The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.

(a) Define your variables.

(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides.

(c) Explain your answer to Part B.

Answer:

- The equation is: [tex]\frac{249}{2}=2(x+\frac{17}{4})+2x[/tex]

- The width of the postage stamp is 29 milimeters.

- The length is 33.25 milimeters.

Step-by-step explanation:

1. The length ([tex]y[/tex]) is [tex]4^{\frac{1}{4} }mm=\frac{17}{4}mm[/tex] longer than the width ([tex]x[/tex]):

[tex]y=x+\frac{17}{4}[/tex]

2. The perimeter is [tex]124^{\frac{1}{2}}mm=\frac{249}{2}mm[/tex].

3. The perimeter of a rectangle is:

[tex]Perimeter=2Length+2Width[/tex]

4. Substitute values:

[tex]\frac{249}{2}=2(x+\frac{17}{4})+2x[/tex]

5. Solve for the width [tex]x[/tex]:

[tex]\frac{249}{2}=2x+\frac{34}{4}+2x\\x=\frac{116}{4}\\x=29[/tex]

6. Calculate the length:

[tex]y=x+\frac{17}{4}\\y=29+\frac{17}{4}\\y=33.25[/tex]

The width and length of the postage stamp are calculated by formulating and solving an equation based on the given perimeter and the relationship between the length and width. The width is found to be 29 mm, and the length is 33.25 mm.

The subject of this question is Mathematics and it's related to the concept of the perimeter of a rectangle. If we denote the width of the postage stamp as 'W' (in millimeters), then it's length will be 'W + 4.25' millimeters because it's stated in the problem that the length is 4.25 mm longer than the width.

The perimeter of a rectangle (which is the shape we can assume for a postage stamp) is calculated as follows: Perimeter = 2(Length + Width). Substituting the value for length that we've assigned, we get this equation:

124.5 = 2[(W + 4.25) + W]

Solving this equation step-by-step will lead you to the answer. First, distribute the 2 into the parentheses which gives: 124.5 = 2W + 8.5 + 2W. Combine like terms to simplify: 124.5 = 4W + 8.5. Then, subtract 8.5 from both sides of the equation: 116 = 4W. Lastly, divide by 4 to find 'W': W = 29 mm. Therefore, the width of the postage stamp is 29 mm, and the length is 29 mm + 4.25 mm = 33.25 mm.

https://brainly.com/question/31126899

#SPJ3

Unit rate for 8 hours: $9.00/hr. Unit rate for 6 hours: $9.50/hr. ($72.00/8 = $9.00, $57.00/6 = $9.50)

To find the unit rate, which is the amount earned per hour, you divide the total earnings by the number of hours worked.

For babysitting 8 hours and making $72.00:

Unit rate = Total earnings / Number of hours worked

Unit rate = $72.00 / 8 hours

Unit rate = $9.00 per hour

For babysitting 6 hours and making $57.00:

Unit rate = Total earnings / Number of hours worked

Unit rate = $57.00 / 6 hours

Unit rate = $9.50 per hour

So, the unit rate in dollars per hour for each scenario is:

- $9.00 per hour for babysitting for 8 hours and making $72.00.

- $9.50 per hour for babysitting for 6 hours and making $57.00.

The complete question is here:

Babysitting for 8 hours and making $72.00 or babysitting for 6 hours and making $57.00. What is the unit rate in dollars per hour?

The quotient and remainder of the given division operations are:

4)76 = 19

3)92 = 30 remainder 2

6)53 = 8 remainder 5

From the question, we are to evaluate the given divisions

The divisions can be evaluated as follows:

  19    

4)76

-  4      

   36

-   36  

 = 19

  30    

3)92

-  9      

   02

-     0  

     2

= 30 R 2

  08    

6) 53

-  0      

    53

-   48    

      5

= 8 R 5

a) (x,y) =(x-3, y-2)

Answer:

a) (x,y) → (x - 3, y - 2)  

Step-by-step explanation:

Comparing the pre-image points, r, s and t, to the image points, r', s' and t', we see that the x-coordinates of the image are all 3 less than the x-coordinates of the image:

10-7 = 3; 8-5 = 3; 6-3 = 3

This means the first part of the translation rule will be x-3.

Now comparing the y-coordinates, we see that the y-coordinates of the image are all 2 less than the y-coordinates of the pre-image:

6-4 = 2; 4-2 = 2; 6-4 = 2

This means the second part of the translation rule will be y-2.

