A play train travels around a Christmas
tree in a circle. The train track measures 6
feet in diameter. What is the distance that
the train travels?

Domain: [tex][-2,6][/tex]

Range: [tex][0,5][/tex]

Explanation:

Domain:

The domain of a function is the set of all possible values of the independent variable x. From the graph, we can see that the function has the set of all possible values from -2 to 6. Hence, the domain is from -2 to 6.

Thus, writing the domain in interval notation, we have,

[tex]-2\leq x\leq 6[/tex]

This also can be written as [tex][-2,6][/tex]

Hence, the domain is [tex][-2,6][/tex]

Range:

The Range of a function is set of all possible values of y obtained by substituting the values for x in the function. From the graph, we can see that the function has the set of all possible values from 0 to 5. Hence, the range is from 0 to 5.

Thus, writing the range in interval notation, we have,

[tex]0\leq y\leq 5[/tex]

This also can be written as [tex][0,5][/tex]

Hence, the range is [tex][0,5][/tex]

The domain and range in interval notation represent sets of possible values a function can take. For instance, for the function f(x) = 2x + 3 where x can be any real number, both the domain and range would be (-∞, ∞). Square brackets denote inclusive endpoints, while parentheses denote exclusive endpoints in interval notation.

In mathematics, particularly in functions, the domain and range represent sets of possible input and output values respectively. When expressed in interval notation, domain and range convey a concise representation of these sets.

Let's illustrate with an example. If we have the function f(x) = 2x + 3, and x can be any real number, the domain in interval notation would be (-∞, ∞). As for the range, since the function can also output any real number, the range would also be (-∞, ∞).

To write the domain and range in interval notation, remember that square brackets [ ] represent inclusive endpoints, while parentheses ( ) represent exclusive endpoints. The symbol '∞' is always cloaked by parentheses.

https://brainly.com/question/38282670

#SPJ12

Answer:

24

Step-by-step explanation:

4 times 6 =24

Answer:

Ishaan is 2 years old and Ben is 8

Step-by-step explanation:

Ben is 4 x (2) = 8

Ben is 6 + (2) = 8

Answer:

1 1/2 feet

Step-by-step explanation:

We know that she needs 1 3/4 feet of wrapping paper per gift and she has a total of 8 1/2 feet.

The number of gifts she can wrap is:

[tex]8.5/1.75=4.86[/tex]

She can wrap four gifts

Therefore:

[tex]4\cdot{1.75}=7[/tex]

She will use 7 feet of wrapping paper and she has:

[tex]8.5-7=1.5[/tex]

She has 1 1/2 feet of wrapping paper left

Answer:

11/2

Step-by-step explanation:

Step-by-step explanation:

Let Jim earned $ x

Therefore, Debbie earned = $(x + 1600)

According to the given information:

[tex]x + (x + 1600) = 7200 \\ \therefore \: 2x = 7200 - 1600 \\ \therefore \: 2x =5600 \\ \\ \therefore \: x = \frac{5600}{2} \\ \\ \therefore \: x =2800 \\ [/tex]

Thus, Jim`s earning = $2800

Debbie`s earning = 2800 + 1600 = $4400

Lets Jim earn $ x

Therefore, Debbie earned=$(x+1600)

calculate Debbie's earnings

According to the given information :

[tex]x+(x+1600)=7200\\$$\therefore 2 x=7200-1600\\$$\therefore 2 x=5600\\$$\therefore x=\frac{5600}{2}\\$$\therefore x=2800\\$[/tex]

thus, Jim's earnings =$2800

Debbie's earnings =2800+1600=$4400

An example of earning is to be paid five dollars for washing a car. An example of earning is getting a promotion for being very good at your job. An example of to earn is to take a vacation after completing a difficult and time-consuming project. To gain (success, reward, recognition) through applied effort or work.

Definitions of earnings. something that remunerates. “they saved a quarter of all their earnings” synonyms: pay, remuneration, salary, wage.

