Find the length of the short leg of a 30 - 60 - 90 triangle If the long side is 4/3 units.

Answers

Answer 1

Answer:   CB=2/3

Step-by-step explanation:

The triangle's  angles are 30-60-90 degrees. So This is right triangle.

Let the triangle is ABC. B is right angle=90 degr . A=30 degrees, C=60 degrees

The long side of right triangle is hypotenuse AC=4/3 units.

In right triangle with 30 degr the side CB that is opposite to acute angle 30 degrees is twice shorter than hypotenuse AC

So CB=4/3/2=2/3

Finally using Pithagor theorem we find AB= sqrt( AC^2-CB^2)=

=sqrt(16/9-4/9)=sqrt(12/9)= 2*sqrt(3)/3

2*sqrt(3)/3>2/3  so AB>CB

So the shortest leg of ABC is  CB=2/3


Related Questions

Write 9x + 3y = 15 in slope-intercept form.

Answers

Answer:

y=−3x+5

Step-by-step explanation:

The equation 9x + 3y = 15 in slope-intercept form is y = -3x + 5 where the slope is -3 and intercept is 5

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be 9x + 3y = 15

Now , the equation can be simplified as

9x + 3y = 15

Divide the equation by 3 , we get

3x + y = 5

Now , the equation of line is of the form y = mx + c , where m is the slope and c is the y intercept

So ,

Subtracting 3x on both sides , we get

y = -3x + 5

So , the equation of line is y = -3x + 5

Hence , The equation 9x + 3y = 15 in slope-intercept form is y = -3x + 5 where the slope is -3 and intercept is 5

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ2

find domain and range using interval notation

Answers

Hey there! :)

Answer:

D: [8, 12].

R: [-10, -6].

Step-by-step explanation:

Notice that the endpoints of the graph are closed circles. This means that square brackets will be used:

The graphed equation is from x = 8 to x = 12. Therefore, the domain of the function is:

D: [8, 12].

The range goes from y = -10 to -6. Therefore:

R: [-10, -6].

Answer:

D: [8 , 12]

R: [-10 , -6]

Step-by-step explanation:

Well for this parabola domain and rage are acttually limited because of the solid dots you see on the graph.

So first things first, what is range? Well range is the amount of y values on a line or anything in a graph.

And what’s domain? Domain is the amount of x values on a line or whatnot.

So let’s do domain first.

On the parabola the first x value is 8 and the last is 12 so we have to write this in interval notation which is  [8 , 12].

Now for range the lowest y value is -10 and the highest is -6 so in interval notation it is [-10 , -6].

Brent counted 10 red cards, 10 black cards, and 20 blue cards in a deck of cards. What is the ratio of red cards to other cards? Answers: A) 1:1 B) 1:2 C) 2:1 D) 1:3

Answers

Answer:

1:3

Step-by-step explanation:

10 red cards, 10 black cards, and 20 blue cards

We want the ratio of red to other cards

red : blue and black

10 : 10+20

10 : 30

Divide each side by 10

10/10 : 30/10

1:3

evaluate 6 to the power of -2

Answers

Answer:

1/36

Step-by-step explanation:

6^-2 = 1/6^2 = 1/36.

Apply the product rules to determine the sign of each expression

Answers

Answer:

Step-by-step explanation:

1). [tex](\frac{-4}{9})\times (\frac{7}{4})=(-1)(\frac{4}{9})(\frac{7}{4} )[/tex]

                [tex]=-\frac{7}{9}[/tex] [Negative]

2). [tex](-2\frac{3}{4})(-1\frac{1}{5})=(-1)(2\frac{3}{4})(-1)(1\frac{1}{5})[/tex]

                        [tex]=(-1)^2(2\frac{3}{4})(1\frac{1}{5})[/tex]

                        [tex]=(2\frac{3}{4})(1\frac{1}{5})[/tex] [Positive]

3). (3)(-3)(-3)(-3)(-3) = 3.(-1).3.(-1).3.(-1).3(-1).(3)

                              = (-1)⁴(3)⁵

                              = (3)⁵ [Positive]

4). [tex](-\frac{1}{6})(-2)(-\frac{3}{5})(-9)[/tex] = [tex](-1)(\frac{1}{6})(-1)(2)(-1)(\frac{3}{5})(-1)(9)[/tex]

