the perimeter of an athletic field is 352 m. if the width is 68 m, find the length. write your answer as an integer or simplified fraction

The operations of functions results in another function which are shown as below.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

There are two functions given.

f(x) = x² + 7

g(x) = 2x + 1

7. Addition of functions

   (f + g)(x) = f(x) + g(x)

                 = x² + 7 + 2x + 1

                 = x² + 2x + 8

8. Subtraction of functions

    (f - g)(x) = f(x) - g(x)

                 = (x² + 7) - (2x + 1)

                 = x² - 2x + 6

9. (g - f)(x) = g(x) - f(x)

                 = (2x + 1) - (x² + 7)

                 = -x² + 2x - 6

10. Multiplication of Functions

     (f . g)(x) = f(x) . g(x)

                  = (x² + 7) . (2x + 1)

                  = 2x³ + 14x + x² + 7

                  = 2x³ + x² + 14x + 7

11. Division of functions

   [tex]\frac{f}{g}[/tex](x) = [tex]\frac{f(x)}{g(x)}[/tex]

          = (x² + 7) / (2x + 1)

12.  [tex]\frac{g}{f}[/tex](x) = [tex]\frac{g(x)}{f(x)}[/tex]

            = (2x + 1) / (x² + 7)

Hence the operations of the functions are done.

Learn more about Functions here :

https://brainly.com/question/12431044

#SPJ1

Answer:

Step-by-step explanation:

here goes your solution down

Answer:282.6 cm²

Step-by-step explanation:

The formula for the surface area of a cylinder is 2πr(r+h) where r is the radius and h is the height.

Since the diameter is given, we can find the radius by dividing the diameter by 2, so r = 6/2 = 3 cm.

Then we can plug in the values into the formula:

2πr(r+h) = 2π(3)(3+12) = 2π(3)(15) = 90π cm²

To round the answer to the nearest tenth, we can use the following method:

If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.

If the digit in the thousandths place is greater than 5, we round up the hundredths digit.

Since π is an irrational number it can't be rounded to the nearest tenth. But an approximation for π is 3.14 and 90π is approximately 282.6 cm².

The level of the sound with the given properties is 200

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

I0 = 10^-12

I = 10^-8

Also, we have the equation to be

β = 10log(I I0)

Substitute the known values in the above equation, so, we have the following representation

β = 10 * log(10^-12 * 10^-8)

Evaluate

β = -200

Hence, the level of sound is -200

Read more about sound intensity at

https://brainly.com/question/12172048

#SPJ1

Complete question

use the following information for determining sound intensity. The level of sound β in decibels, with an intensity of I, is given by β = 10log(I I0), where l0 is an intensity of 10^-12 watt per square meter, corresponding roughly to the faintest sound that can be heard by the human ear find the level of sound β. l = 10^-8 watt per m^2 (quiet radio)

Displacement is the difference between the initial position and the final position of an object.

We can determine the displacement with the following formula:

Displacement = Final position - Initial position

In this case, the initial position is 0 m and the time is 6 seconds. We can find the displacement using the equation of motion:

Displacement = Initial Velocity × Time + ½ × Acceleration × Time2

Given that the acceleration of the object is 4 m/s2, the equation of motion becomes:

Displacement = 0 + ½ × 4 × 62

Therefore, the displacement of the object after 6 seconds is 72 m.

Learn more about displacement here;

https://brainly.com/question/2193360

#SPJ4

The estimate errors in the adjacent side and the hypothenuse are ≅ ±0.29 cm and ≅ ±0.145 cm respectively. The percentage errors in the adjacent side and hypothenuse are 2.009% & 0.502%.

Hypothenuse y₁ = 25/sin x = 25cosec x

Adjacent y₂ = 25/tan x = 25cot x

Opposite angle is 60° = π/3

Possible error, dx ≅ ±0.5° = 0.5 × π/180 = ±π/360

Differentiating y₁ = 25cosec x

dy₁ = -25(cosec x · cot x)dx

dy₁ = -25(cosec (π/3) · cot (π/3))×±π/360

= -25(2/√3)(1/√3)(±π/360)

= ≅ ±0.145 cm

Similarly

dy₂ = -25 cosec²x .dx

dy₂ = -25 cosec²(π/3) .×±π/360

= -25(2/√3)²×±π/360

≅ ±0.29 cm

So the errors in the hypothenuse = ±0.145 cm

Error in the adjacent side = ±0.29 cm

Percentage error in the adjacent side = 0.29/(25/√3) = 2.009 %

Percentage error in the hypothenuse = 0.145/(25/sin60) = 0.502%

To know more about hypothenuse, here

https://brainly.com/question/29130771

#SPJ4

A approach to geometrically represent complex numbers is by using the complex plane, commonly known as the Argand plane or the Gauss plane.

