Express the statement as an equation. (Use k as the constant of proportionality.). A varies inversely as r. Use the given information to find the constant of proportionality. If r = 3, then A = 7. k=

Answer:

Step-by-step exAnswer:

see the attachments for the two solutions

Step-by-step explanation:

When the given angle is opposite the shorter of the given sides, there will generally be two solutions. The exception is the case where the triangle is a right triangle (the ratio of the given sides is equal to the sine of the given angle). If the given angle is opposite the longer of the given sides, there is only one solution.

When a side and its opposite angle are given, as here, the law of sines can be used to solve the triangle(s). When the given angle is included between two given sides, the law of cosines can be used to solve the (one) triangle.

___

Here, the law of sines can be used to solve the triangle:

A = arcsin(a/c·sin(C)) = arcsin(25/24·sin(70°)) = 78.19° or 101.81°

B = 180° -70° -A = 31.81° or 8.19°

b = 24·sin(B)/sin(70°) = 13.46 or 3.64

Answer:

O The maximum height of the water balloon occurs at x = 0.    

O The water balloon is in the air for 2 s.    

O The maximum height of the water balloon is 64 ft.

Step-by-step explanation:

Firstly, by simply looking at the x axis on the graph (time), you will see that it starts at 0 and the 64 ft maximum height is aligned with the starting point of 0 seconds.  

The graph also shows (x axis) the 'time' represented, and as the height rapidly decreases the graph eventually reaches the 2 second mark, going no further and no lower.  

Finally, the graph shows (y axis) the peak of the water balloon's height is 64 ft, as it is the highest number reached while the water balloon was airborne.

The following statement is True.

A true statement to be chosen from the following.

The graph is a demonstration of curves  that gives the relationship between the x and y-axis.

From the graph, the following points are to be noted.
The water balloon is at 64 ft at x = 0.
The water balloon takes 2 sec to reach y = 0.
The water balloon has a maximum height of x = 0.

Thus, points 1,2, and 5 are true.

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Answer:

X = 4x-18

Step-by-step explanation:

X = “a number”^^

Answer:

The equation equals 0

Step-by-step explanation:

12 ( 1/3 ) + 5 - 9

4 + 5 - 9

9 - 9

= 0

The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

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

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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The reasonable domain to plot the function is 0 < d <= 1.4, the y-intercept of the function is 7 and the average rate of change from d = 4 to d = 11 is 0.64

The function is given as:

f(d) = 7(1.06)^d

The maximum radius is 13.29.

So, we have:

7(1.06)^d = 13.29

Divide both sides by 7

(1.06)^d = 1.90

Take the logarithm of both sides

dlog(1.60) = log(1.90)

Divide both sides by log(1.60)

d = 1.4

Hence, the reasonable domain to plot the function is 0 < d <= 1.4

This is when d = 0.

So, we have:

f(0) = 7(1.06)^0

Evaluate

f(0) = 7

Hence, the y-intercept of the function is 7

From d = 4 to d = 11

Calculate f(4) and f(11)

f(4) = 7(1.06)^4 = 8.84

f(11) = 7(1.06)^11 = 13.29

The average rate of change is

Rate = (13.29 - 8.84)/(11 - 4)

Rate = 0.64

Hence, the average rate of change from d = 4 to d = 11 is 0.64

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Answer:

First, convert the hour to minutes.

1 hr = 60 mins

15 mins: 60 mins

1:4

Oh wait I read the question wrong, give me 5 minutes lol. Edit: Nvm, I read it right :). This is the answer.

Answer:

3:2

Step-by-step explanation:

1 hour and 15 minutes can be seen as 75 minutes so it would be

75:50

The highest common mutiple of 75 and 50 are 25. Divide both (75&50) by 25.

The answer would be 3:2

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

Explanation:

f(x) is equal to both x^2-2x+3 and also -6x at the same time. Set those two expressions equal to one another and solve for x.

x^2-2x+3 = -6x

x^2-2x+3+6x = 0

x^2+4x+3 = 0

(x+3)(x+1) = 0 .... see note below

x+3 = 0 or x+1 = 0

x = -3 or x = -1

Note: 3 and 1 multiply to 3, and also add to 4.

---------------------

Once we get the x values, we plug them into either equation to find the y value.

So if x = -3, then

f(x) = x^2-2x+3

f(-3) = (-3)^2-2(-3)+3

f(-3) = 9 + 6 + 3

f(-3) = 18

or we could say

f(x) = -6x

f(-3) = -6(-3)

f(-3) = 18

Both versions produce the same output when x = -3.