This gives us (x, y)→(x-3, y-2).

I believe it’s 6.8 if I’m wrong I’m sorry

By using the formula of  perimeter of rectangle,

Length of the rectangle is 24 inches

What is perimeter of a rectangle?

Perimeter of a rectangle is the length of the boundary of the rectangle.

If the length of the rectangle is l and breadth of the rectangle be b, then perimeter of rectangle is [tex]2(l + b)[/tex]

Let the length of rectangle be l inch

Width of rectangle = 10 inch

Perimeter of rectangle = [tex]2(l + 10)[/tex] inch

By the problem,

[tex]2(l + 10) = 68\\l +10 = \frac{68}{2}\\l + 10 = 34\\l = 34 -10\\[/tex]

[tex]l = 24[/tex] inches

Length of the rectangle is 24 inches

To learn more about perimeter of rectangle, refer to the link:

https://brainly.com/question/19819849

#SPJ2

Answer:

Exact Form = 8/5

As a decimal = 1.6

As a Mixed Fraction =  1 3/5

Step-by-step explanation:

If it would make it esier for you to understand I would sugest turning the fraction, "46/5" into a decimal.

You do that by dividing 46 by 5. You then get, 9.2.

Then do 9.2 divided by 5.75 and you get 1.6.

If you would like the answer as a fraction just turn the answer into a fraction.

Hope this helps :-)

To divide 46/5 by 5.75, multiply the numerator and denominator of 46/5 by the reciprocal of 5.75/1, which is 1/5.75. Simplify the expression to get 8/23.

To divide 46/5 by 5.75, we can first express 5.75 as a fraction by dividing 5.75 by 1. This gives us 5.75/1. Next, we can multiply both the numerator and denominator of 46/5 by the reciprocal of 5.75/1, which is 1/5.75. This gives us (46/5) * (1/5.75). Simplifying the expression, we get 8/23.

https://brainly.com/question/18511795

#SPJ2

Answer:

990 pounds

Step-by-step explanation:

If one troop eats 11 pounds and there are 90 troops, you only need to multiply 90 by 11.

The length of pine street would be; 7.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We have been given that maple street is 3 times as long as pine street.

We need to find the length of pine street.

Therefore,

We have to divide 21 divided by 3 which is;

21/3 = 7

Hence, A pine street would be; 7.

Learn more about division here:

https://brainly.com/question/26411682

#SPJ2

I hope I am reading the problem right: The price of a mountain bike increased by 20% in the past year. The value is $150. What was the value of the mountain bike last year?

Let's simplify this. One year, there was this radical mountain bike that used to have an unsaid price, x. That year, that price of x increased by 20% more than it was before, or 120% times the original value. Because of that, it's now $150.

We can equation this.

1.20x = 150

x = 150/1.2

x = 125

The bike, I believe, cost $125 last year. Hope this helps!

Final answer:

To find the value of the mountain bike last year, we can use the concept of percentage increase and decrease.

Explanation:

To find the value of the mountain bike last year, we can use the concept of percentage increase and decrease. If the price of the bike increases by 20%, then the current value is 120% of the previous value.

To find the previous value, we can set up an equation: 120% of the previous value is equal to $150. Mathematically, this can be written as 1.2x = 150, where x is the previous value.

Solving the equation, we divide both sides by 1.2 to isolate x: x = $125. Therefore, the value of the mountain bike last year was $125.

PEMDAS:

20 + [tex]4^{3}[/tex] ÷ -8

Exponent

20 + 64 ÷ -8

Divide

20 +  -8

Add

20 + -8 = 12

hope this helps :)

The value of [tex]20+4^{3} /(-8)[/tex] is 12.

Given:

[tex]20+4^{3} /(-8)[/tex]

Simplifying the equation by the PEMDAS rule

We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).

[tex]$\quad 4=2^{2}$[/tex]

[tex]$(4)^{3}=\left(2^{2}\right)^{3}=2^{6}$[/tex]

Substituting the values in the given equation,

[tex]$20+\frac{2^{6}}{-8}$$[/tex]

Dividing exponents as

[tex]$2^{6}$[/tex] divided by [tex]$2^{3}=2^{(6-3)}=2^{3}$[/tex]

[tex]$20+-8$$[/tex]

Simplify,

[tex]$20+-8$$[/tex]

Therefore, the value of [tex]20+4^{3} /(-8)[/tex] is 12.

