There are 48 crayons in a box. There are 12 boxes in a carton. Mr Johnson ordered 6 cartons of crayons for the school. How many crayons did he get? 2

Given :

Fitness center A has a $60 enrollment fee and costs $35 per month. Fitness center B has no enrollment fee and costs $45 per month.

To Find :

A) Identity the variables then write system of linear equations to represent the situation.

B) In how many months will both fitness centers cost the same? What will the cost be? Use the substitution method to solve this real-world application.

Solution :

a) Linear equation of center A :

F = 35x + 60   ...1)

Linear equation of center B :

F = 45x  ...2)

b) Let, after n months both fitness centers cost the same fee :

So, 35m + 60 = 45m

10m = 60

m = 6 months

Putting value of m in equation 1) or 2) is :

F = (35×6) + 60 = $270 or F = 45×6 = $270 .

Therefore, the cost when they have same fee is $270 .

Hence, this is the required solution.

Answer:

$2

Step-by-step explanation:

Let, price of individual child ticket is $x, and price of individual adult ticket is $y.

Now, on Friday we can write an equation is 55x+20y=200....(1).

and on Saturday we can write an equation is 72x+36y=306.....(2).

so, Equation 1: 55x+20y=200

Equation 2: 72x+36y=306

now, we are going to solve both equations.

after solving you will find x=2 and y=4.5

Hence, we can say that the cost of child ticket is $2, and the cost of adult ticket is $4.50.

The cost of a child's ticket will be $2.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Let, the price of an individual child ticket is $x, and the price of an individual adult ticket is $y.

Now, on Friday we can write an equation is 55x+20y=200....(1).

On Saturday we can write an equation is 72x+36y=306.....(2).

The first equation is:-

55x+20y=200

The second equation will be written as:-

72x+36y=306

Now, we are going to solve both equations. After solving you will find x=2 and y=4.5

Hence, we can say that the cost of a child ticket is $2, and the cost of an adult ticket is $4.50.

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Answer:

When you substitute 0 for the exponent x, the expression simplifies to a times 1, which is just a. This is because any number to the 0 power equals 1. Since the initial value is the value of the function for an input of 0, the initial value for any function of this form will always be the value of a

Step-by-step explanation:

Hopefully this helped, if not HMU and I will try to get you a better answer! :)

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Answer:

 y  = -x + 8

Step-by-step explanation:

We are to write the expression is slope intercept format;

  coordinate  = (3,5)

   slope  = -1

The equation of a straight line is given as;

     y  = mx + c

y and x are the coordinates

m is the slope

c is the y-intercept

      y  = mx + c

      5  = -1 (3) + c

      5  = -3 + c

      c = 8

The equation of the line is ;

 y  = -x + 8

Answer:

C =diameter times π

24π mm

Answer:

Step-by-step explanation:

Is their a 32.50d + 475? If not I don't know what the answer is because you have the same two things twice in a pattern.

Answer:

Step-by-step explanation:

Total cost per d persons:

Answer:

300 is greater than 3x + 75

The equation you would use to solve would be

300=75+3x

x= the amount of movies he watches

meaning x= 75

300=75+3x

225=3x

x=75

he can rent up to 75 movies

Answer/Step-by-step explanation:

1. -14

2. 3

3. -3

4. 10

5. -8

1. 4 x -3 = -12 - 2 = 14

2. -3 x 2 = -6 + 9 = 3

3. 8 divided by 4 = 2 - 5 = -3

4. 3/2 = 1.5 x 2 = 3 + 7 = 10

5. -9/3 = -3 - 5 = -8

Answer:

4th choice, 20, 21, 29 would be the answer.

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

a= 20, b= 21, c= 29 ( c has to be the C, hypotenuse, because it is the longest)

therefore,

20^2 + 21^2 = 29^2

              into

400 + 441 = 841,

which is true, makes the Pythagorean Theorem work.

Answer:

B) 17

Step-by-step explanation:

3(4)+5

12+5

Answer:

m is greater than -4. The graph is correct.

