Determine if the following relations are functions, and justify why.
a) **{(1, −2), (−2, 0), (−1, 2), (1, 3)}
Function?: ____________
Justification: ____________________________________________________________________________

Answer:

C

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle f(x) \text{ and } g(x)=\sin^{-1}(f(x))[/tex]

And we want to find the ratio that represents:

[tex]\displaystyle \frac{f^\prime(x)}{g^\prime(x)}[/tex]

To do so, we will compute the derivatives of both functions.

For f,  we can simply write that:

[tex]f^\prime(x)=f^\prime(x)[/tex]

For g, we will use the chain rule:

[tex]\displaystyle (u(v(x))^\prime=u^\prime(v(x))\cdot v'(x)[/tex]

We can let:

[tex]u(x)=\sin^{-1}(x)\text{ and } v(x)=f(x)[/tex]

We can double check this by doing the composition:

[tex]g(x)=u(v(x))=\sin^{-1}(f(x))[/tex]

Therefore, by the chain rule, we acquire that:

[tex]\displaystyle g^\prime(x)=\frac{1}{\sqrt{1-(v(x))^2}}\cdot v'(x)[/tex]

By substitution:

[tex]\displaystyle g^\prime(x)=\frac{f^\prime(x)}{\sqrt{1-(f(x))^2}}[/tex]

Hence, our ratio is:

[tex]\displaystyle \frac{f^\prime(x)}{g^\prime(x)}=\frac{f^\prime(x)}{\dfrac{f^\prime(x)}{\sqrt{1-(f(x))^2}}}[/tex]

Simplify:

[tex]\displaystyle \frac{f^\prime(x)}{g^\prime(x)}=\sqrt{1-(f(x))^2}[/tex]

Hence, our answer is C

Answer:

This isn't the answer as you can see it above, but do you have the rest of the questions?

Step-by-step explanation:

Thank you in advance.

Answer:

35x-35y

Step by step explanation: I

0.5(20x-50y+36)-0.25(100x+40y-12)

10x-25y+18+25x-10y+3 -------- after we distribute 0.5&-0.25

10x+25x-25y-10y+18+3. ---------we collect the like terms to add them or substract

35x-35y+21 -----------------------------simplified form

Answer:

35x-35y

Step-by-step explanation:

simply simplify both sides then subtract

Plug the formula into Desmos and even just visually

C.  " y = -6x - 8

is the answer

The equation of the line tangent to the function f(x) = 1 – x² at x = –3 will be y = –6x – 8. Option C is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the function is,f(x) = 1 – x²

We have to find the equation of the line tangent to the function f(x) = 1 – x² at x = –3.

Determine the function's first derivative f(x), To get the slope at a given location, plug the specified point's x value into f'(x). To determine the tangent point's y coordinate, plug the value of x into f(x). The point-slope formula may be used to combine the slope from step 2 with the point from step 3 to produce the equation for the tangent line.

Thus, the equation of the line tangent to the function f(x) = 1 – x² at x = –3 will be y = –6x – 8.Option C is correct.

Learn more about the equation here,

https://brainly.com/question/10413253

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Answer:

a

Step-by-step explanation:

its 6 loses over 14 wins

Answer:

1. 30°

2. [tex]1:1:\sqrt{2}[/tex]

3. 20cm

4. 5cm

Step-by-step explanation:

for the first one:

we have the triangle RVT and we know that

[tex]\angle V = 90\\\\\angle R = 60[/tex]

so [tex]\angle T[/tex] [tex]+ \angle V+\angle R[/tex] = 180

so

[tex]\angle T = 30[/tex]

for the second one

we know by specials right triangles that the sides are

[tex]x:x:x\sqrt{2}[/tex]

divide by x and get

[tex]1:1:\sqrt{2}[/tex]

for the third one

again by 30-60-90 triangle we know that

[tex]2BC=AB\\\\2(10)=AB\\\\AB=20[/tex]

for the fourth one

here we can use excersie 3 and the ratio of XY:YC = 1:1

that means they are equal so

XY=YC

XY = 5

Answer:

25 miles per gallon.

