A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.

Part A. Write and solve a system of equations to model this situation.

Part B. Then explain the meaning of your solution.

The speed of the boat if it were in still water is 11.25 miles per hour and the speed of the current is 3.75 miles per hour.

According to the question,

We have the following information:

A boat take 4 hour to travel upstream 30 miles. On the return trip downstream it took 2 hours.

Now, let's take the speed of the boat in still water to be s miles per hour and the speed of the current to be c miles per hour.

Upstream speed = speed in still water - speed of current

Downstream speed = speed in still water + speed of current

Upstream:

s-c = 30/4

s-c = 7.5

s = 7.5+c ...(1)

Downstream:

s+c = 30/2

s+c = 15

Putting the value of s from equation 1:

7.5+c+c = 15

7.5+2c = 15

2c = 15-7.5

2c = 7.5

c = 7.5/2

c = 3.75 miles per hour

Putting this value in equation 1:

s = 7.5+c

s = 7.5+3.75

s = 11.25 miles per hour

Hence, the speed of the boat if it were in still water is 11.25 miles per hour and the speed of the current is 3.75 miles per hour.

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Answer:  

 a.  (-2,-1)

  b.   y = -(1/2)x-2

Step-by-step explanation:

We will look for an equation of the form y=mx+c, where m is the slope and b is the y-intercept (the value of y when x = 0).

Put the two given points into a table to make it easier to calculate the slopes for Lines A and B.  See the attachment for the table.  Slope is the change in y for a change in x, often termed the "Rise/Run."  Using Line A as the example, the change in y (the Rise) is obtained by taking the Point 2 value for y (7) and subtracting the Point 1 value for y (3):  Rise = (7 - 3) = 4.  The Run is obtained by taking the Point 2 value for x (2) and subracting the Point 1 value of x (0).  The ratio of Rise/Run is 4/2, so the slope is 2.  The same process is used for Line B to obtain a slope of 3 for that line.

The two equations can be written with these slopes:

Line A:  y = 2x + c

Line B:  y = 3x + c

We need to find a value of c for each equation that will force the line through either of their two given points.  c can be determined by entering either of that line's points into the equation(s) above and solving for c:

Line A:  

y = 2x + c

3 = 2*(0) + c    for point (0,3)

c = 3

The equation for Line A is y = 2x + 3

Line B:

y = 3x + c

2 = 3*(-1) + c  for point (-1,2)

c = 5

The equation for Line B is y = 3x + 5

The graph of these lines is attached.  They intersect at point (-2,-1).

[As a note, the solution may also be found by using substitution and solving for both x and y:

y = 2x+3

y = 3x+5

The solution exists when both y's and x's are equal:

Assume y is equal:

 2x+3 = 3x+5

 -x = 2;  x = -2

----

Assume x is equal:

Rearrange:

 y = 2x+3

  2x = y-3

   x = (y-3)/2

Use this definition of x in the second line equation:

 y = 3x+5

 y = 3((y-3)/2)+5

 y = (3y - 9)/2 + 5

2y = 3y - 9 + 10

-y = 1

 y = -1

The solution is (-2,-1), the same as was found by graphing.]

==================================================

A perpendicular line has a slope that is the negative inverse of the referenced line.  For Line A, the perpendicual line would be -(1/2).  The equation for this line would take the form y = -(1/2)x + c.  We want this perpendicular line to intersect the same point that is the solution to the first problem:  (-2,-1).  Enter this point to find c:

y = -(1/2)x + c

-1 = -(1/2)*(-2) + c  for (-2,-1)

-1 = 1+ c

c = -2

The perpendicular line is y = -(1/2)x - 2

See the attached graph.

The length of the second rectangle is 30cm

Two rectangles are similar when the corresponding adjacent sides have the same ratio. We do not need to check the angles as all angles in a rectangle are 90 degrees.

all rectangles are not similar rectangles. The ratio of the corresponding adjacent sides may be different.

length the length and width of first rectangle be L1 and W1 and length and width of second rectangle be L2 and W2

then the ratio of length should be equal to ratio of width since both rectangles are similar

L1/L2 = W1/W2

L1 = 21cm, W1 = 14cm, W2 = 20cm

21/L2 = 14/20

cross multiply

14L2 = 420

L2 = 420/14

L2 = 30cm

In conclusion the length of second rectangle is 30cm

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The measure of each interior angle of a regular pentagon is 108° and each exterior angle is 72°.