Answer:

20 pencils

Step-by-step explanation:

Ratio: 4:5 (4 to 5)

16: (?)

16 ÷ 4 (the 4 in 4:5) = 4

So:

4 x 5 = 20

Final Answer:

16:20

Hopefully this helps! Sorry if wrong. You are loved and you are beautiful/handsome!

-Bee

Answer:

The system of equations that can be used to determine the three numbers are equation 1 and 6

x + y + z = 27 ----- ( 1 )

37.33 x - 56 y + 0 = 0  ---- ( 6 )

Step-by-step explanation:

x + y + z = 27 ----- ( 1 )

x * z = 56 ------ ( 2 )

y / x  = 1.5  -------- ( 3 )

from equation 3

x = y / 1.5  -------- ( 4 )

input equation 4 into ( 2 )

( y / 1.5 ) * z = 56

y * z = 37.33 ------  ( 5 )

from equation 5 ;  z = 37.33 / y input  back to equation 2

x ( 37.33 / y ) = 56

37.33 x = 56 y  

37.33 x - 56 y  + 0 = 0  ---- ( 6 )

Answer:

Maybe -2,0,2,4 but I'm not sureee

Eekkkkk sorryy

Answer:

is 4.2 the circumference

Step-by-step explanation:

Answer:

2.1 cm

Step-by-step explanation:

Answer:

y = 1x +1

Step-by-step explanation:

1 is your b, you go up 1 over 1, 1/1, which equals 1. so your awnser is y=1x+1 :)

Answer:

Step-by-step explanation: sowwy I dunno

Answer:

20 days

Step-by-step explanation:

2212 divided by 114 =19.40350877, so round it up to the nearest tenth, which is 20. he has read for 20 days

$51.49+$17.65=$69.14

$80-$69.14=$10.86

Given:

Tickets to a football game cost $6 per ticket.

To find:

The equation that represents this relationship between tickets purchased and total cost.

Solution:

Let t represents the number of tickets purchased and c represents the total cost.

Cost of 1 ticket = $6

Cost of t ticket = $6t

Since, c is the total cost oft tickets, therefore the equation for given situation is

[tex]c=6t[/tex]

Therefore, the required equation is [tex]c=6t[/tex].

Answer:

<A = 76°

<B = 63°

<C = 41°

Plug in the value of x

<C = 34 + 7

<C = 41°

Step-by-step explanation:

[tex] 63 + (2x + 8) + (x + 7) = 180 [/tex] (sum of ∆)

Solve for x

[tex] 63 + 2x + 8 + x + 7 = 180 [/tex]

Add like terms

[tex] 78 + 3x = 180 [/tex]

Subtract 78 from each side

[tex] 78 + 3x - 78 = 180 - 78 [/tex]

[tex] 3x = 102 [/tex]

Divide both sides by 3

x = 34

<A = 2x + 8

Plug in the value of x

<A = 2(34) + 8 = 76°

<B = 63°

<C = x + 7

Plug in the value of x

<C = 34 + 7

<C = 41°

Answer:

Janice will need 2 cups of oil.

Step-by-step explanation:

You know that Janice needs to prepare 2[tex]\frac{2}{3}[/tex] servings. A mixed number is a numerical way of representing a fraction greater than unity, that is, of representing fractions in which the numerator is greater than the denominator (improper fraction). To calculate the number of cups of oil needed, first it is convenient to transform the mixed number to an improper fraction. For that, the integer part is multiplied by the denominator and the numerator is added to it. The result obtained is the numerator of the improper fraction. The denominator is the same as that of the rational part of the mixed number.

In this case:

[tex]2\frac{2}{3} =\frac{3*2+2}{3} =\frac{8}{3}[/tex]

Knowing that the recipe calls for [tex]\frac{3}{4}[/tex] cups of oil per serving and Janice needs to prepare [tex]\frac{8}{3}[/tex] servings, you can apply the following rule of three: if [tex]\frac{3}{4}[/tex] cups of oil are required for 1 serving, [tex]\frac{8}{3}[/tex] servings how many cups of oil require?