Step-by-step explanation:

The answer is 25 because 200 divided by 8 is 25.

P.S Can I have brainliest?

Answer:

x = 9.25

Step-by-step explanation:

It is given that ABC is an isosceles triangle.

m∠A = 43° and m∠C = (6x+13)°

We need to find the value of x.

The sum of a triangle is equal to 180°.

∠A is the vertex angle. For a triangle sum of angle of triangle is equal to 180°

∠A+∠B +∠C=180

43+∠B+(6x+13)°=180

6x+∠B+56=180

6x+∠B = 124

∠B =124-6x

For an isosceles triangle,

∠B = ∠C

124-6x = (6x+13)

124-13 = 6x+6x

111 = 12x

x = 9.25

So, the value of x is 9.25.

Answer:

This is the simplest form

Step-by-step explanation:

I don't think further simplification is possible

The correct answer is B. Every year, we bought a homemade apple pie that cost only $5 at a little store on the road to the cabin.

Explanation:

In the sentences presented the section "that cost only $5" is a modifier because this describes the noun "homemade apple pie". Moreover, this modifier should be placed right after the noun it describes to clarify the "$5" refer to the cost of the pie.

This occurs in option B "a homemade apple pie that cost only $5" because this places the modifier after the noun, and this makes the sentence to be clear. On the other hand, in other options the meaning is confusing. For example in A "a homemade apple pie at a little store that cost only $5," it is not clear if the cost refers to the apple or the store.

Answer:

Number of small boxes purchased : 2

Number of large boxes purchased : 5

Step-by-step explanation:

Let,

x be the number of small boxes of nails purchased

y be the number of large boxes of nails bought

Then according to given statement;

50x+350y = 2550     Eqn 1

y = x+5        Eqn 2

Putting value of y from Eqn 2 in Eqn 1

50x + 350(x+5) = 2550

50x + 350x + 1750 = 2550

400x = 2550-1750

400x = 800

Dividing both sides by 400

[tex]\frac{400x}{400}=\frac{800}{400}\\x=2[/tex]

Putting x=2 in Eqn 2

y = 2+5

y = 7

Hence,

Number of small boxes purchased : 2

Number of large boxes purchased : 5

Answer:

Following are the solution to this question:

Step-by-step explanation:

We used sampling technique to collect samples throughout the instance of Options a and b because here each successive sample frame has the same gap of 10 (in the example) and in 'b' is 1, but we use a simple random sampling in 'b' and 'c' to collect the test because they can't follow any specific pattern from of the collecting systems here.

Answer:

The Volume of triangular prism

                     V = 450 cm³

Step-by-step explanation:

Explanation:-

Given The area of cross section of a prism A = 45cm²

and     height (h) = 10 cm

The Volume of triangular prism

                V = ( Base area X Height )

                    =  45 X 10

                    = 450 cm³

The Volume of triangular prism

                     V = 450 cm³

Answer: It means depression

Step-by-step explanation:

Answer:

Being sad means your body has entered a mini-clinical state, bringing back grief and usually making you remember past traumas for no existential reason. Sadness can drive you to feeling alone - not isolated, but alone with your inner thoughts. Your interior feeling cold, and like no one is there to put their hand out and help you become warm again. Sadness can drive you to loneliness, and loneliness can lead you to depression. Depression inverts your brain waves and makes you feel useless, no-good, nothing useful, just a joke.  

Answer:

Every number of years 365 and I have been trying

The gradient of the line segment between points (1, 2) and (3, -8) will be -5.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

(1, 2) and (3, -8)

Then the gradient of the line segment will be given as,

m = (- 8 - 2) / (3 - 1)

m = - 10 / 2

m = - 5

The gradient of the line segment between points (1, 2) and (3, -8) will be -5.

More about the linear equation link is given below.

https://brainly.com/question/11897796

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Answer:

[tex]\huge\boxed{(-19)^{-8}=19^{-8}}[/tex]

Step-by-step explanation:

Use

[tex]a^n\times a^m=a^{n+m}[/tex]

[tex](-19)^{-12}\times(-19)^4=(-19)^{-12+4}=(-19)^{-8}[/tex]

Answer:

They r correct lol

Step-by-step explanation:

Answer: 15 gallons .