                                   = [tex](-1)^4(\frac{1}{6})(2)(\frac{3}{5})(9)[/tex]

                                   = [tex](\frac{1}{6})(2)(\frac{3}{5})(9)[/tex] [Positive]

5). [tex](-\frac{4}{7})(-\frac{3}{5})(-9)=(-1)(\frac{4}{7})(-1)(\frac{3}{5})(-1)(9)[/tex]

                            [tex]=(-1)^3(\frac{4}{7})(\frac{3}{5})(9)[/tex]

                            [tex]=-(\frac{4}{7})(\frac{3}{5})(9)[/tex] [Negative]

6). [tex](-\frac{10}{7})(\frac{8}{3})=(-1)(\frac{10}{7})(\frac{8}{3})[/tex]

                    [tex]=-(\frac{10}{7})(\frac{8}{3})[/tex] [Negative]

Not sure how I would solve this

Answers

Answers:

The first ordered pair is   ( -4 , -3 )

The second ordered pair is   ( 8, 3 )

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

Explanation:

The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x

x-2y = 2

x-2(-3) = 2 ... replace every y with -3; isolate x

x+6 = 2

x = 2-6

x = -4

The first point is (-4, -3)

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

We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y

x-2y = 2

8-2y = 2

-2y = 2-8

-2y = -6

y = -6/(-2)

y = 3

The second point is (8, 3)

A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing. What is the expected number (mean) of sales of this store from this sample of 30?

Answers

Answer:

The expected number of sales of this store from this sample of 30 is 6.

Step-by-step explanation:

For each prospect, there are only two possible outcomes. Either there is a trade, or there is not. Prospects are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability.

This means that [tex]p = 0.2[/tex]

Suppose 30 prospects are randomly selected from a city-wide mailing.

This means that [tex]n = 30[/tex]

What is the expected number (mean) of sales of this store from this sample of 30?

[tex]E(X) = np = 30*0.2 = 6[/tex]

The expected number of sales of this store from this sample of 30 is 6.

The expected number (mean) of sales of this store from this sample of 30 is 6.

Calculation of the expected number or mean:

Since A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing.

So here the expected mean should be

= 20% of 20

= 6

Hence, The expected number (mean) of sales of this store from this sample of 30 is 6.

Learn more about mean here: https://brainly.com/question/797669

Two cylindrical cans of beef stew sell for the same price. One can has a diameter of 8 inches and a height of 4 inches. The other has a diameter of 6 inches and a height of 7 inches. Which can contains more stew & is , therefore ,a better buy?

Answers

Answer:

Can 1 will contain more stew

Step-by-step explanation:

Can -1

diameter= 8

radius=d/2=4

height=4

therefore volume= [tex]\pi[/tex] r2 h= 201.06

Can-2

Diameter= 6

radius=d/2=3

height= 7

therefore volume= [tex]\pi[/tex] r2 h= 197.92

The cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.

What is the volume of a right circular cylinder?

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

The more volume of a can is, the more stew it can store.

For first can:

Height = 4 inches, diameter of base = 8 inches.

Since radius = diameter/2, so radius of base = 8/2 = 4 inches.

Thus, volume of first can: [tex]V = \pi (4)^2 (4) = 64\pi \: \rm unit^3[/tex]

For second can:

Height = 7 inches, diameter of base = 6 inches.

Since radius = diameter/2, so radius of base = 6/2 = 3 inches.

Thus, volume of first can: [tex]V = \pi (3)^2 (7) = 63\pi \: \rm unit^3[/tex]

Thus, as π > 0, so first can can contain more stew.

Thus, the cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.

Learn more about volume of cylinder here:

https://brainly.com/question/12763699

Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x2 y2

Answers

Answer:

hello your question is incomplete here is the complete question

Use cylindrical coordinates Find the volume of the solid that lies within both the cylinder x^2 + y^2=16 and the sphere x^2 + y^2 + Z^2= 81

Answer : [tex]\frac{4 \pi }{3} [729 - 65\sqrt{65} ][/tex]

Step-by-step explanation:

The given data

cylinder  = x^2 + y^2 = 16

sphere = x^2 + y^2 +z^2 = 81

from the given data the solid is symmetric around the xy plane hence we will calculate half the solid volume above the plane then  multiply the sesult by 2

Note : we are restricting our attention to the cylinder  x^2 + y^2 = 16 and also finding the volume inside the sphere which gives bound on the z-coordinate as well

the r parameter goes from 0 to 4

ATTACHED IS THE REMAINING PART OF THE SOLUTION

showing the integration

In the figure below, what is the value of xº?