To learn more about earning, refer

https://brainly.com/question/22263734

#SPJ2

Answer: X = 28

Step-by-step explanation: The diagram shows a triangle which is actually in fact, two triangles placed into each other. The first one is triangle APR (the larger one) while the second one is triangle CDR (the smaller one).

Also the diagram shows line AP as being parallel to line CD. That makes triangle APR similar to triangle CDR.

We can now determine the ratios of the similar sides

If triangle APR = triangle CDR, then

Line PD/DR = AC/CR or

PD/PR = AC/AR or

CD/RD = AP/RP

Therefore to calculate X, we use the ratio,

PD/DR = AC/CR

15/42 = 10/x

{we reduce the left hand side to it's simplest form}

5/14 = 10/x

When we cross multiply we now have

5x = 14 × 10

5x = 140

Divide both sides of the equation by 5

x = 28

The greatest integer that will divide both 4900 and 168 exactly is 28.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

For example, the LCM of 6 and 8 is 24. Hence 24 is divisible by both 6 and 8.

First, Prime Factorizing 4900

4900 = 7 x 7 x 2 x 2 x 5 x 5

and, Prime Factorizing 168

168 = 2 x 2 x 2 x 3 x 7

So, the Common multiple of 4900 and 168 is 2 x 2 x 7 = 28.

Learn more about Least Common Multiple here:

https://brainly.com/question/30060162

#SPJ2

Final answer:

The greatest integer that will divide both 4900 and 168 exactly is 4.

Explanation:

The greatest integer that will divide both 4900 and 168 exactly is 4.

To determine this, we can use the concept of greatest common divisor (GCD). The GCD is the largest positive integer that divides two given numbers without leaving a remainder. In this case, the GCD of 4900 and 168 is 4.

One way to find the GCD is to factorize both numbers and determine the common factors. In this case, the prime factorization of 4900 is 2^2 * 5^2 * 7^2, and the prime factorization of 168 is 2^3 * 3 * 7.

The common factors are 2^2 and 7^1, which multiplied together give us 4. Therefore, 4 is the greatest integer that will divide both 4900 and 168 exactly.

Answer:

Step-by-step explanation:

hello :

the system is :

4x-4<8 ....(*)

9x+5>23...(**)

means :

4x < 12

9x > 18

x<3 and x>2  means : 2<x<3

Answer:

Let the number of balcony seats be b

Let the number of gallery tickets be g

Let the number of main floor tickets be m

b + g + m  = 1020

b = 2g

m = b + 225

The number of balcony tickets = 318

The number of gallery tickets = 159

The number of main floor tickets = 543

Step-by-step explanation:

Let the number of balcony seats be b

Let the number of gallery tickets be g

Let the number of main floor tickets be m

i) Therefore we can write b + g + m  = 1020

ii) there were twice as many balcony tickets sold as gallery tickets

   therefore b = 2g      [tex]\Rightarrow[/tex]  g = 0.5b

iii) there were 225 more main floor tickets than balcony tickets

   therefore m = b + 225

iv) using equation ii) and equation iii) in equation i) we can write

     b + g  + m = b + 0.5b + b + 225  = 1020      [tex]\Rightarrow[/tex] 2.5b  = 795     [tex]\Rightarrow[/tex]  b = 318

v) g  = 0.5 b  = 0.5 [tex]\times[/tex] 318 = 159

vi) m = b + 225 = 318 + 225 = 543

Answer:

D. Gallery: g

Balcony: 2g

Main Floor: 2g+225

Step-by-step explanation:

Gallery is g

Balcony had 2 times as many tickets than Gallery so 2•g (2•gallery)

Main floor had 225 more tickets than Balcony so Balcony’s equation plus 225 tickets. 2g + 225

The measure of the third angle is 119 degrees

Step-by-step explanation:

The given is:

We need to find the measure of the third angle in the triangle

The sum of the measures of the interior angles of a triangle is 180°

∵ The measure of an angle = 26°

∵ The measure of another angle = 35°

∵ The some of measures of the 3 angles = 180°

∴ 26° + 35° + x° = 180°, where x is the measure of the 3rd angle

- Add the like terms in the left hand side

∴ 61° + x° = 180°

- Subtract 61 from both sides

∴ x = 119°

The measure of the third angle is 119 degrees

Learn more:

You can learn more about the triangles in brainly.com/question/3945600

#LearnwithBrainly

Answer:

Step-by-step explanation:

The dollar amount of the reduction was $200 - $140, or $60.