To calculate the measure of each interior and exterior of a regular polygon, we have the following formulae:

The measure of each exterior angle of a regular polygon with n sides is given by "360/n".

And the measure of each interior angle of a regular polygon with n sides is given by "180 - 360/n".

The number of sides of a regular pentagon is n = 5.

So, the measure of each exterior angle of the regular pentagon is

= 360/n

⇒ 360/5 = 72°

Thus, the measure of each interior angle of the regular pentagon is

= 180 - 360/n

⇒ 180 - 72 = 108°

Therefore, the measure of each interior and exterior angle of a regular pentagon are 108° and 72°.

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Answer:

1/√5-√2 = −√2+√5 (-0.967)

√5-√2 = −√2+√5 (0.821854)

Subtract the answers as the decimal and/or the equation:

-0.967-0.821854 = -1.518854

As equation:

−√2+1/5√5 - √2+√5 = −2√2 + −4/5√5 (Decimal: -4.617282)

Using the unitary technique, we can determine that each tank can hold 53.65 gallons of water.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Since the tanks are equal in size then to find the volume of 1 tank

divide the total by 12

one tank  = 53.65

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Answer:

The answer is n < 14.

Step-by-step explanation:

First, we need to distribute 6, then 3 through the parentheses.

6n - 30 < 3(n + 4)

6n - 30 < 3n + 12

We now need to move the variable to the left-hand side and change its sign.

6n - 30 - 3n < 12

Next, we have to move the constant to the right-hand side and change its sign.

6n - 3n < 12 + 30

Now we need to collect like terms.

3n < 12 + 30

Then, we need to add the numbers.

3n < 42

Last but not least, we need to divide both sides of the inequality by 3. This gets us to:

n < 14

The ratio of red to blue beads.

Own bracelets: 2 : 3

New bracelets: 2 : 3

Yes, the ratio of red to blue beads of her own bracelet and the new bracelet is the same.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Julie made her own bracelet with 30 red beads and 45 blue beads.

The ratio of red to blue beads.

= 30 : 45

= 6 : 9

= 2 : 3

Now,

The new bracelets.

The ratio of red to blue beads.

= 20 : 30

= 4 : 6

= 2 : 3

We see that,

The ratio of red to blue beads of her own bracelet and the new bracelet is the same.

Thus,

The ratio of red to blue beads.

Own bracelets: 2 : 3

New bracelets: 2 : 3

Yes, the ratio of red to blue beads of her own bracelet and the new bracelet is the same.

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Answer:

D) The economy has done well for a while and is at its highest point of the cycle.

Step-by-step explanation:

I believe that it is "D" considering this is the highest point on the graph. Also the fact that, that's the only statement that makes sense for point "A".

I hope this helps!!!

Answer: C

Step-by-step explanation:

A just means that the growth of the cycle will keep increasing and will not decrease, which is wrong.

B means that point A is at its lowest point in the cycle, which is wrong too.

C is correct because before the dot that’s labeled A the growth was going down. But then point A showed the cycle growing slowly.

D is incorrect because point a isn’t the highest point, point A and point C are equal.

When a freeway is 600 miles long, its length on a map will be 6 inches, and 50 miles will be represented by 0.5 inches.

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4). The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

Here,

Length of freeway=600 miles

if 0.5 inch make 50 miles in map,

600:x=50:0.5

=0.5*600/50

=6 inch

The length of the freeway on the map will be 6 inch when it is 600 miles long and 0.5 inch make 50 miles in map.

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Answer:

mnp / 1000

Step-by-step explanation:

m%       of  p%     of  n

m/100    ·   p/100   ·   n

mnp / 1000

mpn/10000

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer: x equals to 5 over 2

Step-by-step explanation:

Answer: the answer is x=2.5

Step-by-step explanation:

4x+2=2x+7

4x+2-2=2x+7-2

4x=2x+5

4x-2x=2x-2x+5

2x=5

2x/2=5/2

x=2.5

Based on the slope formula applied, we can conclude that, the line that passes through P(9, 7) and Q(16, 2) is not perpendicular to the line that passes through  R(3, 8) and S(11, 0).

Using the slope formula, the slope of a line is calculated as:

m = change in y / change in x.

If two lines are such that one is perpendicular to the other, both lines will have slopes that are negative reciprocal to each other and will therefore have a product of -1.

