Which represents the imverse of the function f(x) = 4x?

Answer:

Slope is 0

Step-by-step explanation:

y-2/3=0

y=2/3

There is no x value?

Answer:

x = 2

Step-by-step explanation:

A line with an undefined slope indicates that the line is vertical and parallel to the y- axis.

The equation of a vertical line is

x = c

Where c is the value of the x- coordinates the line passes through.

The line passes through (2, 5) with x- coordinate 2, hence

x = 2 ← equation of line

Answer:

The equation of the graph below is y = 0.5 csc[0.5(x + π/2)] - 1 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the trigonometry transformation

- If the equation is y = A csc(B(x + C)) + D

# Amplitude is A

- The Amplitude is the height from the center line to the peak .

  Or we can measure the height from highest to lowest points and

  divide that by 2

# period is 2π/B

- The Period goes from one peak to the next

# phase shift is C (positive is to the left)

- The Phase Shift is how far the function is shifted horizontally

  from the usual position.

# vertical shift is D

- The Vertical Shift is how far the function is shifted vertically from

 the usual position.

- If y = csc(x)

∴ A = 1 , B = 1 , C = 0 , D = 0

- That means the amplitude is 1, the period is 2π, no phase shift

 or vertical shift

* Now lets solve the problem

- From the graph

# The amplitude = (-0.5 - -1.5)/2 = 0.5

∴ A = 0.5

# The period is from 2.5π to -1.5π

∴ The period is 4π

∵ The period = 2π/B

∴ 4π = 2π/B ⇒ by cross multiplication

∴ B = 2π/4π = 1/2 = 0.5

* There is only one answer has A = 0.5 and B = 0.5

∴ y = 0.5 csc[0.5(x + π/2)] - 1

* The equation of the graph below is 0.5 csc[0.5(x + π/2)] - 1

* For more understand look to the color graph

- The blue graph is y = csc(x)

- The green graph is y = 0.5 csc[0.5(x + π/2)] - 1

Answer:

C. y = 0.5csc [0.5 (x + pi/2)] - 1

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps!

Answer:

5. 77.32°

6. 54.46°

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

I find the mnemonic SOH CAH TOA to be extremely helpful for problems like this. It reminds you ...

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

___

Based on your notes of problems 5 ad 6, I'd say you need to be a little careful of notation. The relationship between angles and side ratios is ...

• TrigFunction(angle) = ratio . . . . . . . . trig functions are sin, cos, tan, csc, sec, cot

• InverseTrigFunction(ratio) = angle . . . inverse trig functions are arcsin, arccos, arctan, arccsc, arcsec, arccot. These are also written with a -1 superscript, for example, sin⁻¹ for arcsin.

__

5. sin(x°) = 40/41 . . . . . . . . . . . . opposite/hypotenuse

x° = arcsin(40/41) ≈ 77.32°

__

6. tan(x°) = 7/5 . . . . . . . . . . . . . . opposite/adjacent

x° = arctan(7/5) ≈ 54.46°

__

7. tan(39°) = 11/x

x = 11/tan(39°) . . . . . . . . . multiply both sides of the equation by x/tan(39°)

x ≈ 13.6

__

8. cos(46°) = x/28

x = 28·cos(46°) ≈ 19.5

__

9. tan(51°) = 8/x

x = 8/tan(51°) ≈ 6.5 . . . . . solve as in problem 7

__

10. sin(24°) = x/31

x = 31·sin(24°) ≈ 12.6

7 rollercoasters because 4 shows plus 3 more rollercoasters equal 7 and 4 shows .

It takes 5 minutes to ride on the rollercoaster plus the estimated 30 minute wait equals 35 and 35*7=245 and it takes 25 minutes to watch show and 25*4=100 and 245+100=345 so he can ride 7 rollercoasters and 4 shows in 345 minutes.

Answer:

C. 1/4

Step-by-step explanation:

There are in total 12 marbles in the bag.  So the probability of picking a red marble is 3/12.  If you simplify that, you get 1/4.

B, because 2/5 is the same as 20/50. Hope that helps!