Answers

Answer:

[tex] \boxed{\sf x \degree = 62 \degree} [/tex]

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

[tex] \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree[/tex]

In the given figure, the value of x is 62°.

What is angle ?

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

The given angles are,

x°, 38° and 100°.

To find the value of angle x, use exterior angle property.

According to exterior angle property,

The  sum of two interior angles is equal to exterior angle.

Since, 100° is the exterior angle of x and 38.

x + 38 = 100

x = 100 - 38

x = 62.

The required value of angle x is 62°.

To learn more about Angle on:

https://brainly.com/question/28451077

#SPJ5

A square matrix is called a permutation matrix if it contains the entry 1 exactly once in each row and in each column, with all other entries being 0. All permutation matrices are invertible. Find the inverse of the following permutation matrix.
A = [0 0 1 0, 0 0 0 1, 0 1 0 0, 1 0 0 0]

Answers

The inverse of the given permutation matrix A is

                          [tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]

To find the inverse of the given permutation matrix A:

[tex]\[ A = \begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\\end{bmatrix} \][/tex]

Utilize the concept that the inverse of a permutation matrix is its transpose.

Therefore, the inverse of matrix A is:

[tex]\[ A^{-1} = A^T \][/tex]

Taking the transpose of matrix A, gives

[tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]

Learn more about Matrix here:

https://brainly.com/question/29132693

#SPJ6

Identify the vertex of the function. PLEASE HELP!!!

Answers

Answer:

Step-by-step explanation:

y-|x|+3

y=|x|+3

vertex=(0,3)

y=|x-4|-7

vertex(4,-7)

Question 1 (1 point)
A CODE has 4 digits. you remember that the 4 digits are 1, 3, 5, and 7, but you
cannot remember the sequence. What is the probability that you guess the code
correctly on the first try?

Answers

Answer:

24 ways

Step-by-step explanation:

There are 4!=24 ways to make distinct codes with the given distinct digits. So the probability of guessing it the first time is 1/24.

The probability that you guess the code correctly on the first try will be 1/24.

What is the probability?

Probability is synonymous with possibility. It is concerned with the occurrence of a random event.

Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.

If the code is arranged then the total number of ways possible is;

⇒4!

⇒4×3×2×1

⇒24

Possible outcome = 1

Total outcome = 24

Probability = Possible outcome/total outcome

Probability = 1/24

Hence the probability that you guess the code correctly on the first try will be 1/24.

To learn more about probability, refer to the link: https://brainly.com/question/795909.

#SPJ2

Which describes the intersection of line m and line n?

Answers

Answer:

Point W

Step-by-step explanation:

The intersection of two lines is a point. In this case, the point is named W.

Find the velocity. Please help. Thank you!

Answers

Answer:

His final velocity is 48.03 m/s

Step-by-step explanation:

Using SI units  (m, kg, s)

a = 3.7

x0 = 25

x1 = 300

v0 = 16.5

Apply kinematics formula

v1^2 - v0^2 = 2a(x1-x0)

solve for v1

Final velocity

v1 = sqrt(2a(x1-x0)+v0^2)

= sqrt( 2(3.7)(300-25)+16.5^2) )

= 48.03 m/s

Consider the matrices. A=⎡⎣⎢4−3−578−2⎤⎦⎥ and B=⎡⎣⎢−27−35−12⎤⎦⎥ What is the result of A−B? Enter your answer by filling in the boxes.