For example, if the slope of a line is -1/2, the negative reciprocal of -1/2 is 2, which will be the slope of the line that it is perpendicular to.

Find the slope of PQ and RS using the slope formula:

Slope of PQ = change in y / change in x = (7 - 2) / (9 - 16) = 5/-7

Slope of PQ = -5/7

Slope of RS = change in y / change in x = (8 - 0) / (3 - 11) = 8/-8

Slope of RS = -1.

-1 is not the negative reciprocal of -5/7, this implies that both lines are not perpendicular.

Therefore, we can state that lines PQ and RS are not perpendicular to each other.

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We know that it would take Mabel 20 minutes to edit a 15-minute-long video by solving simple mathematical operations.

An operation, in maths, is a mathematical function that converts zero or more input values into a precisely defined output value.

The arity of the operation is decided by the number of arithmetic operations.

Most people seem to agree that addition, subtraction, multiplication, and division are the four basic mathematical processes.

So, what time it will take Mabel to dit a 15-minute long video:

Time to edit 15 min videos = New video * Total time taken/Length of added video

Time to edit 15 min videos = 15 * 4/3

Time to edit 15 min videos = 5 * 4

Time to edit 15 min videos = 20

Therefore, we know that it would take Mabel 20 minutes to edit a 15-minute-long video by solving simple mathematical operations.

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The statements that are true about translations will be 1, 3, 5, and 6.

A point, line, or numerical figure can be changed over in one of four ways, and each significantly affects the item's construction or potential position. Picture, after interpretation, alludes to the article's definitive association and position. Not long before the alludes to the material's underlying condition.

The translation does not change the shape and size of the geometry. But changes the location. And the orientation will remain the same.

The statements that are true about translations will be 1, 3, 5, and 6.

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Answer:

[tex]\bf r=0[/tex]

Step-by-step explanation:

[tex]\bf -2r+15=-3\left(-2r-7\right)-6[/tex]

Expand: *-3(-2r-7)-6 = 6r+15* :-

[tex]\bf -2r+15=6r+15[/tex]

Subtract 6r from both sides:-

[tex]\bf -2r+15-6r=6r+15-6r[/tex]

[tex]\bf -8r+15=15[/tex]

Subtract 15 from both sides:-

[tex]\bf -8r+15-15=15-15[/tex]

[tex]\bf -8r=0[/tex]

Divide both sides by -8:-

[tex]\bf \cfrac{-8r}{-8}=\cfrac{0}{-8}[/tex]

[tex]\bf r=0[/tex]

__________________

Hope this helps you!

Have a good day!

Answer:

r=0

Step-by-step explanation:

-2r+15=-3(-2r-7)-6

-2r+15= 6r+21-6

-2r+15=6r+15

-6r.     -6r

-8r+15=15

    -15.  -15

-8r=0

/-8. /-8

r=0

hopes this helps

The equations that represent the hanger are -

x + x + x = 1 + 1 + 1 + 1 + 1 + 1 and 3x = 6.

Given are the expressions as given in the question.

The equations that represent the hanger are -

x + x + x = 1 + 1 + 1 + 1 + 1 + 1

and

3x = 6

Therefore, the equations that represent the hanger are -

x + x + x = 1 + 1 + 1 + 1 + 1 + 1 and 3x = 6.

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Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.

Which percentage does that mean?

A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total.

                       The proportion therefore refers to a component per hundred. Percent signifies for every 100. The letter "%" stands for it.

In this problem, researching in the internet, it is found that:

A total of 1260 + 650 + 180 = 2090 people were surveyed.

Of those, 1260 were completely satisfied.

Hence

      P = 1260/2090 * 100%  = 20.29%

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The total value of the account after 4 years is; $8800.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

We have given Principal = P = $8,000

Rate = R = 2.1%

Amount = A

Time = 4 years

Simple Interest = (P x R x T) / 100

= (8000 x  2.1 x 4 ) / 100

= 800

Amount = Simple interest + Principal

A = 800 + 8000

A = 8800

Thus, The total value of the account after 4 years is; $8800.

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Answer:

d) 3 km, and the Mariana Trench is deeper

Step-by-step explanation:

The Mariana Trench is, so to speak, -11 km while the Peru-Chile Trench is -8 km (because they are both below sea level).

For determining the difference between the two, you have to understand that they're both negative, and there is a 3 km difference between -11 and -8. Subtracting a negative makes a positive.