Answer:

B  2/5

Step-by-step explanation:

The experimental probability of tails is the number of tails of the total number of tries

P (tails) = 20/(20+30)

             =20/50

            =2/5

I set up an equal proportion [tex]\frac{100}{0.25} = \frac{80}{x}[/tex]

cross multiply to get 80 * 0.25 = 100x

20 = 100x; divide both sides by 100

0.2 = x so the answer is choice B

Answer:

B. 0.2 meters.

Step-by-step explanation:

Let x represent meters of spring stretched by 80 newtons.

We have been given that a force of 100 newtons will stretch a spring 0.25 meters.

We will use Hooke's law, which states that the force needed to compress or extend a spring is directly proportional to the distance we stretch it.[tex]N=kx[/tex], where,

N = Force in Newtons,

k = The spring constant,

x = Amount of extension in meters.

Let us find spring constant by substituting [tex]N=100[/tex] and [tex]x=0.25[/tex].

[tex]100=k*0.25[/tex]

[tex]\frac{100}{0.25}=\frac{k*0.25}{0.25}[/tex]

[tex]400=k[/tex]

So, our equation would be [tex]N=400x[/tex].

Now, we will substitute [tex]N=80[/tex] in our equation to find x.

[tex]80=400x[/tex]

Upon dividing both sides of our equation by 400 we will get,

[tex]\frac{80}{400}=\frac{400x}{400}[/tex]

[tex]\frac{1}{5}=x[/tex]

[tex]0.2=x[/tex]

Therefore, the force of 80 newtons will stretch the spring 0.2 meters and option B is the correct choice.

Answer:

D

Step-by-step explanation:

A does not work, because you stop on the way to the meeting (which you don't)

B does not work, because you speed up on the way to the meeting, when in reality you slow down

C does not work, because it does not show that you went back home or changed speed at all

D is correct!

Answer:

D

Step-by-step explanation:

Answer:

Unfortunately, your picture doesn't show all the graphs of the possible answers.

However, the graph should look like the one I attached, passing by the (5,0) point.  Which is logic since a value of 5 for x would make the y the cubic root of 0... which is 0.

When trying to identify a graph of a formula, always try to see which values of x could make y = 0 or what would happen to y if x = 0, that will always give you a pretty good idea of which graph to choose from.

Answer:D

Step-by-step explanation:

Odd numbers take the form [tex]2n-1[/tex], where [tex]n\ge1[/tex] is an integer. When [tex]n=400[/tex], the last odd number would be 799. So we're adding

[tex]S=1+3+5+\cdots+795+797+799[/tex]

By reversing the order of terms, we have

[tex]S=799+797+795+\cdots+5+3+1[/tex]

and we can pair up terms in both sums at the same position to write

[tex]2S=(1+799)+(3+797)+(5+795)+\cdots(795+5)+(797+3)+(799+1)[/tex]

so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:

[tex]2S=400\cdot800\implies S=160,000[/tex]

###

We could also make use of the formulas,

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

[tex]\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2[/tex]

We have

[tex]S=\displaystyle\sum_{i=1}^{400}(2i-1)=2\sum_{i=1}^{400}i-\sum_{i=1}^{400}1=400(400+1)-400=400^2=160,000[/tex]

Answer:

1.44 pi meters squared

Step-by-step explanation:

Area of circle form: pi r squared

pi is there so we need to find radius

2.4/2 is 1.2

1.2 squared is 1.44

Answer:

The distance between Amanda and the helicopter be x

cos 60  = x / 4000

x = 4000 ×  cos 60 

 = 4000 × 1/2

 = 2000 feet

Step-by-step explanation:

The distance between Jeremiah and the helicopter is given by the trigonometric relation and d = 2000 feet

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of sides of the triangle are

The distance between Amanda and Jeremiah = 4000 feet

Amanda’s angle of elevation to see the helicopter is 60° and Jeremiah’s angle of elevation to see it is 30°

So , from the trigonometric relations ,

cos θ = adjacent / hypotenuse

cos 60° = d / 4000

Multiply by 4000 on both sides , we get

d = ( 4000 ) ( 1/2 )

d = 2000 feet

Hence , the distance is 2000 feet

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The complete question is attached below :

Amanda and Jeremiah are standing on the same side of a large lake. They are separated by a horizontal distance of 4000 ft. Both Amanda and Jeremiah can see a helicopter that is directly above the horizontal distance between them. Amanda’s angle of elevation to see the helicopter is 60° and Jeremiah’s angle of elevation to see it is 30°. What is the distance between jeremiah and the helicopter? Round to the nearest feet

Answer:

1/26

Step-by-step explanation:

there are 4 jacks in a deck and one heads on a coin. So you take 4/52 and mutiply it by 1/2 and get 1/26

Mark has a standard deck of 52 cards and a fair two-sided coin. What is the probability that he will pull a jack from the deck of cards and toss the coin to land on heads?