Step-by-step explanation:

Step 1

4 quarts = 1 gallon

therefore 60 quarts = (60 quarts x 1 gallon) / 4 quarts

= 15 gallons .

Step 2-- The converted amount which is 15  has fewer units than the original which is 60.

Answer:

-42/7

Step-by-step explanation:

Answer:

x=25°

y=25°

Step-by-step explanation:

E^+F+EG^F=180°(sum of int. angles of triangle)

x+35+90+30=180

x=180-90-30-35

×=25

HE^G+H+G=180° (sum of int. angles of triangle)

35+30+y+90=180

y=180-90-35-30

y=25

Answer:

1. 38 oz / 2 lbs 6 oz

2. 254 in / 7 yd 2 in

3. 21 pt / 3 gal 2 qt 1 pt

4. 18,480 ft / 3 mi 2,640 ft

5. 180 oz / 6 lbs 12 oz

6. 525 s / 8 min 45 s

7. 318 in / 8 yd 2 ft 10 in (9.99996 inches not simplified)

8. 9 pt / 4 qt 1 pt

9. 15,885 s / 4 hr 24 min 45 s

The first answers are the ones I got originally and the second answers are the simplified ones.

Answer:

5=tens

6=ones

1=tenths

3=hundredths

Hope this helps

Step-by-step explanation:

Answer:

5/6 of a box is left over.

Step-by-step explanation:

2 - 1/2 - 2/3 = 0.83333333333

0.83333333333 in fraction form is 5/6.

Answer:

20 miles

Step-by-step explanation:

Given the equation of the line of the graph, y = 8x, where,

y = distance the hurricane travelled in miles

x = time of travel in hours

8 = slope/speed in miles/hour

To find how far the hurricane travelled in 2.5 hours, substitute x = 2.5 into y = 8x

This:

y = 8(2.5)

y = 20 miles

Thus, from the graph, we can estimate this also. On the x-axis, between 2 and 3, we have 2.5 hours. The corresponding value of x = 2.5 is y = 20.

Answer:

80%

Step-by-step explanation:

24/30 = x/100

100/30= 3 1/3

24 x 3 1/3= 80

Answer:

[tex]- 8y^6 - 88y^5-6y^3 + 71y^2 + 55y[/tex]

Step-by-step explanation:

Given

[tex](-6y + 8y^4 - 5)(y^2 - 11y)[/tex]

Required

Evaluate

[tex](-6y + 8y^4 - 5)(y^2 - 11y)[/tex]

Expand Brackets

[tex]y^2(-6y + 8y^4 - 5)- 11y(-6y + 8y^4 - 5)[/tex]

Open brackets

[tex]-6y^3 - 8y^6 + 5y^2 + 66y^2 - 88y^5 + 55y[/tex]

Collect Like Terms

[tex]- 8y^6 - 88y^5-6y^3 + 5y^2 + 66y^2 + 55y[/tex]

[tex]- 8y^6 - 88y^5-6y^3 + 71y^2 + 55y[/tex]

Answer:

18

Step-by-step explanation:

Answer:

5x

Step-by-step explanation:

-6 + 2x + 4 + 3x - (-2)

rearrange to make it easier to solve

2x + 3x - 6 + 4 - (-2)

add like terms, negative time negative is positive

5x - 2 + 2

5x

Answer:

11x +4

Step-by-step explanation:

Answer:

Third option: 0

Step-by-step explanation:

edge2020

Answer:

The answer is 0!

Step-by-step explanation:

edge 2021

Answer:

Please check the attached graph below.

Step-by-step explanation:

We know that a dot plot illustrates a visual display of data using dots.

Given that Ramon recorded how many miles he biked each day in the table, such as:

Distance (mi)              Frequency

1                                    2

2                                   2

3                                   4

4                                   4

5                                   2

6                                   2

The dot plot of data points plotted as dots on a graph with an x- and the y-axis is attached below.

Answer

got the quiz right

Step-by-step explanation:

     x x

     x x

x x x x x x

x x x x x x