The second version is easier to work with.

Since x = -3 leads to y = 18, we know that (-3, 18) is one of the solutions. That explains where your teacher got (-3, 18) from.

-----------

We'll use this idea for x = -1 now

f(x) = x^2-2x+3

f(-1) = (-1)^2-2(-1)+3

f(-1) = 1 + 2 + 3

f(-1) = 6

or we could say

f(x) = -6x

f(-1) = -6(-1)

f(-1) = 6

Like before, both versions of f(x) produce the same output when the input is x = -1.

The other solution is (-1, 6)

Answer:

if the 5 numbers are different, the maximum difference is 64

Step-by-step explanation:

We have 5 positive (different) integers, a, b, c, d and e (suppose that are ordered from least to largest, so a is the smallest and b is the largest.

The mean will be:

M = (a + b + c + d + e)/5 = 15.

Now, if we want to find the largest difference between a and e, then we must first select the first 4 numbers as the smallest numbers possible, this is:

a = 1, b = 2, c = 3 and d = 4

M = (1 + 2 + 3 + 4 + d)/5 = 15

M = (10 + d)/5 = 15

10 + d = 15*5 = 75

d = 75 - 10 = 65

then the difference between a and d is = 65 - 1 = 64.

Now, if we take any of the first 4 numbers a little bit bigger, then we will see that the value of d must be smaller, and the difference between d and a will be smaller.

The cost of each ticket bought by each of the group is $15.

The linear equation that represents the total cost spent by group 1 on the tickets is:

Amount spent = total amount spent on the tickets - discount

9x - 120

The linear equation that represents the total cost spent by group 2 on the tickets is:

3x - 30

Where:

x = is the cost of the tickets

If both groups spend the same amount, the above two linear equations would be equal to each other

3x - 30 = 9x - 120

In order to determine the value of x, take the following steps:

Combine similar terms together: 120 - 30 = 9x - 3x

Add similar terms: 90 = 6x

Divide both sides by 6

x = 90 / 6

x = 15

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Answer: Exact Form:

√

97

6

Decimal Form:

1.64147630

Btw that's 97 radical 6

~ zachary

Answer:

\(d=\frac{\sqrt{97}}{6}\approx1.6415\)

Step-by-step explanation:

We have the two points: (2, 5/2) and (8/3, 1).

And we want to find the distance between them.

So, we can use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Let (2, 5/2) be (x₁, y₁) and let (8/3, 1) be (x₂, y₂). Substitute:

\(d=\sqrt{(\frac{8}{3}-2)^2+({1-\frac{5}{2})^2\)

Evaluate the expressions within the parentheses. For the first term, we can change 2 to 6/3. For the second term, we can change 1 to 2/2. So:

\(d=\sqrt{(\frac{8}{3}-\frac{6}{3})^2+({\frac{2}{2}-\frac{5}{2})^2\)

Evaluate:

\(d=\sqrt{(\frac{2}{3})^2+(-\frac{3}{2})^2\)

Square:

\(d=\sqrt{\frac{4}{9}+\frac{9}{4}\)

Add. We can change 4/9 to 16/36. And we can change 9/4 to 81/36. So:

\(d=\sqrt{\frac{16}{36}+\frac{81}{36}}\)

Add:

\(d=\sqrt{\frac{97}{36}}\)

We can separate the square roots:

\(d=\frac{\sqrt{97}}{\sqrt{36}}\)

Simplify. So, our distance is:

\(d=\frac{\sqrt{97}}{6}\approx1.6415\)

Answer:

------------------------

The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.

The remainder of the distance is reducing by:

Time to travel before they meet:

Add the first hour to this to get total travel time of 4 hours.

Answer:

c=200+0.4Yd find determine equlibirum level investment is =400

Answer:im pretty sure its D

Step-by-step explanation:it goes through the origin

⊥T

Hope this is what you're looking for! (✿◠‿◠)

Answer:

You'll see this character in the list over on Wikipedia, and you'll notice that there's a code next to it, in this case 0287 is the Unicode character code for the upside-down T

Step-by-step explanation:

please mark me brainliest

Answer:

2

Step-by-step explanation:

Answer: 3N+6

Step-by-step explanation:

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer:

Step-by-step explanation:

Mike's total pay is the result of dividing a fixed amount of time between two jobs. The total hours and the total pay give us two relations that let us solve for the time at each job.

Let x represent the number of hours Mike works at Job B. Then 56-x is the number of hours he works at Job A. His total pay for both jobs is ...

