Write the composite function in the form f(g(x)). [identify the inner function u = g(x) and the outer function y = f(u).] y = 3 1 5x

The hands of a clock are perpendicular to each other twice in every 12-hour cycle, once at 3:00 and once at 9:00. Therefore, the petrography contest will be stopped at either 3:00 or 9:00.

To understand why this is the case, we need to consider the angles between the hands of the clock. In a standard clock, the minute hand completes a full revolution (360 degrees) in 60 minutes, while the hour hand completes a full revolution in 12 hours (720 minutes). This means that the minute hand moves 6 degrees every minute (360/60) and the hour hand moves 0.5 degrees every minute (360/720).

When the hands of the clock are perpendicular, the angle between them is 90 degrees. Let x be the number of minutes past some starting time when the hands are perpendicular. At time x, the minute hand will be at x*6 degrees and the hour hand will be at (x/12)*360 + 90 degrees. We want to find the values of x that satisfy the equation (x/12)*360 + 90 - x*6 = 90, which simplifies to x/2 - x/60 = 1. Solving for x, we get x = 30 or x = 360/11, which is approximately 32.73. Since the contest started at 5:00, the two times when the hands are perpendicular to each other fall at 3:00 and 9:00.

Learn more about revolution here:

https://brainly.com/question/25272851

#SPJ11

Answer:

D

Step-by-step explanation:

the third side must be between the numbers added together and the number subtracted from each other.

15-8 = 7

15+8=23

Let Charles age be x

Adam age will be 5x  

8 years later , add 8 to both expressions

Charles age = x+8

Adam age = 5x+8

add their ages and equate them to twice adam's present age 2*5x

x+8+5x+8 = 2*5x

6x+16=10x

4x=16

x=4

x = Charles' age

Adam's age  5x = 5(4) = 20

The diameter of a circular track is 90 m and 282.74334  far would you walk in one lap around the track.

Hence, The diameter of a circular track is 90 m and 282.74334  far would you walk in one lap around the track.

learn more about unitary method click here:

brainly.com/question/24587372

#SPJ4

Answer: 3.42 miles

Step-by-step explanation:

5.5 cm converts to 3.41754e-5 miles

The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Learn more about scale factors click;

https://brainly.com/question/29464385

#SPJ1

The equation that represents the height of the pine tree will be y = 34x + 2.

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 linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Six 2-foot tall pine trees were planted during the school's perception of Earth Mindfulness Week in 1990. The trees have developed at a typical pace of 34 feet each year.

Let 'x' be the number of years and 'y' be the height of the tree. Then the equation is given as,

y = 34x + 2

The equation that represents the height of the pine tree will be y = 34x + 2.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ1

The ordered pair of the inequality will be (9,-3).

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that inequality is given as y ≤ 1/3x−6.

The ordered pair can be calculated as:-

y ≤ 1/3x−6

Substitute the value of x equal to 9 and get the value of y,

y ≤ 1/3(9) - 6

y ≤ 3 - 6

y ≤ -3

Hence, the ordered pair will be (9,-3).

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ9

Answer:

It is a traingle

Step-by-step explanation:

Answer:

They are instructions...

Step-by-step explanation:

Probably finding out the angles of a triangle

There may be patterns in the triangles..

the answer is correct.x= -7

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

for similar questions on triangles.

https://brainly.com/question/1058720

#SPJ8

Answer:

1040 fries

Step-by-step explanation:

Mass of Fries + Bag= 2268 grams

Mass of Bag ONLY = 284 grams

2268 g - 284 g = 1984 g

Fries ONLY = 1984 g

Mass of 125 Fries= 238 grams

Now we use a proportion

125 fries / 238 g = x fries / 1984 g

125/238 = x/1984

Cross multiply.

238x = 125 × 1984

238x = 248,000

x = 1042

Answer: 1040 fries

The reflection paper is about REHB 200. Each student is expected to use appropriate person-first language. The paper must be a minimum of 5 pages.

This reflection paper about REHB 200 requires a minimum of 5 pages from each student. The paper must include a summary of what will be discussed in the body of the paper. To write the reflection paper, the following points should be considered: three things not known about disability before taking this course, the favorite video clip(s) and why, laws designed to protect people with disabilities, thoughts associated with employment obstacles faced by people with disabilities, inclusion and normalizing disability in society, compare and contrast intellectual, physical, cognitive, and psychiatric disability, thoughts about the accessibility audit activity and discussion board questions, and biggest takeaway from the class.

