Plot the Trapezoid ABCD with vertices A(-8,-4),B(-5, -1), C(0, -2), and D(-4,-8) in the x-axis.

The domain of the function f(x) that has a range of [-2, ∞) is [-2, ∞)

The inverse of a function that maps x into y, maps y into x.

The given coordinates of the points on the radical function, f(x) are; (-3, -2), (1, 0), (6, 1)

To determine the domain of

[tex] {f}^{ - 1}( x)[/tex]

The graph of the inverse of a function is given by the reflection of the graph of the function across the line y = x

The reflection of the point (x, y) across the line y = x, gives the point (y, x)

The points on the graph of the inverse of the function, f(x), [tex] {f}^{ - 1} (x)[/tex] are therefore;

[tex]( - 3, \: - 2) \: \underrightarrow{R_{(y=x)}} \: ( - 2, \: - 3)[/tex]

[tex]( 1, \: 0) \: \underrightarrow{R_{(y=x)}} \: ( 0, \: 1)[/tex]

( 6, \: 1) \: \underrightarrow{R_{(y=x)}} \: ( 1, \: 6)

The coordinates of the points on the graph of the inverse of the function, f(x) are; (-2, -3), (1, 0), (1, 6)

Given that the coordinate of point (x, y) on the image of the inverse function is (y, x), and that the graph of the function, f(x) starts at the point (-3, -2) and is increasing to infinity, (∞, ∞), such that the range of y–values is [-2, ∞) the inverse function, [tex] {f}^{ - 1}( x)[/tex], which starts at the point (-2, -3) continues to infinity, has a domain that is the same as the range of f(x), which gives;

The domain of the inverse of the function, [tex] {f}^{ - 1}( x)[/tex], using interval notation is; [-2, ∞)

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Figure 1 was enlarged to figure 2

Hence the side |AB| is corresspounding to the side |PQ|

The initial price is $38.21, and it got an increase of 7%, so the new price is the old one multiplied by 1.07:

Then, the new price decreased by 7%, so let's multiply it by 0.93 (that is, 1 minus 0.07):

So the price in August is $38.02.

Given from the number line:

D = -2 and F = 13

So, the distance DF = 13 - (-2) = 13 + 2 = 15

1) find E such that, DE : EF = 2 : 1

so,

so, x : (15 - x) = 2 : 1

x = 30 - 2x

3x = 30

x = 10

So, E = -2 + 10 = 8

=========================================================================

2) E is 4/5 of the distance from F to D

So, the distance from F = 4/5 * 15 = 12

So, E = 13 - 12 = 1

=====================================================================

3) the ratio of DE : EF = 2 : 3

So,

3x = 2 ( 15 - x)

3x = 30 - 2x

5x = 30

x = 30/5 = 6

E = -2 + 6 = 4

=================================================

4) E is 1/3 of the distance from D to F

So, the distance DE = 1/3 * 15 = 5

So, E = -2 + 5 = 3

=====================================================

As a summery:

1) E = 8

2) E = 1

3) E = 4

4) E = 3

Given,

The coordinates of the point is (-8, 0).

There are two methods of bearing is:

Compass bearing

True bearing.

The figure of the point is,

The bearing of the point with respect to anticlockwise from north is,

The bearing of point from west is 0 degree and from anticlockwise north is 90 degree.

The true bearing is,

Given:

The quadrilateral PQRS is given.

The aim is to locate the given quadrilateral into first quadrant only.

The graph will be reflected across x=4 then the graph will not be located to the first quadrant.

The x intercept is the value of x when y = 0

Given that x intercept = - 1, the coordinate is (- 1, - 0)

The y intercept is the value of y when x = 0

Given that y intercept = - 2, the coordinate is (0, - 2)

Slope = (y2 - y1)/(x2 - x1)

x1 = - 1, y1 = 0

x2 = 0, y2 = - 2

Slope = (- 2 - 0)/(0 - - 1)

slope = - 2/1

slope = - 2

Light house is located at (-5,2)

Lighthouese beacon will illuminate a distnce =12 km

Use the distance formula to find the equation :

Distance formula is expressed as :

Substitute the given values :

Problem

Determine the functions value when x= -1?

a. g(-1) = -3

b. g(-1) = 0

c. g(-1) = 1

d. g(-1) = 27​

Solution

For this case we just need to find the value of g when x= -1 and if we look at the table we got:

g(-1)= (-1)^3 + 6(-1)^2 +12(-1) +8

g(-1)= -1 +6 -12+8 = 5-12+8= 1

And then the solution for this case would be:

c. g(-1) = 1

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:

y = kx

for some constant k , called the constant of proportionality . This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.

From the given options, the baove property is satisfied by,

Thus, the correct option is A.

the rriangle is 3 4 5 triangle so 5×5 is 25

Given:

So the value is:

(a)

(b)

(c)

The dot product of v and u.

dot product is:

The doat product (i.i = 1) and ( j.j=1) and ( i.j=0) and ( j.i = 0)

Given:

The points are (8, -3) and (-5, 1).

To find the slope of the line:

The slope formula is,

Hence, the slope of the line is -0.31 (rounded to the nearest two decimal places).

