BC, line EF parallel to BC passing through A and lines BE and CF , perpendicular to BC passing through B and C respectively.

In rectangle ADBE,

we get,

                     ar(ΔABE)=ar(ΔADB)

Similarly, in rectangle ADCF,

                     ar(ΔADC)=ar(ΔACF)

Now, area of rectangle BCFE, from axiom,

                               =(length)⋅(breadth)

                               =AB⋅BC

                              =AD⋅BC

Also,

ar(BCFE)

                                   =ar(ADBE) + ar(ADCF)

                                   =2⋅ar(ΔADC) + 2⋅ar(ΔADB)

                                   =2(ar(ΔADC) + ar(ΔADC)

                                   =2(ar(ΔABC))

From (1) and (2),

                                   2(ar(ΔABC)) = AD⋅BC

                                    ar(ΔABC) = 1/2AD⋅BC

                                   ar(ΔABC) = 1/2(base)⋅(height)

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6x^2 - 2x = 0

-> 2x ( 3x - 1 ) = 0

For this equation to hold true, either 2x or 3x-1 must be equal to 0.

-> 2x = 0 - > x = 0

-> 3x - 1 = 0 -> x = 1/3

It will take the ship 5 hours to travel 75 miles

A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

if it takes 2 hours to cover 30 miles by the ship and 4 hours to cover 60 miles.

let d be the distance covered in miles and t time taken in hours

The d ∝ t

introducing a constant

d = kt

when d = 30, t = 2

30 = 2k

k = 30/2

k = 15

The equation relating d and t is

d = 15t

to find t when d = 75, making t the subject of the equation

t = d/15

t = 75/15

t = 5 hours

In conclusion, 5 hours is the time taken to cover 75 miles.

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The table of values and the equation for C, in terms of p, representing the total cost, in dollars are

p        C(p)

0        300

1          375

2         450

3         525

4         600

and so on.

Given,

Chloe is in the business of manufacturing phones.

She pay a daily cost $300 to rent for the building and equipment.

and, also pays a cost of $75 per phone produced for materials and labor.

Now, According to the question;

How to make a table of values and the equation for C, in terms of p, representing the total cost, in dollars?

The given parameters are:

Cost per phone = $75

Fixed cost of labor and material = $300

The total cost is represented as;

C(p) = Fixed cost + Cost per phone x Number of phones

So, we have

C(p) = 300 + 75 * p

Evaluate

C(p) = 300 + 75p

Hence, Using the above equation, the table of values is

p        C(p)

0        300

1          375

2         450

3         525

4         600

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By using the law of sine, the measure of ∠C is 39°

Law of sine:

Law of sine refers the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

Given,

Here we have the triangle.

Now, we have to find the angle ∠C.

While we looking into the given diagram,

We have the length of,

AB = 6

AC = 9

∠B = 105°

So, based on the law of sine it can be written as,

=> sin 105° / 9 = sin x°/6

Apply the value of sin 105° = 0.97, then we get,

=> 0.97/9 = sin x° / 6

Cross multiply them, then we get,

=> 5.82/9 = sin x°

=> 0.64 = sin x°

=> x = sin⁻¹ (0.64)

=> x = 39°

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The corerect equation for the given linear equation in one variable is 24 = 31.4n + (-8.4)

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable of the form an x + b = 0 are solved using simple algebraic techniques.