$60 is what percentage of $200?

 $60

---------- = 3/10 = 0.30

$200

The reduction was 30%; the jacket sold for 70% of its original price.

Answer:

Step-by-step explanation: set up a proportion:

140/200 = x/100 answer is 70%

to cross check - .70 multiplied by 200 =140

Answer:

44-2n

Step-by-step explanation:

Hope it helps!

Final answer:

The expression '44 decreased by twice a number' can be represented as 44 - 2n, where n is the unknown number.

Explanation:

The question involves expressing a given mathematical relationship using a variable. Here, the relationship is '44 decreased by twice a number.' To represent this situation with the variable n, we use the expression 44 - 2n. To simplify further, just substitute the variable 'n' with the unknown number. This represents the original number 44 being reduced by two times the value of some unknown number n.

Answer:

2.4

Step-by-step explanation:

Answer:

$76.5

Step-by-step explanation:

We have been given that inflation from last year to this year was 2% and a pair of designer jeans sold for $75 last year. We are asked to find the price of pair of designer jeans this year.

An inflation of 2% will increase the price of pair of jeans by 2%, so price of pair of jeans this year would be $75 plus 2% of $75.

[tex]\text{Price of pair of jeans this year}=\$75+\$75\times\frac{2}{100}[/tex]

[tex]\text{Price of pair of jeans this year}=\$75+\$75\times0.02[/tex]

[tex]\text{Price of pair of jeans this year}=\$75+\$1.5[/tex]

[tex]\text{Price of pair of jeans this year}=\$76.5[/tex]

Therefore, the price of pair of jeans would be $76.5 this year.

A- The circumference of the tire is about 7.85 feet

B- The tire will rotate about 672 times to travel 1 mile

Step-by-step explanation:

∵ The diameter of a tire is 2.5 ft

∴ d = 2.5 ft

∵ C = π d, where C is the circumference of tire

∴ C = π(2.5) = 7.85398 ft

∴ C ≅ 7.85 feet

A- The circumference of the tire is about 7.85 feet

∵ The tire have to travel 1 mile

∵ 1 mile = 5280 feet

∴ S = 5280 feet

- To find the number of rotation of the tire divide S by C

∵ n =  [tex]\frac{S}{C}[/tex]

∴ n = [tex]\frac{5280}{7.85}[/tex] ≅ 672 revolution

B- The tire will rotate about 672 times to travel 1 mile

Learn more;

You can learn more about rotation in brainly.com/question/2860697

#LearnwithBrainly

Answer:

The circumference of the tire is about 7.85 feet

B- The tire will rotate about 672 times to travel 1 mile

Step-by-step explanation:

   The formula of the circumference of a circle is C = π d, where d is the diameter of the circle

   If a circle rotates for n turns and make a distance S, then n =

∵ The diameter of a tire is 2.5 ft

∴ d = 2.5 ft

Step-by-step explanation:

Answer:

3x^4-x^2-x^2-5x^4+3

-2x^4-2x^2+3 is the answer

To simplify the given expression, combine like terms by adding or subtracting the coefficients of the same powers of x.

The given expression is 3x4 - x2 - x2 - 5x4 + 3.

To simplify this expression, combine like terms by adding or subtracting the coefficients of the same powers of x.