Answers

Answer:

Step-by-step explanation:

hello

[tex]A-B=\left[\begin{array}{cc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\\\=\left[\begin{array}{cc}4+2&2\\-10&8+1\\-5+3&-4\end{array}\right] \\\\=\left[\begin{array}{cc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]

hope this helps

    If two matrices are given as,

[tex]X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}[/tex] and [tex]Y=\begin{bmatrix}h & k\\ l & m\end{bmatrix}[/tex]

Then [tex]X-Y=\begin{bmatrix}a-h & b-k\\ c-l & d-m\end{bmatrix}[/tex]

Following this rule answer will be → [tex]A-B=\begin{bmatrix}6 & 2\\ -10 & 9\\ -2 & -4\end{bmatrix}[/tex].

  It's given in the question,

Two matrices, [tex]A=\begin{bmatrix}4 & 7\\ -3 & 8\\ -5 & -2\end{bmatrix}[/tex] and [tex]B=\begin{bmatrix}-2 & 5\\ 7 & -1\\ -3 & 2\end{bmatrix}[/tex]

Therefore, [tex]A-B=\begin{bmatrix}4+2 & 7-5\\ -3-7 & 8+1\\ -5+3 & -2-2\end{bmatrix}[/tex]

                  [tex]A-B=\begin{bmatrix}6 & 2\\ -10 & 9\\ -2 & -4\end{bmatrix}[/tex]

Learn more,

https://brainly.com/question/14302687

need answer asap helpppp!!!

Answers

Answer:

A.

Step-by-step explanation:

Minor arcs are arcs that are less than 180°. If that is the case, then our only option would be A.

Sue has $1.80 in dimes and nickels. If she has 9 more dimes than nickels, How many of dimes and nickels does she have?

Answers

Answer:

15 dimes6 nickels

Step-by-step explanation:

Let d represent the number of dimes. Then d-9 is the number of nickels. The total value (in cents) is ...

  10d +5(d-9) = 180

  15d -45 = 180 . . . . . simplify

  d -3 = 12 . . . . . . . . . .divide by 15

  d = 15

  15 -9 = 6 = number of nickels

Sue has 15 dimes and 6 nickels.

Answer:

15 dimes, 6 nickels

Step-by-step explanation:

D = # of dimes, and N = # of nickels

10D + 5N = 180

D = N + 9

Substitute:

10 (N + 9) + 5N = 180

10N + 90 + 5N = 180

15N = 90

N = 6

D = 15

Pleaseeeee help, I need this now...

Answers

Answer:

7/16.  

Step-by-step explanation:

The first triangle has no shading.

The second triangle has 1/4 shaded.

The third has 3/9.

The fourth has 6/16.

Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.

The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.

So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.

Hope this helps!

ABC and ADC are triangles. The area of triangle ADC is 52m^2

Answers

Given that,

ABC and ADC are triangles.

The area of ΔADC is 52 m².

Suppose , AD is the median.

According to figure,

We need to find the area of ΔABC

Using theorem of triangle

[tex]\bigtriangleup ADB +\bigtriangleup ADC=\bigtriangleup ABC[/tex]

Here, Δ ADB = Δ ADC

So, [tex]2 \bigtriangleup ADC=\bigtriangleup ABC[/tex]

Put the value of Δ ADC

[tex]\bigtriangleup ABC =2\times52[/tex]

[tex]\bigtriangleup ABC = 104\ m^2[/tex]

Hence, The area of ΔABC is 104 m².

The difference of m2 + n2 and m + n is

Answers

its just now (m + n) so it would be *4 since *2 + *2

the sum of the interior angles of a triangle is sometimes, but not always , 180 degrees

Answers

Answer:

180 degrees

Step-by-step explanation:

The sum of all the interior angles in a triangle is always equal to 180 degrees.

Answer:

The correct answer is TRUE.

Step-by-step explanation:

Find the measure of x.

Begin by setting up an equation of the five angles equal to 180°.

x + 37° + 41° + 29° + 51°  = 180° • The sum of the angles is 180°.

x + 158° = 180°       • Add the known values on the left side.

x = 22° • Subtract 158° from both sides.

The measure of angle x is 22°.

Solve: 4^3x=4^2
I need help

Answers

Answer: 2/3

Step-by-step explanation:

As the base of the two sides are equal, we can say that

3x = 2 which gives

x = 2/3

Answer:

2/3

Step-by-step explanation:

4^3x=4^2

The bases are the same so the exponents are the  same

3x =2

Divide by 3

3x/3 = 2/3

x = 2/3

At a DBE lecture of 100 students there are 29 women and 23 men. Out of these students 4 are teachers and 24 are either men or teachers. Find the number of women teachers attending the lecture. ​

Answers

Answer:

The number of women teachers attending the lecture is 1

Step-by-step explanation:

Let M denotes men , W denotes women and T denotes teachers.