A approach to geometrically represent complex numbers is by using the complex plane, commonly known as the Argand plane or the Gauss plane. The real and imaginary halves of a complex number are represented by displacements along the x and y axes, respectively, in what is essentially a modified Cartesian plane.

Similar to how we may represent the set of real numbers on a number line, we can represent the set of complex numbers on a complex plane. At the coordinates (0,0)left parenthesis, 0 comma, 0 right parenthesis, two number lines that make up the complex plane cross at a right angle.

You may think of the y-axis as the hypothetical axis.

The actual axes are on the x-axis.

In light of this, we can say:

A: (-2, 3i) (-2, 3i)

B: (-1, -i) (-1, -i)

C: (3, -4i) (3, -4i)

D: (4, I (4, i)

To learn more about Complex plain refer to:

https://brainly.com/question/16835201

#SPJ1

A rectangle's perimeter is 40 cm. The rectangle's length is 2 cm longer than its width. Find the rectangle's length and width, which are both 6 cm.

Perimeter of rectangle [tex]$=40 \mathrm{~cm}$[/tex] (given)

condition :- length [tex]=2 \times$ breadth $+2$[/tex]

[tex]$\Rightarrow 1=2 \mathrm{~b}+2[/tex]

perimeter [tex]$\mathrm{p}=2(1+\mathrm{b})=40$[/tex]

[tex]& \Rightarrow 2(2 b+2+b)=40 \\[/tex]

[tex]& \Rightarrow 2(3 b+2)=40 \\[/tex]

[tex]& \Rightarrow 6 b=40-4=36 \\[/tex]

[tex]& \therefore b=6 \mathrm{~cm}[/tex]

[tex]1=2 \times 6+2=12+2=14 \mathrm{~cm}[/tex]

[tex]\therefore \text { length }=14 \mathrm{~cm} \text {, breadth }=6 \mathrm{~cm}[/tex]

The complete question is:

The perimeter of a rectangle is 40 cm. The length of rectangle is more than double its breadth by 2 cm. Find the length and breadth of rectangle .

To learn more about rectangle , refer to:

https://brainly.com/question/25292087

#SPJ4

We can be 90% confident that the interval [76.4, 79.3] contains the true mean monthly percentage of on-time departures. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.

To find the 90% confidence interval, we first need to calculate the margin of error. To calculate this, we need to use the standard error, which is calculated by dividing the standard deviation by the square root of the sample size. The standard deviation for the given data is 2.2 and the sample size is 72 (6 years × 12 months). So, the standard error is calculated as 2.2/√72 = 0.44. The margin of error is then calculated by multiplying the standard error by the critical value for 90% confidence, which is 1.645. The margin of error is therefore 0.44 × 1.645 = 0.72. The confidence interval is then calculated by adding and subtracting the margin of error from the sample mean. The sample mean is 77.8, so the 90% confidence interval is 77.8 ± 0.72, or [76.4, 79.3]. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.

Learn more about percentage here

https://brainly.com/question/14695543

#SPJ4

The piecewise function for the price of n gallons of diesel at Buc-ee’s would be = $1.00

The price paid for 3 gallons or less = $2.68 per gallon

That is, $2.68 =/< 3 gallons

Therefore $x= 1 gallon

Make X the subject of formula;

X = 2.68/3

X= $0.89

The price paid for 4 gallons or less = $2.41 per gallon

That is, $2.41 per =/< 4 gallons

Therefore $y = 1 gallon

Make y the subject of formula;

y = 2.41/4

y = $0.60

From the both outcomes, it can be concluded that the n gallons of diesel at Buc-ee’s would be approximately $1.00.

Learn more about cost price here:

https://brainly.com/question/25109150

#SPJ1

Step-by-step explanation:

70% = 0.7

15% = 0.15

65% = 0.65

x = gallons of the 70% solution.

0.7x + 0.15×20 = 0.65(x + 20)

70% + 15% solution = 65% solution (which has a many gallons as the combination of x and 20 gallons).

0.7x + 3 = 0.65x + 0.65×20

0.05x + 3 = 13

0.05x = 10

x = 10/0.05 = 200 gallons

so, 200 gal of the 70% pesticide solution is needed to make combined with 20 gal of the 15% solution a final solution that is 65% pesticide.

Answer:

Step-by-step explanation:

The distance traveled by the plane can be represented by the expression: distance = speed x time

In this case, the speed of the plane is given as x-110 mph and the time it travels is 3.5 hours.

So the expression for the distance traveled is:

distance = (x-110) * 3.5 miles

This expression represents the distance traveled in miles. The variable x represents the speed of the plane in mph.

Answer:

First find a number you can take out of both numbers.

In this case 3.

You get left with 2+3y

So the answer is 3(2+3y).

x/40 = 48/60

x= 4/5 × 40

x= 4 × 8

x = 32

Answer:

32

Step-by-step explanation:

by use of similarity and enlargement the answer can be evaluated.

use the formula: IMAGE LENGTH ÷OBJECT LENGTH.

Answer:

- 4x^3 + 17

Step-by-step explanation:

14 - 4x^3 + 3

- 4x^3 + 17

A convex pentagon has five exterior angles, and the sum of the measures of these angles is equal to 360 degrees.

We know that the measures of the exterior angles of a convex pentagon are 75°, 62°, 68°, and 101°, we need to find the measure of the last exterior angle.

To find the measure of the last exterior angle, we can use the formula:

Sum of all exterior angles = (n-2) x 180

where n is the number of sides in the polygon.

For a pentagon, n = 5, so the sum of all exterior angles is (5-2) x 180 = 540 degrees

So we can use this information to find the measure of the last exterior angle:

75 + 62 + 68 + 101 + x = 540

x = 244

Therefore, the measure of the last exterior angle is 244 degrees.

Contour Interval: The contour interval is the difference in elevation between two adjacent contour lines. In this case, the contour interval is 50 feet, as indicated in the bottom-left corner of the map.

Contour lines are lines on a map that connect points of equal elevation above a reference surface, usually sea level. They indicate the steepness of a terrain or landform and are often used to represent hills, valleys, and other relief features.

Ridge Line: A ridge line is a line formed by two or more contour lines that form a peak. In this map, the ridge line is marked by the contour lines labeled 1200 and 1250.
Valley: A valley is a line formed by two or more contour lines that form a low point. In this map, the valley is marked by the contour lines labeled 950 and 1000.

To learn more about contour
https://brainly.com/question/29602160
#SPJ1

Let A and B be two countable sets. Then there exists a bijective function f from A to B.

Since f is onto, for every element b in B, there exists a unique element a in A such that f(a)=b. This implies that the number of elements in B is equal to the number of elements in A, i.e. B is also countable.

Formally, if A = {a1, a2, ..., an}, then B = {f(a1), f(a2), ..., f(an)}. Since f is onto, B has n elements, which implies that B is countable.

Let A be a countable set and let B be a set with an onto function f from A to B. Since A is countable, it can be written as an infinite sequence of distinct elements an, where n is a natural number. To show that B is also countable, we can construct a one-to-one correspondence between the elements of A and B. We can do this by assigning bi to the element ai in A, for each i. Thus, we can write B as an infinite sequence of distinct elements bn, where n is a natural number. Therefore, B is countable.

Learn more about countable set here:

https://brainly.com/question/13424103

#SPJ4

Answer:

Domain:  (-∞, ∞)

Range:  [2, ∞)

Input:  (f) = 2

Output:  f(1) = 3

Step-by-step explanation:

The domain is the set of all possible input values (x-values).

There are arrows at both endpoints of the graphed continuous line, indicating that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  

The range is the set of all possible output values (y-values).

Assuming that each square is 1 unit, from inspection of the graph, the minimum y-value is y = 2.

The arrow at the endpoint in quadrant I indicates that the line continues horizontally at y = 2.

The arrow at the endpoint in quadrant II indicates that the line continues indefinitely towards y = ∞.

Therefore, the range of the relation is restricted:  

To find the value of f(4), find x = 4 and trace up to the line then read the y-value at that point.  Therefore:

To find the x-value when y = 3, find y = 3 and trace horizontally to the line then read the x-value at that point.  Therefore:

Statements A and C are correct.

We have to select the true statements from the given four statements in options.

step 1:

I think the statements A and C are true from the mathematical point of view.

If the original function is y=[tex]\sqrt{x}[/tex] and then by reflecting it about the x-axis

the equation will become y= - [tex]\sqrt{x}[/tex] and then shrinking it vertically by a

factor of 1/2 the function will finally become y= 1/2 [tex]\sqrt{x}[/tex]

Hence, statement A is true.

step2:

Again, the original function y= [tex]\sqrt{x}[/tex] has domain x ≥ 0 and range y ≥ 0, but in the transformed equation  y=-1/2 [tex]\sqrt{x}[/tex] has domain same as original equation i.e. x ≥ 0 but the range is different i.e. y ≤ 0.

Hence, statement C is also true.

To learn more about Domain and Range refers to;

https://brainly.com/question/14164154

#SPJ1

1.14 kg  is the total weight of the rocks, in kilograms.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

2 such rocks weigh 20 ounces each.

i.e. weight of 2 rocks = 20*2

                                  =40 ounces

now,

a kilogram is 35.2 ounces

the total weight of the rocks, in kilograms = 40/35.2

                                                                       =1.14 kg.