To learn more about the PEMDAS rule

https://brainly.com/question/550188

#SPJ2

The answer to your question is  

d.

78.5 m^2

78.54 m² is your answer. So to recap, a goat tethered to a stake in the ground with a 5 m rope has 78.54 meters to graze.

We get this answer by putting the information into an equation. We know that a circle has 360° (360 degrees) and so when we see the problem say that the goat can graze 360 degrees around the stake, we instantly know it's talking about a circle. Look at the question, it's asking about the area of the circle. Now we can make an equation to find the area of this circle.

The area of a circle is A = πr²

That's Area = Pi times Radius squared.

We'll use 3.14 as substitute for Pi. The radius was given to us, it is 5 m. Put the information into the formula.

A = 3.14 * 5²

Now we do the order of operations. In the order of operations, we have no parenthesis to work with, but we do have an exponent. So we take 5 to the second power, (5² = 5 * 5) and we update our problem.

A = 3.14 * 25

Now we finish the problem by multiplying 3.14 and 25.

A = 78.54

We're not entirely done. Now we include our units of measurement. In this case, we were using m for meters. When solving for area, the unit is always squared in the final answered. So this would be our final answer:

A = 78.54 m²

If two lines are intersected by a transversal, and the alternate interior angles are equal, then the lines are parallel.

Conversely, if two lines are parallel, then the alternate interior angles formed by the transversal are equal.

So, Ray can made the conclusion that l and m are parallel because alternate interior angles are equal since m∠3 = m∠6.

Ray can conclude that lines l and m are parallel because alternate interior angles are equal.

Ray knows that the measure of angle 3 (m∠3) is equal to the measure of angle 6 (m∠6). When two lines are intersected by a transversal (a line that intersects two other lines), and the corresponding angles on either side of the transversal are equal, it is a characteristic of parallel lines.

In this case:

- Angle 3 and angle 6 are corresponding angles because they are on the same side of the transversal and in the same relative position with respect to lines l and m.

- The fact that m∠3 = m∠6 indicates that lines l and m have corresponding angles that are equal.

Therefore, based on the given information that m∠3 = m∠6, Ray can conclude that lines l and m are parallel because alternate interior angles (corresponding angles) are equal, which is a property of parallel lines.

Learn more about angle  at https://brainly.com/question/1309590

#SPJ4

The answer would be 0.002

The answer to 0.45 / 225 = 0.002

Hope this helps you..

Allen missed 5 targets.

Hope this helped! :)

a. The independent variable is r. The dependent variable is m.

b. The domain is the set of numbers used in the independent variable. You can rent 0 videos, or 1 video, or 2 videos, etc., up to the amount of money you have. If you rent 0 videos, you are left with m = 30 - 3r = 30 - 3(0) = 30 - 0 = 30 dollars. If you rent 10 videos, you will have m = 30 - 3(10) = 30 - 30 = 0 dollars left. The domain is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The range is {0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30}. Both the domain and range are discrete.

c. I can't do it online.

Answer:

Number sentences.

Addition-Addend-Sum.

Subtraction-Difference.

Step-by-step explanation:

1. By definition Number sentences contains number and common symbols.

2. They can be: "Addition" (which has "Addend" that form the "Sum") and "Subtraction" (whose result is known as "Difference").

3. You can see the answer of the tree map in the figure attached.

The solution of expresison is, r = - 38

We have to give that,

An expression to simplify,

12r - 18 = 13r + 18

Now, We can simplify the expression as,

12r - 18 = 13r + 18

Subtract 12r on both sides,

12r - 18 - 12r = 13r - 12r + 18

- 18 = r + 18

Subtract 18 on both sides,

- 18 - 18 = r

r = - 36

Therefore, The solution is, r = - 36

To learn more about subtraction visit:

https://brainly.com/question/17301989

#SPJ6

(1) y = 7x , (2) y = 11x , (3) y = 9x , (4) y = 28x

given y varies directly as x then y = kx ( k is the constant of variation )

(1) find k using the given conditions k = [tex]\frac{y}{x}[/tex] = [tex]\frac{63}{9}[/tex] = 7

equation is y = 7x

(2) k = [tex]\frac{121}{11}[/tex] = 11

equation is y = 11x

(3) k = [tex]\frac{36}{4}[/tex] = 9

equation is y = 9x

(4) k = [tex]\frac{224}{8}[/tex] = 28

equation is y = 28x

None of those show another way to 64

6*6*6*6=1296

4*4*4*4*4*4=4096

6+6+6+6=24

6*4=24

Another way to show 64 is 8*8 or 4^3

find his total number of miles: 10,368 + 2,832 = 13,200

subtract from 15000 to see how many more he needs: 15,000 - 13,200 = 1,800

divide by 2 to find the number of dollars: 1800/2 = 900

he'll need to charge $900 to get 15,000 miles.