Number of women = n(W)=29

Number of men = n(M)=23

Number of teachers=n(T)=4

We are given that 24 are either men or teachers.

So,n(M∪T)=24

We are supposed to find the number of women teachers attending the lecture. ​

n(M∪T)=n(M)+n(T)-n(M∩T)

24=23+4-n(M∩T)

n(M∩T)=3

So,No. of teachers those are men is 3

Total number of teachers = 4

So,  the number of women teachers attending the lecture= 4-3 = 1

Hence the number of women teachers attending the lecture is 1

Find the lengths of the remaining sides of the triangle. a = 18 a is 60 degrees b is 30 degrees b = c =

Answers

Answer:

b= 10.39

c = 20.79

Step-by-step explanation:

a = 60 °

b = 30°

c= 180-(60+30)

c = 180-(90)

c = 90°

Length facing angle a = 18

Let's look for length facing angle b

b/sinb = a/sin a

b/sin 30 = 18/sin 60

b =( 18 * sin30)/sin 60

b = (18*0.5)/0.8660

b = 9/0.8660

b= 10.39

Let's look for c

c/sin c = a/sin a

c/sin 90 = 18/sin 60

c = (18 * sin 90)/sin 60

c =18/0.8660

c = 20.79

Help me pls pls pls pls ​

Answers

Answer:

The valid point is (5/2, 5)

Step-by-step explanation:

In order to check which ones are valid we will apply all of them to the expression.

(5,15):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}5 - \frac{1}{5}15 \geq 0\\\\-1 \geq 0[/tex]

False.

(1/2, 5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{1}{2} - \frac{1}{5}5 \geq 0\\\\-\frac{4}{5} \geq 0[/tex]

False.

(5/2, 5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{5}{2} - \frac{1}{5}5 \geq 0\\\\0 \geq 0[/tex]

True.

(2,5):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}2 - \frac{1}{5}5 \geq 0\\\\-\frac{1}{5} \geq 0[/tex]

False

(-1,0):

[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}(-1) - \frac{1}{5}0 \geq 0\\\\-\frac{2}{5} \geq 0[/tex]

False.

g A population consists of twenty bowerbirds, six of which have bowers featuring reflective decor. If three of the bowerbirds are randomly sampled with replacement from this population, what is closest to the expected number of them that have bowers featuring reflective decor?Group of answer choices00.90.953

Answers

Answer:

a ) 0.9

Expected number of bower-birds that have bowers featuring reflective decor

         μ = 0.9

Step-by-step explanation:

Explanation:-

Given Sample size 'n' = 20

Given data A population consists of twenty bower-birds, six of which have bowers featuring reflective decor.

probability of success

                          [tex]p = \frac{x}{n} = \frac{6}{20} =0.3[/tex]

Given  three of the bower-birds are randomly sampled with replacement from this population.

So we will choose sample size 'n'= 3

Let 'X' be the random variable in binomial distribution

Expected number of bower-birds that have bowers featuring reflective decor

                       μ = n p

                           = 3 × 0.3

                           =0.9

conclusion:-

Expected number of bower-birds that have bowers featuring reflective decor

         μ = 0.9

Previous 20 Two groups leave on different flights from the same airport. Group A flies 200 miles due south, then turns 68° toward west and flies 75 miles. Group B flies 75 miles due north, then turns 51° toward east and flies 200 miles. Which group is farther from the airport?

Answers

Answer:

Group B is farther from the airport.

Step-by-step explanation:

To find the distance of each group to the airport we can use the law of cosines in the triangle created with the two movements done and the resulting total distance.

Law of cosines:

[tex]c^2 = a^2 + b^2 - 2ab*cos(angle)[/tex]

For group A, we have the sides of 200 miles and 75 miles, and the angle between the sides is (180-68) = 112°, so the third side of the triangle is:

[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(112)[/tex]

[tex]c^2 = 56863.198[/tex]

[tex]c = 238.46\ miles[/tex]

For group B, we also have the sides of 200 miles and 75 miles, and the angle between the sides is (180-51) = 129°, so the third side of the triangle is:

[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(129)[/tex]

[tex]c^2 = 64504.612[/tex]

[tex]c = 253.98\ miles[/tex]

The distance from group B to the airport is bigger, so group B is farther from the airport.