Solution:

According to the word problem,

The formation of Linear Equation will be

24 = 31.4n + (-8.4)

and it can be also written as

24 = 31..4n - 8.4

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Answer:

Step-by-step explanation:

Area of the square = 6^2 = 36 cm^2

radius = 6 : 2 = 3 cm

Area of the four semicircles = 3^2 * π * 2 = 18 π cm^2

Total area in terms of π= 36 + 18π = 18(2+π) cm^2

Total area = 18(5.141593) = 92.548668 = 92.5 cm^2

Answer: 1712

Step-by-step explanation:

[tex]a_{n} = a_{1} + d(n -1)[/tex]

[tex]a_{1} = -16[/tex]

[tex]d = 2 - (-16) = 18\\[/tex]

       [tex]20 - 2 = 18[/tex]

[tex]-16 + 18(n+1)[/tex]

[tex]-16 + 18(97+1)[/tex]

[tex]-16 + (1728)\\[/tex]

[tex]1712[/tex]

Answer:

180

Step-by-step explanation:

If you are 14 you are 3 years away from 17 Wich would mean $60 would have to be multiplied by 3

60x3

3x6= 18

18x10= 180

(sorry if this is wrong)

The linear equation will be y=34x+12 and the slop is 34 and y intercept is 12. And the sunflower will be 420 inches tall after a year.

Here, the sunflower was 12 inches when first planted and it grows 34 of an inch each month

So, the linear equation will be

y=34x+12

Where,

y=height

x=month

now,

the slope-intercept equation is

y=mx+c

Where,

m=slope

c=y intercept

Comparing this equation with equation (1)

We will get

m=34

c=12

so, the slope is 34 and y intercept is 12.

now,

The tree is 12 inches when it first planted and since then it grows 34 of an inch every month

So,

Height of tree after a year =12+34×12

Height of tree after a year = 12+408

Height of tree after a year = 420 inches.

Hence,

The tree will be 420 inches tall after a year.

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The relationship between the triangles is angle angle side.

We know that triangles could be related in certain ways. The way that a triangle is related to each other can be used to determine the relationship then the several ways that triangles could be related to eacjh other are;

Side angle side

Angle angle side

side side side.

We can see that the angles and the sides of this triangles are the same so the relationship between then can be said to be on the basis of angle side angle.

Looking at the images, it is clear that the triangles are congruent because there are two sides and an angle that are equal.

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The sum of the interior angles of a polygon with 28 sides is 4680°.

According to the question,

We have the following information:

The number of sides of a polygon = 28

We know that the following formula is used to find the sum of the interior angles of a polygon:

(n-2)*180 where n is the number of sides

Putting the value of n in this formula for the given polygon:

(28-2)180

We will first solve the bracket and then we will multiply the obtained result by 180:

26*180

4680°

Hence, the sum of the interior angles of a polygon with 28 sides is 4680°.

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Answer:

It will take 6 days to catch up and they both will have read 210 pages

Step-by-step explanation:

to find this out we just find where the line intersects

It intersects at 6 days and 210 pages

Hopes this helps please mark brainliest

Answer: i put this here so you can mark the other person brainliest

Step-by-step explanation:

The option that describes the similarity relationship between the triangles is the option; The triangles are not similar, no expression for x can be found.

Similar triangles are triangles that  have all three interior angles of one triangle, congruent to the three angles of the other triangle.

The parameters of the triangles can be presented as follows;

ΔABC

∠A = 47°

∠C = 62°

AC = y

AB = w

BC = x

The measure of angle  ∠B = 180° - 47° - 52° = 81°

ΔDEF

∠D = 71°

∠E = 47°

DE = z

EF = u

DF = r

Therefore;

∠F = 180°- 71° -  47° = 62°

The angles of triangle ΔABC are not congruent to the angles of triangle ΔDEF, therefore; triangle ΔABC  and triangle ΔDEF are not similar.

Therefore;

The triangles are not similar, no expressions for x can be found.

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Step 1: Estimate

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2.

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2.

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: Divide

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: Average

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667 Step 4: Repeat

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667 Step 4: RepeatTo get a more accurate number, keep repeating step 2 and 3.

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667 Step 4: RepeatTo get a more accurate number, keep repeating step 2 and 3.