( C. 1/13 )

Answer:

c

Step-by-step explanation:

a and b ar out because suplementry angels are 180 so its just c and d

When parallel line are cut by a traversal line,

Then corresponding angles are congruent.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

The parallel lines are cut by a traversal line.

(A) The sum of the degree measure of complementary angles is 180 degrees.

This is a contradictory statement.

Because, the sum of the degree measure of supplementary angles is 180 degrees.

(B) The sum of the degree measure of corresponding angles is 180 degrees.

This is a contradictory statement.

Because, the sum of the degree measure of supplementary angles is 180 degrees.

(C) Corresponding angles are congruent.

This is a true statement.

(D) The angles in a vertical pair are acute

This is also ca contradictory statement.

Therefore, corresponding angles are congruent.

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C is the right answer

Answer:

(C) 38 cm²

Step-by-step explanation:

Top length = 6 cm

Bottom length = 5 + 8 = 13 cm

Area

= 1/2 ( 6 + 13) (4)

= 1/2(19)(4)

= 38 cm²

The area of the trapezoid is 38 cm2.

Answer:

see explanation

Step-by-step explanation:

(a)

Using the relationship

distance = speed (s) × time (t) ← speed is rate of change, then

speed = [tex]\frac{distance}{time}[/tex], thus

[tex]\frac{54}{0.75}[/tex] = 72

[tex]\frac{216}{3}[/tex] = 72

[tex]\frac{252}{3.5}[/tex] = 72

[tex]\frac{432}{6}[/tex] = 72

[tex]\frac{576}{8}[/tex] = 72

Thus rate of change is constant, hence

(b)

d = 72t ← explicit formula

Hence function 's graph is option D .

Cos function is ration of adjacent side to hypotheses.

Range of function lies between [-1,1]

Cos x = 2 n [tex]\pi[/tex]

where x is angle

Hence option D where y=3cos ([tex]\frac{\pi }{2}[/tex]X) is function

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Answer: 3cos(4x)

Step-by-step explanation:

The probability that Jase makes an A given that he studies for the geometry test is [tex]\(\frac{68}{75}\)[/tex].

Let's denote the event that Jase studies for the geometry test as [tex]\(S\)[/tex] and the event that he makes an A as [tex]\(A\)[/tex].

The probability that Jase studies for his geometry test is given as [tex]\(P(S) = \frac{15}{16}\)[/tex].

The probability that Jase studies and makes an A is given as [tex]\(P(S \cap A) = \frac{17}{20}\).[/tex]

To find the probability that he makes an A given that he studies [tex](\(P(A|S)\))[/tex], we use the conditional probability formula:

[tex]\[ P(A|S) = \frac{P(S \cap A)}{P(S)} \][/tex]

Substitute the given values:

[tex]\[ P(A|S) = \frac{\frac{17}{20}}{\frac{15}{16}} \][/tex]

To divide by a fraction, multiply by its reciprocal:

[tex]\[ P(A|S) = \frac{17}{20} \times \frac{16}{15} \][/tex]

Simplify the expression:

[tex]\[ P(A|S) = \frac{17 \times 16}{20 \times 15} \][/tex]

[tex]\[ P(A|S) = \frac{272}{300} \][/tex]

Now, simplify the fraction:

[tex]\[ P(A|S) = \frac{68}{75} \][/tex]

So, the probability that Jase makes an A given that he studies for the geometry test is [tex]\(\frac{68}{75}\)[/tex].

Since it is not perfectly straight it’s not linear so

*nonlinear association

The line goes down not up so it’s

*negative association

If your teacher wants to count the point outside of the regular line it would be no association

The two that most fit this graph are nonlinear and negative association

Answer:

There is a non linear association and negative association between variable A and B.

Step-by-step explanation:

A nonlinear relationship between two entities indicates that a change in one entity does not correspond with the constant change in the other entity.

Here, we can see the scatter plot that shows a non linear relationship.

There also exists a negative association between variable A and variable B. We can see that B increases as A increases, but points do not lie on a straight line.

Therefore, there is a non linear association and negative association between variable A and B.

Answer:

Option D : 86.7% is the answer.

Step-by-step explanation:

Given information is :

A farmer grows vegetables on 7 acres of land.

He grows fruit on 6 acres of land.

And he grows flowers on 2 acres of land.

Total farming acres are = [tex]7+6+2=15[/tex] acres.

Now, we have to find what the theoretical probability that the ladybug was not found within the acres of flowers. This means it was not found in 2 acres of land. It must have been in 13 acres of land.

So, probability will be : [tex]\frac{13}{15} \times100[/tex] = 86.66% ≈86.7%

Therefore, option D is the answer.

Answer: d

Step-by-step explanation:

Answer:

n = 62 + x

Step-by-step explanation:

From the problem given, it is clear that the orange has LESS calories than a nectarine. HOW much less? "x" less.

Also, orange has 62 calories. So, nectarine MUST HAVE 62 + x calories.

If we let nectarine's calories be n, we can write:

n = 62 + x

Answer:

D ≈ 14.32 cm

Step-by-step explanation:

C = 2πR, or C=πD

D=C/π = 45/π ≈ 14.32 cm

option A is correct, the range of the temperature data in degrees Fahrenheit is 15°F.

Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness.

Scatter plots are the graphs that present the relationship between two variables in a data-set.

The scatter plot represents the average daytime temperatures recorded in New York for a week.

The highest temperature in a week from the scatter plot is 45°F.

The  lowest temperature in a week from the scatter plot is 30°F.

Range is the difference between the highest temperature and lowest temperature.

Range=45°F-30°F

=15°F

Hence, option A is correct, the range of the temperature data in degrees Fahrenheit is 15°F.

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A because that’s the only logical

Answer:

-3 -3i

Step-by-step explanation:

[tex]\((-5)(-4) - 6 - 4(6) = -10\)[/tex]

Certainly! To evaluate the expression [tex]\((-5)(-4) - 6 - 4(6)\)[/tex], follow these steps:

Multiply the first set of parentheses:

[tex]\((-5)(-4) = 20\)[/tex]

Subtract the result from step 1 from the second term:

[tex]\(20 - 6\)[/tex]

Multiply the number 4 by 6:

[tex]\(4 \times 6 = 24\)[/tex]

Subtract the result from step 3 from the result in step 2:

[tex]\(20 - 6 - 24\)[/tex]

Now, combine the terms:

[tex]\[20 - 6 - 24 = -10\][/tex]

Answer:

$347.03

Step-by-step explanation:

$1029 * (1/3) = $343    (Discounted Price)

$343 * 0.95 = $325.85 (With the extra 5% discount you only pay 95%)

$325.85 * 0.065 = 21.18 (Sale Tax)

$325.85 + 21.18 = $347.03 (Added Sale Tax)

Answer:

$347.03

Step-by-step explanation:

Hope that helped

The density of maple trees per square kilometer for the cosidered rectangular patch of land is 283 maple trees/sq. km approximately.

Density is like rate. It tells you how much of a thing is available for each unit other thing which contains the first thing.

Density = (Total amount available)/(total space which contains that amount)

For this case, we're specified that:

Density of trees will be expressed in terms of number of trees per unit area

Area of the considered land = [tex]3 \times 4 = 12 \: \rm km^2[/tex]

Thus, the density of the maple trees in terms of maple trees per sq. kilometers is:

[tex]D = \dfrac{3400}{12} = 283.3\overline{3} \approx 283 \: \rm \text{maple trees/sq. km}[/tex] (approximated to integers as trees cannot be in decimal).

Thus, the density of maple trees per square kilometer for the cosidered rectangular patch of land is 283 maple trees/sq. km approximately.

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Answer:

[tex]x=37[/tex]

Step-by-step explanation:

Use the alternating interior angles theorem.

It states that alternating interior angles are congruent.

Therefore,

[tex]3x+4=115 \\ \\ 3x=111 \\ \\ x=37[/tex]