Combining like terms, we have: -2x2 - 2x4 + 3.

https://brainly.com/question/16601020

#SPJ12

Answer:

False

Step-by-step explanation:

Factors of 10 and 14:

10:  1 , 2, 5, 10

14:  1, 2, 7, 14

As you can see, 5 is not a common factor of 10 and 14

The greatest common factor is two

So the answer is false, 5 is not the greatest common factor of 10 and 14

Hope this helps :)

The greatest common factor of 10 and 14 is 2, not 5. The statement is false as 5 is not a factor of 14.

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 10 and 14, we list the factors of each number:

The common factors of 10 and 14 are 1 and 2. Therefore, the GCF of 10 and 14 is 2, not 5. The statement that the greatest common factor of 10 and 14 is 5 is false.

Answer:

shows correct substitution of the values a, b, and c  from the given quadratic equation    into quadratic formula.

Step-by-step explanation:

Given: The quadratic equation

We have to show the correct substitution of the values a, b, and c from the given quadratic equation    into quadratic formula.

The standard form of quadratic equation is  then the solution of quadratic equation using quadratic formula is given as

Consider the given  quadratic equation

Comparing with general  quadratic equation, we have

a = -3 , b = -2 , c = 6

Substitute in quadratic formula, we get,

Simplify, we have,

Thus,  and x_{2}=\frac{2-\sqrt{76} }{-6}

Simplify, we get,

Thus,  shows correct substitution of the values a, b, and c  from the given quadratic equation    into quadratic formula.

Answer:

shows correct substitution of the values a, b, and c  from the given quadratic equation    into quadratic formula.

Step-by-step explanation:

Given: The quadratic equation  

We have to show the correct substitution of the values a, b, and c from the given quadratic equation    into quadratic formula.

The standard form of quadratic equation is  then the solution of quadratic equation using quadratic formula is given as  

Consider the given  quadratic equation  

Comparing with general  quadratic equation, we have

a = -3 , b = -2 , c = 6

Substitute in quadratic formula, we get,

Simplify, we have,

Thus,  and x_{2}=\frac{2-\sqrt{76} }{-6}

Simplify, we get,

Thus,  shows correct substitution of the values a, b, and c  from the given quadratic equation    into quadratic formula.

Answer:

11 + 2x

Step-by-step explanation:

First you will want to separate like variables, so (6, 5) and then (-2x, 4x)

Then you will use the signs to do the math. You can move everything to help visualize the solution easier.

6+5+4x-2x

6+5 = 11

4x-2x = 2x

Because you cannot add or subtract a variable with a non variable, and both numbers are positive you end up with

11 + 2x

The expression 6-2x+5+4x simplifies to 11 + 2x by combining like terms: the constants (6+5=11) and the variables (-2x+4x=2x).

To simplify the expression 6-2x+5+4x, we start by combining like terms. Combining the constant terms (6 and 5) and the variable terms (-2x and 4x), we get:

Constant terms: 6 + 5 = 11

Variable terms: -2x + 4x = 2x

Thus, the simplified expression is 11 + 2x.

Answer:

7) -6, -3, 1, 50

9) -18, -11, -8, 11, 18

Answer:

8:32

Step-by-step explanation:

1x+4x=40

5x=40

x=8

1*8:4*8

8:32

Answer:

[tex]\$18,453.78[/tex]  

Step-by-step explanation:

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final amount owed  

P is the amount borrowed

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=7\ years\\ P=\$8,000\\ r=12\%=12/100=0.12\\n=12[/tex]  

substitute in the formula above

[tex]A=8,000(1+\frac{0.12}{12})^{12*7}[/tex]

[tex]A=8,000(1.01)^{84}[/tex]  

[tex]A=\$18,453.78[/tex]  

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ahs vertices at points A(-4,-4), B(-1,-2) and C(-1,-4).

1 way: First reflect this triangle across the y-axis to form the triangle A''B''C'' which vertices are at points A''(4,-4), B''(1,-2) and C''(1,-4).