Step 1: Estimate10 lies between perfect squares of 3^2 and 4^2. Step 2: DivideDivide 10 by 3. We get 3.33 Step 3: AverageAverage 3.33 and 3, which gives us 3.1667 Step 4: RepeatTo get a more accurate number, keep repeating step 2 and 3. You should get a final answer of 3.16.

a) The combined mass of Mars and Mercury expressed in scientific notation is  9.72 x 10²³

b) The difference in the mass of the two planets expressed in scientific notation is  3.12 x 10²³

Scientific Notation:

Scientific method is the method of expressing numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.

Given,

The mass of Mars is 6.42 x 10²³ kilograms. The mass of Mercury is 3.3 x 10²³ kilograms.

Here we need to find the following,

a) The combined mass of Mars and Mercury expressed in scientific notation

b) The difference in the mass of the two planets expressed in scientific notation

a) The combined mass of Mars and Mercury expressed in scientific notation is calculated by add the both masses then we get,

=> (6.42 x 10²³) + (3.3 x 10²³)

Here we have to take the exponent term as common, then we get,

=> (6.42 + 3.3) x 10²³

=> 9.72 x 10²³

b) The difference mass of Mars and Mercury expressed in scientific notation is calculated by subtract the both masses then we get,

=> (6.42 x 10²³) - (3.3 x 10²³)

Here we have to take the exponent term as common, then we get,

=> (6.42 - 3.3) x 10²³

=> 3.12 x 10²³

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Answer:

20hours;

27houses.......................

The no. of people whole likes only roller coasters is 19.

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Let N(U) be the no. who likes at least one of the rides which is

N(U) = (60 - 8) = 52 as 8 people do not like either kind of ride.

Given, The number of people who like roller coasters is 42 and the number who do not like water rides is 23.

∴ The no. of people who only likes roller coasters is (42 - 23) = 19.

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The number of nametags that should be in the fourth row is 12

It should be noted that this information illustrates sequence.

In this case, the supervisor placed the first three rowsthe first row has 3 nametags, the second row has 5 nametags, and the third row has 8 nametags.

The difference will be:

5 - 3 = 2

8 - 5 = 3

Therefore, the next one will have a difference of 4. This will be:

= 8 + 4

= 13

Check: 12 - 8 = 4

Therefore, the nametags should be 12.

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The given graph can be expressed as an equation of f(x) = tan(-x) - 2.

What is a graph of a trigonometric function?

In these trigonometry graphs, the x-axis values of the angles are in radians, and the y-axis value of the function at each given angle is taken as f(x).

The given graph is of a negative angle of a tangent.

So if we draw the graph of the tangent of a negative angle, the graph will pass through the origin, but

If we subtract 2 from the graph of the tangent of the negative angle then we will get the same graph as shown in the given figure.

So the equation would be f(x) = tan(-x) - 2.

Hence, the equation of the graph will be f(x) = tan(-x) - 2.

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The area of the square increasing when the area of the square is 16 cm² by the rate of 48cm²/s.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Here,

A = s²

(dA)/(dt)

(dA/ds)*(ds/dt)

(ds)/(dt) = 6 cm/s

When A = 16 cm²

16 = s²

s = √(16)

s = 4 cm

(dA)/(dt) = 2 × 4 × 6 = 48 cm²/s

When the square is 16 cm², its area grows by 48cm²/s, or one-fourth of its initial size.

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The number of players the team can bring to the tournament = 19 .

Given : amount raised by team = $1775.50

            rent of bus = $901.50

            budget for meal per player = $46

To find : the number of players the team can bring to the tournament

Equation :

taking bus charge as y - intercept ( since it does not depend on the no . of members riding on it )

taking meal amount as slope ( since it depends on the no . of members a team can bring to the tournament )

Let x be the no . of players a team can bring to the tournament .

Therefore , the equation is :

1775.50 = 46 x + 901.50

874 = 46 x

x = 19

Hence , the number of players the team can bring to the tournament = 19 .

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Answer:

0.33

Step-by-step explanation:

hope this helps :)