The Answer to this is: True.

36 ÷ 4 can be written as:

Thirty-six divided by four.

24 - (6 + 3) can be written as:

The difference of twenty-four and six plus three.

We'll use the expression x - 7 for this one.

The difference between a number and seven.

Hope this helps!

In Δ ABC, let A = x°

By Angle-sum property,

A + B + C = 180°

But, it is given that C = 130°

So, x + B + 130 = 180

B = 180 - 130 - x

B = 50 - x

Since AD and BD are internal bisectors of A and B,

∠ DAB = x/2 and

∠ DBA = [tex]\frac{50-x}{2}[/tex]

[tex]=25-\frac{x}{2}[/tex]

In Δ ADB, by angle-sum property,

∠ DBA + ∠ DAB +∠ ADB = 180°

[tex]=(25-\frac{x}{2} )+\frac{x}{2} +[/tex] + ∠ ADB = 180°

25 + ∠ ADB = 180°

∠ ADB = 180 - 25 = 155°

Hence, ∠ ADB = 155°.

Answer = 155 degrees

If we are trying to solve this then the variable A would be equivalent to 2/5 or A < 2/5

1. Ten times a number increased by four is no more than twenty five is  [tex]\(10x + 4 \leq 25\)[/tex]

2. One fourth of the opposite of the difference of five and the number less than twenty is  [tex]\(\frac{1}{4}(-5-x) < 20\)[/tex].

3. -5a+3>1  This inequality asserts that the result of subtracting three times a value (a) from negative five is greater than one.

1. [tex]\(10x + 4 \leq 25\)[/tex]: This inequality describes a situation where ten times a number (x) increased by four is less than or equal to twenty-five.

It represents a constraint on the possible values of x such that the expression 10x + 4 does not exceed 25.

2. [tex]\(\frac{1}{4}(-5-x) < 20\)[/tex]: This inequality states that one-fourth of the opposite of the difference of five and the number (x) is less than twenty.

It indicates a restriction on the value of x such that when subtracted from five and negated, the result, when multiplied by one-fourth, is less than twenty.

3. Description of Inequality: -5a + 3 > 1

  This inequality asserts that the result of subtracting three times a value (a) from negative five is greater than one.

It signifies a condition where the expression -5a + 3  is strictly greater than 1, setting boundaries on the possible values of a to satisfy this relationship.

The probable question may be:

1. Ten times a number increased by four is no more than twenty five

2. One fourth of the opposite of the difference of five and the number less than twenty.

3. Write a description of each inequality.

-5a+3>1

m = 4, n = 4

Plug in 4 for m and n

10(4) + (4)^2

Simplify. Multiply

4^2 = 4(4) = 16

10(4) = 40

40 + 16 = 56

56 is your answer

hope this helps

Hello!

Explanation:

↓↓↓↓↓↓↓↓↓↓

First, rewrite 10 as 2*5

[tex]2k+2*5[/tex]

Then, factor out common term 2.

[tex]=2(k+5)[/tex]

Answer⇒⇒⇒⇒2(k+5)

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

Answer:

a-bi

Step-by-step explanation:

If a quadratic equation lx^2+mx+n=0 has one imaginary root as a+bi then the other root is the conjugate of a+bi = a-bi

Because we have l, m and n are real numbers and they are the coefficients.

Sum of roots = a+bi + second root = -m/l

When -m/l is real because the ratio of two real numbers, left side also has to be real.

Since bi is one imaginary term already there other root should have -bi in it so that the sum becomes real.

i.e. other root will be of the form c-bi for some real c.

Now product of roots = (a+bi)(c-bi) = n/l

Since right side is real, left side also must be real.

i.e.imaginary part =0

bi(a-c) =0

Or a =c

i.e. other root c-bi = a-bi

Hence proved.