Given the triangle XYZ with the following parameters

The diagram of the triangle is shown below

To find the value of x, we will apply sum of interior angle of triangle theorem

Hence, the value of x is 9.2308°

Given a radio tower of 250 feet and angles of 31 and 29 degrees, the height of the tower is given as 308.58 ft

This is the term that is used to refer to the angle that lies between the horizontal line and the object that would be observed from the horizontal line.

In the question we have the following data

b = 250 feet

angles = 31 degrees, 29 degrees

for the top α = 31 degrees, β = 59

For the bottom α = 29 degrees, β = 61 degrees

We have the formula as

a /sin α = b / sin β = c

tan ∅ = opp / adj

for ΔOCA

h1 = 250 x tan 39 degrees

= 250 x 0.8098

= 202.45

h2 = OCB

= 250 x tan 23

= 250 x 0.4245

= 106.125

The height h = h1 + h2

= 202.45 + 106.125

= 308.58

The height of the tower is 308.58 ft

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Explanation:

We have to find 5% of the original cost first:

And then add it to the original price:

Since it's a price, we have to round this result to the nearest hundredth

Answer:

The new price is $23.09

It takes Garret Choose min to remove 1 ft of hem. He should multiply the number of minutes by Choose... to determine the number of minutes it will take to remove 5 ft of hem.

The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach will come in handy for topics involving ratio and proportion, algebra, geometry, etc. In the unitary technique, we always count the value of a unit or one quantity first before figuring out the values of more or fewer quantities. This method is referred to as the "unitary method" for this purpose.

There are two types of unitary methods because they result in two types of variations and those are given below:

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Step 1 : Let's review the information given to us to answer the problem correctly:

• Annual salary of the governor of New York = $ 1,790,000

• Annual salary of the governor of Tennessee = $ 940,000

Step 2: Let x to represent the annual salary of the governor of New York

and let's find the ratio of the salary of the governor of Tennessee, as follows:

940,000/1,790,000 = 0.525

Step 3: Now, let's write the equation for calculating the salary of the governor of Tennessee for any given year, this way:

• 0.525x = Annual salary of the governor of Tennessee

•

Step 4: If the salary of the governor of New York for the next year is 2,000,000, then we can calculate the salary of the governor of Tennessee, this way:

0.525x = 0.525 * 2,000,000 = 1,050,000

The annual salary of the governor of Tennessee woudl be 1,050,000

Explanation:

This figure is a rectangle and a quarter of a circle. We can find their areas and add them to find the total area of the figure.

The area of the rectangle is:

The area of a circle is:

Where r is the radius of the circle. In this case we have a quarter of a circle, so its area is a quarter of the area of the circle:

The radius of this circle is 8cm:

The total area of the figure is:

Answer:

The area is 220.27 cm²

Solution

- The first integral is bounded by the x-values of [6, 22]

- The second integral is bounded by the x-values of [6, 14]

- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.

- The extra values are from 14 to 22.

- Thus, we have:

Final Answer

For supplementary angles, we can do the following equality

What we have to do, is to clear "x" to find its value.

In conclusion, the value of x is 33

A line segment has the endpoints at (-6, -10) and (23, 6) then the midpoints of the line segment will be (17, -2).

An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be estimated by utilizing either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.

A line segment has the endpoints at (-6, -10) and (23, 6).

Mid point of the line segment is given by [tex]$\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$[/tex]

The midpoints of the line segment will be

=  [tex]$\frac{23+-6}{2}[/tex], [tex]$\frac{-10+6}{2}}[/tex]

= 17, -2

Therefore midpoints of the line segment will be (17, -2).

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Arjun applied the wrong laws of logarithms.

The question can be solved as shown below:

Step 1: Apply the addition rule of logarithm given as

Thus, we have:

Step 2: Apply the subtraction rule of logarithm given as

Thus, we have:

Therefore, the correct answer is:

SOLUTION:

This is a combination problem.

The number of ways 3 students from a class of 23 be chosen for a field trip is;

Answer:

In order of appearance of  boxes

Step-by-step explanation:

The given function f(x) = -2x² + 3 belongs to the quadratic family of equations. A quadratic equation has a degree of 2. The degree is the highest power of the x variable in the function f(x)

The parent f(x) = x²

Going step by step:

2x²  ==> graph x² is vertically stretched by 2. For any value of x in x², the new y value is twice that the old value. For example, in the original parent function x², for x = 2, y = 4. In the transformed function 2x², for x = 2, y = 2 x 4 = 8 so it has been stretched vertically. It becomes skinnier compared to the original

-2x²  => graph is reflected over the x-axis. It is the mirror image of the original graph when viewed from the x-axis perspective

-2x² + 3 ==> graph is shifted vertically up by  3 units

Domain is the set of all x-input values for which the function is defined. For both x² and -2x² + 3 there are no restrictions on the values of x. So the domain for both is the set of all real numbers usually indicated by
-∞ < x < ∞

The range is the set of all possible y values for a function y = f(x) for x values in domain.

The range of f(x) = x² is x≥ 0 since x² can never be negative

Range of -2x² + 3 is  x ≤ 3 : Range of -2x² is y ≤ 0 since y cannot be negative and therefore range of -2x² + 3 is y ≤ 3