Hence, 1.14 kg  is the total weight of the rocks, in kilograms.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ1

The volume of the fish tank is 633,957.5 cubic cm or 0.634 cubic meter.

The formula for calculating the volume of a cuboid is

=  length  × breadth ×height

Given :

the length of fish tank = 105 cm

The width of fish tank= 75 cm

The height of fish tank= 80.5 cm

So, the volume of the fish tank =105×75 ×80.5

                                                =633,957.5 [tex]cm^{3}[/tex]

In metric units ;

1 meter = 100 cm

So, converting all the dimensions into metric units.

length of fish tank = 1.05 m

width of fish tank = 0.75 m

height of fish tank = 0.805 m

So, the volume of fish tank = 1.05 x 0.75 x 0.805

                                         = 0.6339575 [tex]m^{3}[/tex] or

                                         = 0.634 [tex]m^{3}[/tex]

On average, 15-20% of the cost is left as a gratuity. Add the desired decimal percentage tip to the total amount of the check and multiply the result to determine the tip.

How much should you leave for tip?

15% to 20% of the tab is typically left as a gratuity. Add the decimal % tip you want to leave to the total check amount to compute the tip. You would multiply 1 by 0.20 to reach 1.20 if you wanted to leave a 20% tip. To calculate the total amount you would tip, multiply the bill by 1.20.

It is advised that you leave at least 10% of your tip, even if the service was subpar. * Because some restaurants tack on a gratuity, carefully review your tab. Whether or not you should add to that is up to you. In sit-down restaurants, the tip for the wait staff should be between 15 and 20 percent of the pretax total.

To find out the tip amount, we need to first calculate 15% of the bill:

$40.94 x 0.15 = $6.14.

Rounding this amount to the nearest cent, we get $6.14 as the tip amount.

Therefore, the tip total is$ 7.00

To learn more about tip refer to:

brainly.com/question/1247898

#SPJ1

1. The value of x is 1.35

2. The value of x is 0.25

The first step in finding the value of x in an equation is to isolate the variable. To do this, you will need to use the appropriate rules of algebra to rearrange the equation so that x is on one side of the equation and all other terms are on the other side. Then, you can solve the equation by using the appropriate method (e.g. factoring, quadratic formula, etc.) to solve for x.

1) 13 - 5x- 4/6 = 10x - 8

13+  8- 4/6 = 10x + 5x

21-4/6 = 15x

20.3 = 15x

x = 1.35

2) 6(14x-21) = 14(18x - 6)

84x - 126 = 252x - 84

-126 + 84 = 252x - 84x

-42 = 168x

x = 0.25

To learn more about algebra refer to:

https://brainly.com/question/4344214

#SPJ1

Total number of monthly payments, not including the final balloon payment is $1,195.77

The monthly payment is the sum that must be paid each month for the duration of the loan to cover the principal balance. When a loan is taken out, not only the principal—the amount that was initially loaned out—but also the interest—which accrues—must be repaid.

Step1

M = 350,000(0.071/12)(1+0.071/12)² /(1+0.071/12)¹² =3,618.02

M = P(r/12) (1+r/12)¹²×n/(1+r/12)¹²×n -1

Step2:

3,618.02 × 12 × 12 = 520,994.88

The total paid is the product of the monthly payment and the number of payments.

520,994.88 - 350,000 = 170,994.88

= 170,994.88÷143

= 1,195.77

To learn more about monthly payment refers to;

https://brainly.com/question/14064255

#SPJ1

Answer:

False, if this is not what you mean comment and tell me

Step-by-step explanation:

A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.

A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.

Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.

know more about variables here

https://brainly.com/question/17344045#

#SPJ4

Answer:

A. No, because (-1) and (-1, -2) have the same input value.

Step-by-step explanation:

So what exactly is a function? It's very similar to a relation where there is input and for each input we have some output and sometimes multiple. The difference is in a function there is only one output for each input. Now the outputs of two different inputs can be the same, such that the input 2 and 3 will both output 4 or any value, but we cannot have an input such as 2 outputting 3 and 4 since we can only have one output for each input.

In the table given, the input "-1" outputs "2" and -2" which means the table  does not represent a function.

This makes "A" the correct answer to whether it's a function or not and explanation.

Answer:

1) x² + 4x +1 = 1 (You have to put in +1)

2) True

Step-by-step explanation:

1)

2) A range is a representation of values between two points. When you're calculating the range of a parabola, you only know one of those points to start with. Your parabola will go on forever either up or down, so the end value of your range is always going to be ∞ (or −∞ if your parabola faces down.)

Answer: the answer is true

Step-by-step explanation: There are an infinite amount of numbers the parabola can hit, and there is no limit

hence the statement is true