[tex]cups of oil=\frac{\frac{8}{3}servings *\frac{3}{4}cups of oil }{1 serving}[/tex]

Solving:

cups of oil= 2

Janice will need 2 cups of oil.

It take 2 years for the number of male nurses to exceed the number of female nurses.

Given:

f(t) = 7,300 + 25t

m(t) = [tex]2,500(1.02)^t[/tex]

To find the value of t at which m(t) > f(t).

Let's set up the inequality:

[tex]2,500(1.02)^t > 7,300 + 25t[/tex]

We can start with t = 0 (year 2000) and increment t until m(t) exceeds f(t).

For t = 0:

m(0) = [tex]2,500(1.02)^0[/tex] = 2,500

f(0) = 7,300

Since m(0) < f(0), increase t.

For t = 1:

m(1) = [tex]2,500(1.02)^1 =[/tex] 2,550

f(1) = 7,300 + 25(1) = 7,325

Since m(1) < f(1), increase t as

For t = 2:

m(2) = [tex]2,500(1.02)^2 =[/tex] 2,601

f(2) = 7,300 + 25(2) = 7,350

Since m(2) > f(2), the number of male nurses is expected to exceed the number of female nurses after 2 years since 2000.

Therefore, it will take about 2 years.

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Answer:

C. 2.84%

Step-by-step explanation:

We are trying to figure out how much money will be made from the interest each year in percentage form so to set up the problem we need to first find the earnings from this year: 2,056.72 - 2,000 = 56.72

Then we will put 2,000 below that because that was the original full account deposit used to make the interest.  100 automatically goes on the other side because it is the full value of the percentage. Then solve the equation.

56.72       X

--------- = -------

2,000     100

To solve for X start by multiplying the diagonal numbers, in this case 56.72 and 100. Then divide by the remaining number, 2,000.

I hope this helps a little :)

Answer:

The correct option is c. Combining like terms in the first expression and dividing each term by 5.

Step-by-step explanation:

Joe concluded that the expression [tex]3x+15+2x[/tex] is equivalent to the expression [tex]5(x+3)[/tex].

Let's analyze each option :

a. Dividing each term in the first expression by 3.

If we perform this operation it will lead us to :

[tex]\frac{3x+15+2x}{3}=x+5+\frac{2}{3}x[/tex]

And if we sum each term ⇒ [tex]x+5+\frac{2}{3}x=5+\frac{5}{3}x=5(1+\frac{1}{3}x)[/tex]

Which isn't equivalent to the expression [tex]5(x+3)[/tex]

b. Combining like terms in the first expression and dividing each term by 3.

If we perform this operation it will lead us to :

[tex]3x+15+2x=15+5x[/tex] ⇒

[tex]\frac{15+5x}{3}=5+\frac{5}{3}x=5(1+\frac{1}{3}x)[/tex]

Which isn't equivalent to the expression [tex]5(x+3)[/tex]

c. Combining like terms in the first expression and dividing each term by 5.

If we perform this operation it will lead us to :

[tex]3x+15+2x=15+5x[/tex] ⇒ Now if we divide each term by 5 and then we multiply the expression by 5 (in order to keep the equivalence) ⇒

[tex]\frac{15+5x}{5}=3+x[/tex]

And then we multiply by 5 to keep the equivalence ⇒

[tex]5(3+x)[/tex]

Finally, using commutative properties ⇒ [tex]5(3+x)=5(x+3)[/tex]

Which is the same expression that Joe found.

The correct option is c. Combining like terms in the first expression and dividing each term by 5.

Anyway, let's analyze option d. Subtracting 20 and applying the distributive property to the first expression :

[tex]3x+15+2x-20=-5+5x=5(-1+x)[/tex]

Which isn't equivalent to [tex]5(x+3)[/tex]

Answer: The correct option is c. Combining like terms in the first expression and dividing each term by 5.

Step-by-step explanation:

Answer:

i think its just 80 degreed

Step-by-step explanation: