the local music activities coordinator sold 300 tickets to the orchestra concert. student tickets were $4 and adult tickets were $6. if the total sales were $1,600 how many student tickets were sold

The expression for distance AB is :389 tan 88.60°. The angle D is 88.35°.The value of angle CAD in radians is 0.0532 rad.

Step-by-step explanation:

Given the information, you can sketch triangle ACB with ∠C=88.60° and a perpendicular bisector of segment CD as AB that forms 90° at B where the diatnace from C to B given as 389 ft you can find the length of the perpendicular bisector AB which is the distance between tower A and B.

Apply the tangent of an angle rule, where tangent of angle = opposite side length/adjacent side length

tan 88.60°=O/A

tan 88.60°=AB/389

AB=389 tan 88.60° = 15916.87 ⇒ 15917 (nearest foot)

B.

Given distance BD as 459 ft and the distance between tower A and B as 15917 ft you can calculate the value of angle ∠D by applying the tangent of an angle formula.

tan Ф=O/A where Ф=∠D

tan ∠D =15917/459

tan ∠D =34.6772834701

tan⁻(34.6772834701) =88.35°

C.

Finding angle ∠A in radians will be;

Applying the sum of angles in a triangle theorem

∠A=180°-(88.60°+88.35°) = 180°-176.95°=3.05°

Changing degrees to radians, multiply value of degrees by π/180°

3.05×π/180 =0.05323254 ⇒ 0.0532 rad

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Keywords : horizontal distance,towers, elevation, perpendicular line, distance, equation, expression,hundredth

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Answer:

Step-by-step explanation:

Later area of Pyramid =  2 * 1/2 * 9 * 12.3  + 2*1/2*11*11.9

                                     = 9*12.3 + 11*11.9

                                      =  110.7 +130.9

                                      = 241.60 sq.feet

Answer:

Infinitely many solutions

Step-by-step explanation:

the 5x's cancel and -15 + 6 = -9 so -9 equals -9. No matter what value you input for x, the answer is equal.

Answer:

Infinitely  many.

Step-by-step explanation:

5(x - 3) +6= 5x - 9

5x - 15 + 6 = 5x - 9

5x - 9 = 5x - 9.

We can enter any real value of x and both sides will be equal so there are infinitely many solutions.

Answer: 0

Step-by-step explanation: The answer would be 0 since if y = -4, the graph of the line would just be a horizontal line through the point (0,-4). This would be like saying that y = 0x-4. Hope this helped!

Answer:

slope = 0

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through.

y = - 4 ← is therefore a horizontal line

with slope = 0

Answer:

The volume of the larger solid is [tex]592.6\ mm^3[/tex]

Step-by-step explanation:

The question is

If these solids are similar, find the volume of the larger solid

step 1      

Find the scale factor

we know that

If two solids are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

x ----> the height of the larger solid in mm

y ----> the height of the smaller solid in mm

z ---> the scale factor

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=4\ mm\\y=3\ mm[/tex]

substitute

[tex]z=\frac{4}{3}[/tex] ---> scale factor

step 2

Find the volume of the larger solid

we know that

If two solids are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

x ----> the volume of the larger solid in cubic millimeters

y ----> the volume of the smaller solid in in cubic millimeters

z ---> the scale factor

[tex]z^3=\frac{x}{y}[/tex]

we have

[tex]z=\frac{4}{3}[/tex]

[tex]y=250\ mm^3[/tex]

substitute the values

[tex](\frac{4}{3})^3=\frac{x}{250}[/tex]

solve for x

[tex](\frac{64}{27})=\frac{x}{250}[/tex]

[tex]x=250(\frac{64}{27})[/tex]

[tex]x=592.6\ mm^3[/tex]

Answer:

25. rational

26. irrational

Step-by-step explanation:

A rational number is a number that can be written as a fraction. It may have decimals that end or repeating decimals.

An irrational number cannot be written as a fraction. It's decimals continue on and do not repeat.

25.

When you multiply two rational numbers, the product is rational. The square root of 16 is 4, which is rational because it is a whole number. 4/7 is written as a fraction so it is rational.