In conclusion, this reflection paper about REHB 200 requires a minimum of 5 pages from each student. It is expected that each student will comply with appropriate person-first language. The reflection paper includes a summary of what will be discussed in the body of the paper and must cover several points including the comparison and contrast of intellectual, physical, cognitive, and psychiatric disability.

To know more about disabilities visit:

brainly.com/question/9219542

#SPJ11

Two parallel lines in the coordinate system share the same slope, this means that if you have two parallel lines:

For the given equations, the slopes are:

The slopes are different, so this lines are not parallel.

Two lines are perpendicular, when the slope of one of them is the negative inverse of the first one, this is for the perpendicular lines:

For the given equations, using y=17x-8 as reference, the slope of a line perpendicular to this one must be:

The slope of a perpendicular line to y=17x-8 is different from the slope of the second given line, so you can conclude that these lines are not perpendicular.

The correct choice is Neither

Answer:

Length arc AB = 3.14 in

Step-by-step explanation:

Length of arc AB = central angle/360 * 2πr

Central angle = 30°

Radius (r) = 6 in.

Substitute

Length of arc AB = 30/360 * 2*π*6

Length arc AB = 3.14 in. (Nearest tenth)

Answer:

3.14

Step-by-step explanation:

its just right

The properties of the graph are

The equation of the function is given as

f(x) = (x - 2)(x + 6)

The above equation is a quadratic function.

Next, we plot the equation on a graph (see attachment)

Set x = 0 to determine the y-intercept

y-intercept = (0 - 2)(x + 6)

y-intercept = -12

Expand the function to determine the symmetry axis

f(x) = x^2 - 2x + 6x - 12

Differentiate and set to 0

2x - 2 + 6 = 0

This gives

x = -2 --- axis of symmetry

Substitute x = -2 in the function to calculate the vertex/Min/Max

f(-2) = (-2 - 2)(-2 + 6)

f(-2) = -16

This means that

Direction = Up, Min = -16 and Vertex = (2, -16)

Set the function to 0 to determine the roots

(x - 2)(x + 6) = 0

Solve for x

x = 2 and x = -6

Read more about quadratic functions at

https://brainly.com/question/1214333

#SPJ1

The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

Learn more about combination here

https://brainly.com/question/11732255

#SPJ4

Answer:

The second option - 8/81

Step-by-step explanation:

Answer:

below

Step-by-step explanation: 6/81

Answer:

21.97%

Step-by-step explanation:

Through proportionality, we find out that the value of \(y\) is 25/4 when \(x\) is doubled, 25/9 when \(x\) is tripled, 25/36 when \(x\) is increased to 5 times its original value, 1 when \(x\) is increased by 5 times its original value, and 400 when \(x\) is reduced by 75%.

It is given to us that -

\(y\) is inversely proportional to \(x^{2}\)

This implies that -

\(y\) ∝ \(\frac{1}{x^{2} }\)

\(= > y=\frac{k}{x^{2} }\) ----- (1)

where, \(k\) = Constant of proportionality

It is also given to us that for a particular value of \(x\), \(y\) is 25.

From equation (1) and from the above statement, it can be said that -

\(x^{2} =\frac{k}{y} \\= > x^{2} =\frac{k}{25}\\= > x=\frac{\sqrt{k} }{5}\) ------ (2)

Now, we have to find out the value of \(y\) when \(x\) -

a) is doubled

=> \(x_{1} = 2x\) ---- (3)

Using equation (3) in equation (1),

\(= > y=\frac{k}{(x_{1}) ^{2} }\\= > y=\frac{k}{(2x)^{2} }\\= > y=\frac{k}{4x^{2} }\)---- (4)

Substituting the value of \(x\) from equation (2) in equation (4), we have

\(y=\frac{k}{4x^{2} }\\= > y=\frac{k}{4(\frac{\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{4k}\\ = > y=\frac{25}{4}\)

Thus, the value of \(y\) is 25/4 when \(x\) is doubled.

b) is tripled

=> \(x_{2}=3x\) ---- (5)

Using equation (5) in equation (1),

\(= > y=\frac{k}{(x_{2} )^{2} } \\= > y=\frac{k}{(3x)^{2} } \\= > y=\frac{k}{9x^{2} }\)------ (6)

Substituting the value of \(x\) from equation (2) in equation (6), we have

\(y=\frac{k}{9x^{2} }\\= > y=\frac{k}{9(\frac{\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{9k} \\= > y=\frac{25}{9}\)