Find the inverse of the function f(x)=4+ \sqrt{x-2}

Answers

Answer:

y = (x - 4)² + 2 , x ≥ 4.

Step-by-step explanation:

Finding the inverse of

f(x) = 4 + √(x - 2)

Begin by swapping the x and y variables in the equation:

x = 4 + √(y - 2)

Subtract 4 from both sides:

x - 4 = √(y - 2)

Square both sides:

(x - 4)² = y - 2

Add 2 to both sides to get your equation:

y = (x - 4)² + 2

However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.

The surface area of a cube may be found using the formula A=6s^2. What is the edge length of a cube with a surface area of 81 cm^2? Round your answer to the nearest tenth.

Answers

Answer: s = 3.7 (rounded 3.67 to the nearest tenth)

Step-by-step explanation:

Surface Area = 81 cm^2

Surface Area of the cube = 6s^2

A = 6s^2

81 = 6s^2

S^2 = 81/6

S = 3.67

Other Questions
Express 510 & 3/10 % as a decimal fraction. Where did African Americans go after Emancipation If the reaction starts with a mixture of PCl5, PCl3 and Cl2 at pressures of 0.820 atm, 1.322 atm and 0.911 atm respectively, is the reaction at equilibrium How could reading a use-and-care booklet for a product help you decide whether to buy it? and check your answers. At the end of the activity, write a brief evaluation of your work.ActivityYolanda is filling her bathtub. The table shows the number of gallons of water in thebathtub at different times since she started filling it.Time(minutes)Water(gallons)16.5011.524.752.33Answer the following questions based on the information in the table.Part AFind the constant of proportionality (in gallons per minute) using the values in the firstrow of the table. Why was the League of Nations significant?A: it was an effective tool for stopping future warsB: it was the first attempt to create an organization where nations working together for peace C: it helped draft the peace treaties that brought world war 1 to an end D: it helped the United States become a major world power What does the graph indicate about the change in urban populations during this time? Which of these sets of side lengths are pythagorean triples! 1 - The union of what three movements describes the new scientific approach established in scientific revolution? 2 - Who wrote the "New Astronomy"? 3 - What is empirical method? 4 - Who was the leading advocate of the inductive reasoning? 5 - Who wrote Novum Organum? 6 - What kind of reasoning did Descartes advocate? What was his famous book written in 1637? 7 - By what means did Newtons "Principia" describe the physical world? Please may someone help me out asap! Suppose all stocks in Cheyennes portfolio were equally weighted. Which of these stocks would contribute the least market risk to the portfolio? Cook-Rite Co. sold $173,000 of equipment during January under a two-year warranty. The cost to repair defects under the warranty is estimated at 6% of the sales price. On August 15, a customer required a $230 part replacement, plus $167 of labor under the warranty. Required: (a) Provide the journal entry for the estimated warranty expense on January 31 for January sales. Jan. 31 (b) Provide the journal entry for the August 15 warranty work. If an amount box does not require an entry, leave it blank. Aug. 15 Who is the best musician in Nigeria Which of these best describes one of the themes in the play?A. Money creates happiness.B. Humanity cannot win against nature.O C. Hatred destroys the person who feels it.O D. Home is where the family is Choose the correct definition of conflict.A:Conflict is the obstacle that the character has to overcome toreach his goal.B:The nonverbal language of the script is often referred to asconflict. PLLLLLLLLLLZZZZZZZZZ Evaluate the expression ( 1 + 2 i ) ( 2 1 i ) and write the result in the form a + b i . Fill in the gap, The earth ------------- round the sun The train ------------- before we get to the station They resemble each other, resemble is ---------- The shop sank suddenly,what is the verb in the sentence can someone write an explanation of how to perform the following skills in basketball:-passing-dribbling-shooting -layups True or False? When Samantha includes more batteries in her project, the current in her project increases. Current is the independent variable in this situation. True False