26.

The square root of 2 is an irrational number because its decimals go on and do not repeat. 7 is a whole number so it is rational. Subtracting a irrational number from a rational number gives an irrational number.

Answer:

4/3 is 1.3333333333,so the range of it is that

Answer:

I have no idea

Step-by-step explanation:

Final answer:

The value of 17 tens can be written in standard form as 170, in expanded form as (1 × 10²) + (7 × 10¹), and in unit form as '1 hundred 7 tens 0 ones'.

Explanation:

When asked to write the value of 17 tens three different ways, we first recognize that '17 tens' is essentially the number 170, since 17 tens are 17 multiplied by 10.

Standard Form

The standard form is simply writing the number as it is, so in this case, it would be 170.

Expanded Form

The expanded form breaks down the number into its place value components. Since 170 comprises 1 hundred, 7 tens, and 0 ones, it can be written as:
(1 × 10²) + (7 × 10¹) + (0 × 10°)

Unit Form

Last, the unit form expresses each digit's value according to its place value, which for 170 is '1 hundred 7 tens 0 ones'.

What numbers??? You need to either add a picture or just write the numbers

Answer:

The Two Column Proof is given below.

Step-by-step explanation:

Given:

[tex]\overline{MP} \cong \overline{MN}[/tex]

[tex]\overline{PO} \cong \overline{NO}[/tex]

To Prove:

∠ P ≅ ∠ N

Proof:

In  Δ MPO  and Δ MNO

STATEMENT                                              REASONS  

1. MP ≅ MN                                   1. Given

2. PO ≅ NO                                  2. Given

3. MO ≅ MO                                 3. Reflexive property

4. ΔMPO ≅ ΔMNO                       4. Side-Side-Side congruence test}

5. ∠MPO ≅∠MNO                        5. Corresponding parts of congruent Triangles

i.e ∠ P ≅ ∠ N                                 ..................Proved

Answer: at new cost increase is 30%

               after additional $4.50 fee  increase  would be 45%

Step-by-step explanation:

use equation

30:100=39:x

30x=3900

x=3900/30

x=130

130-100=30%

39+4.50=43.5

30:100=43.5:x

30x=4350

x=4350/30

x=145

145-100=45%

The increase percent will be 30%

And, The percent increase if the ticket agent charges an additional​ $4.50 fee with the new ticket​ price is 45%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The old cost of the tickets = $30

And, New cost of the ticket = $39

Now,

The increase percent is calculate as;

Increase percent = (39 - 30) / 30 x 100

                           = 9/30 x 100

                           = 30%

And, When the ticket agent charges an additional $4.50 fee with the new ticket price.

Then, The new cost of the tickets = $39 + $4.50

                                                    = $43.50

Thus, The percent increase if the ticket agent charges an additional $4.50 fee with the new ticket price is calculated as;

Increase percent = (43.50 - 30) / 30  x 100

                          = 13.50/30  x 100

                          = 45%

Therefore, The increase percent will be 30%.

And, The percent increase if the ticket agent charges an additional​ $4.50 fee with the new ticket​ price is 45%.

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Answer:

The initial value of the function is 3.

The range of the function is y > 0.

The simplified base value of the function is 8.

Step-by-step explanation:

The given function is [tex]f(x) = 3(16)^{\frac{3}{4}x }[/tex]

Therefore, the simplified function will be [tex]f(x) = 3(16^{\frac{3}{4} } )^{x} = 3(8)^{x}[/tex] ........ (1)

Now, at x = 0, f(x) = 3.

Hence, the initial value of the function is 3. (Answer)

The value of x in the equation (1) can be any real value but for any value of x, the f(x) value will be greater than 0.