  8x +7(56 -x) = 410

  x +392 = 410 . . . . . . simplify

  x = 18 . . . . . . . . . subtract 392

  56 -x = 38 . . . find Job A hours

Mike works 38 hours at Job A, and 18 hours at Job B.

__

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Answer:

Solution,

\(b = 6 \: ft \\ h = \sqrt{ {5}^{2} - {3}^{2} } \\ \: \: \: \: \: = \sqrt{25 - 9} \\ \: \: \: \: \: = \sqrt{16} \\ \: \: = \sqrt{ {4}^{2} } \\ \: \: \: \: = 4\)

Now,

\(volume = \frac{1}{3} bh \\ \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times {6}^{2} \times 4 \\ \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times 36 \times 4 \\ \: \: \: \: \: \: \: \: \: \: \: = 48 \: {ft}^{3} \)

hope this helps...

Good luck on your assignment..

Answer:

Volume = 48 ft³

Step-by-step explanation:

Finding h first by Pythagorean Theorem:

=> \(c^2= a^2+b^2\)

=> \(5^2= 3^2 + h^2\)

=> \(h^2 = 25-9\\h^2 = 16\)

Taking sqrt on both sides

=> h = 4 ft

Now, The volume:

=> Volume = \(a^2\frac{h}{3}\)

=> Volume = \((6)^2\frac{4}{3}\)

=> Volume = \(36 \frac{4}{3}\)

=> Volume = 12 * 4

=> Volume = 48 ft³

the standard form equation that equals the combination of the two given equations is 4x+5=-4 and y-3=2

How do you solve for standard form?

The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side. Use inverse operations to move terms.

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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If a pole has two wires attached to it, one on each side, forming two right triangles as shown, then the height of the pole is 29.6 feet

Consider the triangle on left hand side

The length of the base = 34 feet

The measure of angle = 41 degrees

Opposite side is the height of the pole

Here we have to use the trigonometric functions

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

Here we have to use the equation of tan θ

Substitute the values in the equation

tan 41 = Opposite side / 34 feet

Opposite side = 34 × tan 41

= 29.6 feet

Therefore, the height of the pole is 29.6 feet

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Answer:

Piis approximately 3.14.

and

Piis approximately StartFraction 22 over 7 EndFraction

Answer:

C,D,E are the right answers

Answer:750

Step-by-step explanation:

multiply the numbers

1250-250x2

1250-500

subract the two numbers and you will get

750

Answer:

Opal saves more

Step-by-step explanation:

According to Riemann sum and expressing the work as an integral,400 ft/lb work is done in pulling the rope to the top of the building.

Given,

heavy rope length = 40ft

weighs = 0.5 lb/ft

building height = 90 ft

If we divide rope into small parts with length Δx, rope weighs 0.5 lb/ft force work on each section is x*i is a point in i the such intervals.

The work done on ith part is

                                          x*i0.5Δx

So the total done is

\(\lim_{n \to \infty}\)= ∑0.5x*iΔx expressing work as an integral

         \(\int\limits^40_0 {(0.5x)} \, dx\) = [0.5 × x²/2]

                             = [0.5 × 40²/2 - 0.5 × 0²/2]

                             = [0.5 × 1600/2 - 0]

                             =  0.5 × 800 - 0

                             = 400 - 0

                             = 400 ft/lb

The work done in lifting the pieces in upper half of rope is

  x*i0.5Δx

The work done in lifting lower half of the rope is

0.5Δx × 20

10Δx

Total workdone,

                 \(\lim_{n \to \infty}\)∑0.5x*iΔx + \(\lim_{n \to \infty}\)∑10Δx

                = \(\lim_{n \to \infty}\)∑(0.5x*i + 10)Δx work as an integral

\(\int\limits^25_0 {0.5} \, dx\) + \(\int\limits^50_25 {10} \, dx\)

= [ 0.5 * x²/2] + [10x]

= [0.5 * 20²/2] +[10(40-20)]

= [0.5 * 400/2] + [10*20]

= 100 + 200

= 300 ft/lb

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The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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The angle on the unit circle is solved to be

56.01 degrees (to the nearest tenth)

To find the angle of the terminal side through the given point on the unit circle, we can use the inverse trigonometric functions.

given that P = ((√5)/4, (√11)/4)

θ = arctan ((√11)/4 / (√5)/4)

θ = arctan((√11)/(√5))

θ ≈ 56.01 degrees

hence to the nearest tenth of a degree, the angle of the terminal side through the point P = ((√5)/4, (√11)/4) on the unit circle is approximately 56.01 degrees.

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