Answer circled questions, please

Answer:

All together:

D:(-∞,∞)

R:(-∞,2]

Individually:

D: (-∞,-2], (-2,∞)

R: (-∞,-2], y=2

Step-by-step explanation:

So the way I like to think about Domain and Range is that the Domain is the set of real numbers which can be put into a function and the Range is the set of real numbers which you can get out from a function.

Looking at your given function, it looks like the piece-wise parts are f(x)=x and f(x)=2. Neither one of the functions has domain restrictions (you can plug anything into the first and second without getting any mathematical errors [like a 0 in the denominator]). And since the graph shows arrows in each end, indicating infinite continuation of the curve, the Domain is (-∞,∞).

Now for the outputs of each function, we can see that you'll be getting any number out for the f(x)=x portion. But, the f(x)=2 portion will always give you 2 for any input. So the Range is (-∞,2).

Now I'm honestly not too sure what the HW is asking you to do with this info... for the first part, maybe they want the individual domain and range values for each piece of the piece-wise while the second part asks for the overall? You might know what it's asking better then me since it's your class.

I'll include the overall and individual answers above. Comment with any questions.

Answer: it is neither

#1

\(\\ \rm\Rrightarrow \dfrac{WX}{GH}=\dfrac{UY}{JI}\)

\(\\ \rm\Rrightarrow \dfrac{8}{14}=\dfrac{UY}{28}\)

\(\\ \rm\Rrightarrow \dfrac{8(28)}{14}=UY\)

\(\\ \rm\Rrightarrow UY=8(2)=16\)

#2

\(\\ \rm\Rrightarrow \dfrac{UV}{UY}=\dfrac{FJ}{JI}\)

\(\\ \rm\Rrightarrow \dfrac{UV}{16}=\dfrac{21}{28}\)

\(\\ \rm\Rrightarrow UV=\dfrac{3}{4}\times 16\)

\(\\ \rm\Rrightarrow UV=3(4)=12\)

#3

\(\\ \rm\Rrightarrow \dfrac{WX}{XY}=\dfrac{GH}{HI}\)

\(\\ \rm\Rrightarrow \dfrac{8}{XY}=\dfrac{14}{35}=\dfrac{2}{5}\)

\(\\ \rm\Rrightarrow 2XY=40\)

\(\\ \rm\Rrightarrow XY=20\)

Answer:

UY = 16

UV = 12

XY = 20

Step-by-step explanation:

If UVWXY ~ JFGHI

then:

UV~JF

VW~FG

WX~GH

XY~HI

UY~JI

The only pair of sides that both have measures is WX and GH:

WX = 8

GH = 14

⇒ GH/WX = 14/8 = 1.75

Therefore, JFGHI is and enlargement of UVWXY by scale factor 1.75

As IJ = 28

⇒ UY = 28 ÷ 1.75 = 16

As JF = 21

⇒ UV = 21 ÷ 1.75 = 12

As HI = 35

⇒ XY = 35 ÷ 1.75 = 20

Example:

f(x) = (x - 1)2, f(x) = 8x , f(x) = x2 - x , f(x) = 7. Summary: From the given functions, f(x) = 7 is the even function.

Answer:

Step-by-step explanation:

The area of the rectangle is 48 square feet.

Write an equation you can use to find the value of x.

48 : 4 = x

12 = x

48=4x is the equation which can be used to find the value of x.

Given that area of the rectangle is 48 square feet.

We have to find the value of x.

We know that area of rectangle is length times width.

Area = length × width

Length =x ft

Width = 4 ft

Area = 48 square feet.

Plug in the values of length, width and area in above formula.

48=4x

Divide both sides by 4:

x=12

Hence, 48=4x is the equation which can be used to find the value of x.

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3) There are 10 sides, so the sum of the angles is \(180(10-2)=1440^{\circ}\)

4) There are 9 sides, so the sum of the angles is \(180(9-2)=1260^{\circ}\).

Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

The unknown angles in the circle are as follows:

a. m∠AEB = 73°

b. arc angle VW = 155°

a.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

m∠AEB = 1 / 2 (99 + 47)

m∠AEB = 146 / 2

m∠AEB = 73 degrees

b.

If two secants intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs .

Therefore,'

arc angle VW = x

55 = 1 / 2 (x - 45)

55 = 0.5x  - 22.5

0.5x = 55 + 22.5

0.5x = 77.5

divide both sides by 0.5

x = 77.5 / 0.5

x = 155 degrees

Therefore,

arc angle VW = 155 degrees

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Using a geometric sequence, it is found that the number of black squares in the first five figures of the Sierpinski Carpet is of 4681.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.