Hence, y > 0 that is the range that the function has. (Answer)

Again, from equation (1) we get the simplified base value of the function is 8. (Answer)  

Answer:

A, C, E

Step-by-step explanation:

Egde 2020

Answer:

[tex]k=\frac{32}{5}[/tex],  [tex]y=\frac{32}{5}x[/tex]

[tex]k=6.4[/tex], [tex]y=6.4x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

Find the value of the constant of proportionality k

take any ordered pair from the data

For x=25, y=160

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{160}{25}[/tex]

simplify

[tex]k=\frac{32}{5}[/tex]

The linear equation is equal to

[tex]y=\frac{32}{5}x[/tex]

or

[tex]y=6.4x[/tex]

1. Is the actual equation, so this is Given

2. removing the parenthesis is the Distributive Property

3. Combining like terms.

4. They add 6x to both sides, this would be the Addition Property of Equality

5. Subtract 4 from both sides, this is the Subtraction Property of Equality.

6. Divide both sides by 8, this would be the Division Property of Equality.

Answer:

1. Given

2. Distributive property

3. Combining like Terms

4. Addition property of Equality

5. Subtraction property of equality

6. Division Property of Equality

A.

(0, 2) , (1,2) , (2,3) , (1,4) , (3,1)

Answer:

A.

(0, 2) , (1,2) , (2,3) , (1,4) , (3,1)

Thats the correct answer.

Answer:

(x − 5) (x + 4)

Step-by-step explanation:

x² − x − 20

Factor using AC method:

1 × -20 = -20

Factors of -20 that add up to -1: -5 and 4

Divide by 1 and reduce: -5/1 and 4/1

(x − 5) (x + 4)

Answer:

[tex]\displaystyle [x + 4][x - 5][/tex]

Step-by-step explanation:

Find two quantities that when differed to −1, they also multiply to −20, and those numbers are 4 and −5.

I am joyous to assist you anytime.

Answer:4

Step-by-step explanation: since he has 24

Yaneliz has 24 X 1/6 = 4

Answer: y = 24 x 1/6

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

Marcos: $24

Yaneliz: 1/6 of the amount of money Marcos has

So, to write an expression we have to multiply the amount of money Marcos has (24) by 1/6.

Mathematically speaking

Y = 24 x 1/6  

Where "y" is the amount of money Yaneliz has.

Solving:

24 x 1/6 = 4

Yaneliz has $4.

Feel free to ask for more if needed or if you did not understand something.

Answer:

20748

Step-by-step explanation:

546 times 38

Answer:

Step-by-step explanation:

sales - expenses = profit

lets x represent number of shirts sold

12x - (3x + 150) > = 300

12x - 3x - 150 > = 300

9x - 150 > = 300

9x > = 300 + 150

9x > = 450

x > = 450/9

x > = 50 <== they would need to sell at least 50 shirts

In order to find \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \), we need to replace every instance of \( x \) in the function with \( x+h \). Here are the steps to do so:

1. Write down the original function:
  \( f(x) = \fraction{x²}{x+3} \)

2. Substitute \( x+h \) for \( x \) in the function to get \( f(x+h) \):
  \( f(x+h) = \fraction{(x+h)²}{(x+h)+3} \)

3. Now expand the numerator and simplify the expression:
  \( (x+h)² = x² + 2xh + h² \)
  Therefore, \( f(x+h) = \fraction{x² + 2xh + h²}{x+h+3} \)

That is the expression for \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \). Note that you could further simplify the expression depending on the context or the specific question asked, but as it stands, this is the correct substitution and form of \( f(x+h) \).

Answer:

Step-by-step explanation:

The complete question is

A scale factor of 1/3 is used to make a reduction, as shown in table below.

What is the base of the reduced triangle?

According to the given table, the original base is 24. If the given scale factor is applied, the reduced base would be

[tex]\frac{1}{3}24=8[/tex]

Remember that a scale factor is a number that multiples the figure, a scale factor can reduced or amplify a figure.

Therefore, the reduced base is 8 units.

Answer:

8 units

Step-by-step explanation:

Answer:

The value of x is 3 ,

The measure of each side is 55 units .