Thus, the value of \(y\) is 25/9 when \(x\) is tripled.

c) increased to 5 times its original value

\(x_{3}= x+5x\\= > x_{3}=6x\)

From equation (2),

\(x_{3}=6x\\= > x_{3}=6(\frac{\sqrt{k} }{5} )\\= > x_{3}=\frac{6\sqrt{k} }{5}\)----- (7)

Using equation (7) in equation (1),

\(y=\frac{k}{(x_{3}) ^{2} } \\= > y=\frac{k}{(\frac{6\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{36k} \\= > y = \frac{25}{36}\)

Thus, the value of \(y\) is 25/36 when \(x\) is increased to 5 times its original value.

d) increased by 5 times its original value

\(x_{4}=5x\\= > x_{4}=5(\frac{\sqrt{k} }{5}) \\= > x_{4}=\sqrt{k}\\\)------ (8)

Using equation (8) in equation (1),

\(= > y=\frac{k}{(x_{4}) ^{2} }\\= > y=\frac{k}{(\sqrt{k} )^{2} } \\= > y=1\\\)

Thus, the value of \(y\) is 1 when \(x\) is increased by 5 times its original value.

e) reduced by 75%

\(= > x_{5}= x-(\frac{75}{100} )x\\= > x_{5}=\frac{100x-75x}{100}\\ = > x_{5}=\frac{25x}{100} \\= > x_{5}=0.25x\)

Substituting the value of \(x\) from equation (2) in the above equation,

\(x_{5}=0.25x\\= > x_{5}=0.25(\frac{\sqrt{k} }{5} )\\= > x_{5}=0.05\sqrt{k}\)----- (9)

Using equation (9) in equation (1),

\(= > y=\frac{k}{(x_{5}) ^{2} }\\= > y=\frac{k}{(0.05\sqrt{k}) ^{2} } \\= > y= \frac{1}{0.0025}\\ = > y= 400\)

Thus, the value of \(y\) is 400 when \(x\) is reduced by 75%.

Therefore, through proportionality, we find out that the \(y\) is 25/4 when \(x\) is doubled, 25/9 when \(x\) is tripled, 25/36 when \(x\) is increased to 5 times its original value, 1 when \(x\) is increased by 5 times its original value, and 400 when \(x\) is reduced by 75%.

To learn more about proportionality visit https://brainly.com/question/22620356

#SPJ1

Step-by-step explanation:

I hope this answer is helpful ):

Answer:

Step-by-step explanation:

Solve:

(a+b+c) (a+b-c)=

(a²+ab-ac+ab+b²-bc+ac+bc-c²)=

a²+ab-ac+ab+b²-bc+ac+bc-c²=

a²+2ab+0ac+b²+0bc-c²=

a²+2ab+b²-c²

Answer:

The answer is a² + 2ab + b² - c²

Step-by-step explanation:

(a + b + c) × (a + b - c)

a² + ab - ac + ba + b² - bc + ca + cb - c²

a² + ab + ba - ac + ca + b² - bc + cb - c²

a² + 2ab + b² - c²

Thus, The answer is a² + 2ab + b² - c²

-TheUnknownScientist 72

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

Answer:

38.30

Step-by-step explanation:

because 230 -6x=0

Answer:

Step-by-step explanation:

20% tip on 52.22 is 10.44

52.22*0.2=10.44

I don't think he has enough to do it though

52.22+10.44=62.664

Answer: He doesn't have enough (2.66 dollars short) Max percentage: 14.9%

Step-by-step explanation:

If Rowan has $60 dollars and wants a 20% tip. He would need to multiply the restaurant bill by 6/5, of if easier 120%

$52.22 x 120% = 62.66 dollars.

62.66 - 60 = 2.66. Therefore, Rowan CANNOT pay off a 20% tip and has $2.66 short.

Now, if we wanted to calculate which percent he can pay at max we look at 60/52.22.

This will give us 1.14898. Because of this, we can determine what percent Rowan can pay at max. 1.14898 - 1 = 0.14898.

Therefore, converting to percent, he can pay 14.9%(rounded)

The formula would you use to calculate the floor space of Firm 3's structure is πr²h.

It should be noted that the formula that can be used on this scenario will be:

= πr²h

where,

h = 60

r = 70/2 = 35

The volume will be:

= πr²h

= 3.14 × 35² × 60

= 230790 feet ³

Learn more about volume on:

brainly.com/question/1972490

#SPJ1