The nth term of a geometric sequence is given by:

\(a_n = a_1r^{n-1}\)

In which \(a_1\) is the first term.

The sum of the first n terms of a sequence is given by:

\(S_n = \frac{a_1(1 - r^n)}{1 - r}\)

In this problem, the parameters are: \(a_1 = 1, r = 8, n = 5\), hence:

\(S_n = \frac{1(1 - 8^5)}{1 - 8} = 4681\)

The number of black squares in the first five figures of the Sierpinski Carpet is of 4681.

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Answer:

1, 8, 5

Step-by-step explanation:

4681, 2,396,745

He travel before passing the first man is 12 kilometer per hour when one man starts out from city and walks.

Given that,

A single man sets off from a city and travels north at a 3 kilometer per hour pace. A second man begins from the same location and walks the same path at a speed of 4 kilometres per hour three hours later.

We have to find how far must he travel before passing the first man.

Here,

Take t,

Distance is 3t

Speed is 4

Time is t-3

So, we know

Distance =Speed×Time

3t=4(t-3)

3t=4t-12

3t-4t=-12

-t=-12

t=12

Therefore, He travel before passing the first man is 12 kilometer per hour when one man starts out from city and walks.

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Answer:

Do u have a photo??

Step-by-step explanation:

cuzz I do not know

The surface area of the cylinder is 905 square centimeters

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

Diameter, d = 12 cm

Height, h = 18 m

This means that

Radius, r = 12/2 = 6 cm

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

Surface area = 2πr(r + h)

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

Surface area = 2π * 6 * (6 + 18)

Evaluate

Surface area = 905

Hence, the surface area is 905 square centimeters

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\(\tan x+\frac{\cos x}{1+\sin x}\\\\ =\frac{\sin x}{\cos x}+\frac{\cos x}{1+\sin x}\\\\=\frac{\sin x(1+\sin x)+\cos^{2} x}{\cos x(1+\sin x)}\\\\=\frac{\sin^{2} x+\cos^{2} x+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1}{\cos x}\\\\=\sec x\)

Hello!

area

= 2*25 + (20 - 2)*(25-8)

= 50cm² + 306cm²

= 356cm²

Answer:

Where is the shaded region i need a picture

Step-by-step explanation:

Answer:

Also need a picture but try either multiplying or dividing

The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.

Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.

Simplifying this, we get 2x - 80 = $670  + 80 2x = $750  x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.

The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.

The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.

Therefore, the cost of the bench is $375, and the cost of the garden table is $295.

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Answer:

The length of the side BC is 6 units.

Step-by-step explanation:

Rectangle ABCD

Coordinates of Point A,B,C,D

\(A = ( 5 , 5)B = (7, 5)C = (7 , -1)D = (5 , -1)\)

As we are asked to find the length of side BC, we'll apply the Distance formula on side BC

BC = \(\sqrt{(7_ {-} 7)^{2} +(-1 {-} 5)^{2}}\)

     = \(\sqrt{(0)^{2} +(-6)^{2}}\)

     = \(\sqrt{ 36}\)

     = \(6\)

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Answer:

\( - \sf \displaystyle \: \frac{ \cos(2x) }{ \sin ^{2} (2x)\sqrt{ \csc(2x) } }\)

Step-by-step explanation:

we are given a derivative

\( \displaystyle \: \frac{d}{dx} ( \sqrt{ \csc(2x) } )\)

and said to figure out the first derivative

to do so

recall chain rule:

\( \sf\displaystyle \: \frac{d}{dx} (f(g(x)) = \frac{d}{dg} (f(g(x)) \times \frac{d}{dx} (g)\)

so we get

\( \displaystyle \: g(x) = \csc(2x) \)

rewrite the derivative using the chain rule:

\( \displaystyle \: \frac{d}{dg} ( \sqrt{ g } ) \times \frac{d}{dx} ( \csc(2x) )\)

use square root derivative rule to simplify:

\( \displaystyle \: \frac{1}{ 2\sqrt{g} } \times \frac{d}{dx} ( \csc(2x) )\)

now we need to again use chain rule composite function derivative to simplify

where we'll take a new function n so we won't mess up two g's and we'll take 2x as n

use composite function derivative to simplify:

\( \sf \displaystyle \: \frac{1}{ 2\sqrt{g} } \times \frac{d}{dn}( \csc(n) ) \times \frac{d}{dx} (2x)\)

use derivative formula to simplify derivatives:

\( \sf \displaystyle \: \frac{1}{ 2\sqrt{g} } \times - \cot(n) \csc(n) \times 2\)

substitute the value of n:

\( \sf \displaystyle \: \frac{1}{ 2\sqrt{g} } \times - 2\cot(2x) \csc(2x) \)

substitute the value of g:

\( \sf \displaystyle \: \frac{1}{ 2\sqrt{ \csc(2x) } } \times - 2\cot(2x) \csc(2x) \)

now we need our trigonometric skills to simplify

rewrite cot and csc:

\( \sf \displaystyle \: \frac{1}{ 2\sqrt{ \csc(2x) } } \times - 2 \dfrac{ \cos(2x) }{ \sin(2x) } \dfrac{1}{ \sin(2x) } \)

simplify multiplication:

\( \sf \displaystyle \: \frac{1}{ \cancel{ \: 2}\sqrt{ \csc(2x) } } \times \cancel{- 2} \dfrac{ \cos(2x) }{ \sin ^{2} (2x) } \)

simplify multiplication:

\( - \sf \displaystyle \: \frac{ \cos(2x) }{ \sin ^{2} (2x)\sqrt{ \csc(2x) } }\)

9514 1404 393

Answer:

  -cot(2x)√csc(2x)

Step-by-step explanation:

Using the chain rule, ...

  (d/dx)(√u) = u'/(2√u)

Here, we have u = csc(2x), so u' = -2cot(2x)csc(2x).

Then ...

  (d/dx)(√csc(2x)) = (-2cot(2x)csc(2x))/(2√csc(2x)) = -cot(2x)√csc(2x)

Answer:

7/1000

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

7(4) = 28

28 - 4 = 24

Answer:

The numbers are 75,68

Step-by-step explanation:

Let the number be a ,b

The sum of two numbers is 143

⇒   x + y = 143 -------------(I)

Their difference is 7

⇒ x - y = 7 --------------(II)

Add the equation (I) & (II) and thus y will be eliminated and we can find the value of x

(I)     x + y = 143

(II)   x -  y = 7        {Now add}

     2x       = 150

            x  = 150 ÷ 2

x = 75

Substitue x =  75 in equaion (I)

75 + y =143

      y = 143 - 75

y = 68

The correct answer is $170.4

Explanation:

The total Georgie spent is equal to the money spent on clothes ($160) added to taxes (6.5% of the price of the clothes). Now, to calculate the money spend on taxes follow this process:

1. Divide the total of money spent on clothes into 100 (this number represents 100%)

160 ÷ 100 = 1.6

2. Multiply this number by the specific percentage (6.5)

1.6 x 6.5 = $10.4 (This is the money spent on taxes)

Finally, add the value of taxes and the price of the clothes:

$160 + $10.4 = $170.4

The line or points has a slope value of -1

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

The slope of -3 up to positive 3

For a start, we represent the above parameters using an ordered pair

The ordered pair is represented as

(x, y) = (-3, 3)

The slope of the point is then calculated using the following slope formula

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3, 3) and (0, 0)

The coordinate (0, 0) represents the origin

Substitute the known values in the above equation

So, we have the following equation

Slope = (3 - 0)/(-3 - 0)

Evaluate the difference

So, we have the following equation

Slope = (3)/(-3)

Evaluate the quotient

So, we have the following equation

Slope = -1

Hence, the slope is -1

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When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

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Answer:

91.4%

Step-by-step explanation:

First do: 32,000/35,000 = X/100

Then multiply 32,000 by 100 which is 3,200,000

Then divide 3,200,000 by 35,000

You will get 91.42857142857143

The scale of the x-axis is 3 seconds per box and the scale of the y-axis is 1 meter per box. The correct option is d.  x -axis is 3 seconds per box   y-axis is 1 meter per box

From the question, we are to determine the scale for each axis

From the given information,

The graph is drawn to be 20 boxes by 20 boxes

The range of values for the x-axis is 0 to 60 seconds

and

The range of values for the y-axis is 0 to 20 meters

Thus,

The scale of the x-axis will be

60 seconds ÷ 20 boxes = 3 seconds per box

The scale of the y-axis will be

20 meters ÷ 20 boxes = 1 meter per box

Hence, x -axis is 3 seconds per box and y-axis is 1 meter per box

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