Then translate this triangle 7 units up to form the triangle A'B'C' with vertices:

[tex]A'(4,-4+7)=A'(4,3)\\ \\B'(1,-2+7)=B'(1,5)\\ \\C'(1,-4+7)=C'(1,3)[/tex]

2 way: First translate this triangle 7 units up to form the triangle A''B''C'' which vertices are at points A''(-4,3), B''(-1,5) and C''(-1,3).

Then reflect this triangle across the y-axis to form the triangle A'B'C' with vertices:

[tex]A'(-(-4),3)=A'(4,3)\\ \\B'(-(-1),5)=B'(1,5)\\ \\C'(-(-1),3)=C'(1,3)[/tex]

Answer:

P = 105°

QR = 11.6

M = 45°

LN = 8.5

Step-by-step explanation:

when reading the order of what is given LMN = PRQ the order DOES matter

so whe looking at what is being asked....

P will equal whatever its place is in the opposite equation. In this case that is L. This means that P = L. Since L = 105° then so does P.

You can do this with the rest of the letters. What ever letter is in it's place in the opposite equation that is what it equals.

Answer:

(2+6)*(4-1) = 24

(2-1)*(6*4) = 24

(2-1)*6*4 = 24

(2-1)*(4*6) = 24

(2-1)*4*6 = 24

(6+2)*(4-1) = 24

6*(2-1)*4 = 24

6*(2-1)*4 = 24

6/(2-1)*4 = 24

6/(2-1)*4 = 24

Answer:

i think its d

Step-by-step explanation:

The question is asking about the inverse of a function, a crucial mathematical concept. We generally calculate this by switching x and y, then solving the new equation for y. Without specific function options, we cannot provide a correct answer.

The question is about determining the inverse of a function, an important concept in Mathematics. Given that the question does not have any specifics about the function itself, it's impossible to determine the correct answer. In general, to find the inverse of a function, we follow a certain procedure: exchange the roles of y and x; once that is done, solve the function for y.

For instance, if you had a function like f(x) = 2x + 3, the inverse would be calculated by flipping x and y and solving the resulting equation for y: x = 2y + 3. Solving for y, you have y = (x - 3) / 2.

Unfortunately, without knowledge of the specific functions mentioned in the options A, B, C, D, we cannot select a correct answer.

https://brainly.com/question/17872426

#SPJ2

Answer: you isolate the variable so you can get a equation of y= 10x or something like that

Step-by-step explanation:

Answer:

a. 157 cm

Step-by-step explanation:

Multiply the diameter times 3.14

3.14 x 50=157 cm.

answer: 157 cm

To find the circumference of a circle given the diameter, multiply the diameter by π (approximately 3.14). Hence, the circumference of the dartboard is approximately 157 cm.

The subject of the question is Mathematics and it covers a topic generally taught in Middle School. When given the diameter of a circle, you can calculate the circumference using the formula C=πd where C is the circumference, π (pi) is about 3.14, and d is the diameter. In this case, the diameter of the dartboard is 50 cm. So, we simply multiply the diameter (50 cm) by π (3.14) to get the circumference. This means the circumference of the dartboard is approximately

157 cm (Option A)

.

https://brainly.com/question/37011717

#SPJ11

Answer:its 29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Answer:

390 miles

Step-by-step explanation:

30 mpg means that he gets 30 miles for every gallon.

If he has 13 gallons means that you multiply 30 by 13.

30 * 13 = 390 miles

Final answer:

Mark can travel 390 miles on 13 gallons of gas, as his car gets 30 miles per gallon and distance is calculated by multiplying fuel efficiency by the number of gallons.

Explanation:

To calculate the distance Mark can travel on 13 gallons of gas, we use the formula: Distance = Fuel Efficiency  imes Number of Gallons.

Mark's car gets 30 miles per gallon. Thus, the distance he can cover on 13 gallons of gas is calculated by multiplying 30 miles/gallon by 13 gallons, which equals 390 miles.

This is a straightforward multiplication problem involving units of fuel efficiency (miles per gallon) and quantity of fuel (gallons).

The solution directly gives us the total number of miles Mark can travel on 13 gallons of gas.