(-8) - (-11) = 3

Since the Mariana Trench is more kilometers below sea level, it's deeper.

Answer: The answer is 48          

Step-by-step explanation:

(60*100)/125=48

The 100 percent is 48 and the 125 percent of 48 is 60 .

Answer:

48

Step-by-step explanation:

"What is 60 is 125% of"

Put this sentence into an expression.  The wording is awkward in the question.  " . . is 60 is 125% of" is not a complete sentence.   I believe it is asking what number results in 60 when we take 125% of it.  I'll rephrase it as "125% of what number is 60."  Please check my logic on this interpretation.

Write this as an expression, using N for the unknown "number:"

 125% (N) = 60

(1.25N) = 60

N = 60/1.25

N = 48

125% of 48 is 60  

Answer:

1/16IB

Step-by-step explanation:

Differnce means to subtract which means we need to subract the two fractions. First find the the lowest of common factor for both fractions. In this case it is 16 because 4 can go into 16 four times as 4x4=16.

Since we know that 4 goes into 16 four times we get the 4 and then multiply it by the numerator (the top number of the fraction) for the fracion 1/4. Now the fraction 1/4 is 4/16. Keep the 3/16 the same as the denominator  (bottom number of fraction) is already our common factors between the two fractions.

Work Shown:

Orginal Equation: 1/4-3/16

Get common Denomiantors: Convert 4 to 16. 4 goes into 16 four times, multiply by 4 by numerator. 4X1=4.

Final Step: Since both are now common fractions just subtract the numerators keeping the denominators the same of the fractions.

4/16-3/16= 1/16

Final Answer: 1/16IB

Check the picture below.

Answer27.1

Step-by-step explanation: c=a^2+b^2 =4.1^2+23^2=27.1

Answer:

4.45

Step-by-step explanation:

This is a transversal question (look at attached). Because the lines are parallel, g will equal to 180(a straight line is 180 degrees is 53 degrees

What is transversal?

A transversal is a line in geometry that connects two lines in the same plane at two different places. When determining whether two or more other lines in the Euclidean plane are parallel, transversals are important.

This is a transversal question (look at attached). Because the lines are parallel, g will equal to 180(a straight line is 180 degrees) - a. Then, because g + f + e = 180 (since it is a straight line), substitute the values that we know and solve. (61) + f +(66) = 180. f = 53

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Answer: alfredo sauce

Step-by-step explanation:

Walnut bread will take about 30-45 minutes to cook

Alfredo sauce will take about 10-15 minutes to make

On solving the question, we got that - The dimensions of the rug should be 18 feet and 24 feet

By multiplying the rectangle's length by its breadth, we may get its area.

Equiangular quadrilaterals, like rectangles, are known in this way. This is so because a rectangle is a four-sided quadrilateral shape with parallel sides that are equal to one another and four corners with 90o angles. Rectangles are sometimes known as equiangular quadrilaterals since all of its angles are 90 degrees.

the parameters provided;

The room is 20 feet by 26 feet in size.

432 feet2 is the largest area rug she can afford.

If the floor will be a uniform stripe around the rug, then each dimension should have its uniform extra length of floor =  (y).

[tex]Area = Length X Width\\432 = ((20=y) X (26-y)\\432 = 520 - 20y - 26y + y^2\\y^2 - 46y+88=0\\[/tex]

here, a= 1, b= -46, c =88

[tex]y = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\[/tex]

[tex]y = \frac{-(-46) +/- \sqrt{(-46)^2 - 4X1X88} } {2} \\\\y = 44 \\or\\ y = 2[/tex]

Therefore, Length = 20-2 = 18 ft

and width = 26-2 = 24ft

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Yes. The duration of the ride can be represented as a function of the time Jayden got on the bus.

We have given that,

Time (minutes)           18  20  20  22  22  23  25  30

Duration (minutes)    38  40  42   41   42  44  47   52

As we can see the duration of the ride seems to increase as the amount of time after 8 am that Jayden got on the bus.

This means that the duration of the ride and the time Jayden got on the bus have the linear relationship.

Therefore the duration of a ride can be represented as a function of the time Jayden got on the bus.

Following are the function of a time:

s(t) = distance a particle travels from tome 0 to t.

v(t) = velocity of a particle at time t.

a(t) = acceleration of a particle at time t.

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Answer:

55.92

Step-by-step explanation:

[tex]f(x)[/tex] doesn't depend on x.