Step-by-step explanation:

Given as :

The sides of the equilateral Triangle are pq , qr , pr

The measure of side pq = 18 x + 1

The measure of side qr = 24 x - 17

The measure of side pr = 15 x + 10

∵ The triangle is equilateral then all sides are equal

i.e pq = qr = pr

So, 18 x + 1 = 24 x - 17

Or, 24 x - 18 x = 17 + 1

Or, 6 x = 18

∴  x = [tex]\dfrac{18}{6}[/tex]

i.e x = 3

So, Putting the value of x

The measure of side pq = 18 × 3 + 1 = 55 unit

The measure of side qr = 24 × 3 - 17 = 55 unit

The measure of side pr = 15 × 3 + 10 = 55 unit

Hence The value of x is 3 ,

And The measure of each side is 55 units . Answer

Answer:

x = 3.

Measure of each side is 55 units.

Step-by-step explanation:

In an equilateral triangle, the length of all the three sides are equal.

Therefore, Side PQ = QR = PR.

⇒ 18X + 1 = 24X - 17

⇒ 24X - 18X = 18

⇒ 6X = 18

⇒ X = 3

Substituting the value of X, we get:

PQ = 18(3) + 1 = 55 Units.

QR = 24(3) - 17 = 55 units.

PR = 15(3) + 10 = 55 units.

We see the length of all the sides are equal.

The sum of slopes b and c is 0

This statement is NOT always true

Step-by-step explanation:

(1) According to the graph, line a and b are parallel to each other. This, therefore, means that they have the same slope/gradient.

(2) Line c however, is perpendicular to both lines a and b. The slope of two lines that are perpendicular to each other is always the negative inverse of the slope of the other. This means that the product of their slopes will become -1.

An example is that if the slope of a line is 2, then a line perpendicular to it will have a slop of – ½

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Answer:

The sum of the slopes of line b and line c is 0

Step-by-step explanation:

Verify each statement

case a) The sum of the slopes of line b and line c is 0

we know that

Line b and line c are perpendicular lines

If two lines are perpendicular, then their slopes are opposite reciprocal

If the slope of line c is n

then the slope of line b is -1/n

[tex]-\frac{1}{n}+n=0[/tex]

Solve for n

[tex]n^{2}=1[/tex]

[tex]n=\pm1[/tex]

That means -----> This statement is true only when the slopes of the perpendicular lines are 1 and -1

therefore

NOT always true

case b) Line a and line b have the same slope

This statement is always true, because the lines are parallel

Remember that

If two lines are parallel, then the lines have the same slope

case c) The product of the slopes of line a and line c is -1

This statement is always true, because the lines are perpendicular

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

case d) The product of the slopes of line c and line b is -1

This statement is always true, because the lines are perpendicular

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

Final answer:

To form the quadratic equation, we consider the original time to cover 6 km at speed v km/h and the new time at speed (v+2) km/h, then equate the difference in time to 4 minutes. Solving for v using a common denominator and simplifying, we obtain the quadratic equation 15v^2 + 30v - 90 = 0.

Explanation:

To form a quadratic equation from the given scenario, we’ll first define the relationship between distance, speed, and time. The time taken to travel 6 km at the original speed v km/h is distance divided by speed, which is 6/v hours. If Wanni increased her speed by 2 km/h, her new speed would be v + 2 km/h, and the new time taken would be 6/(v+2) hours.

We are told that by increasing her speed, Wanni arrives 4 minutes earlier. Since 1 hour is 60 minutes, 4 minutes is 4/60 or 1/15 hours. We can now set up an equation relating the difference between the two times to 1/15 hours:

6/v - 6/(v+2) = 1/15

To solve for v, we first find a common denominator for the fractions on the left side of the equation, which is v(v+2). Multiplying both sides by the common denominator, we get:
6(v+2) - 6v = v(v+2)/15

Expanding the terms and moving everything to one side of the equation, we get our quadratic equation in terms of v:

15v2 + 30v - 90 = 0

Question:

Ming took a cab across town. His fare was $22 and he leaves an 18%, percent tip. What is the total amount Ming pays the cab driver?

Answer:

Ming pays the $25.96 to cab driver

Step-by-step explanation:

Given:

the fare of the car =  $22

Percentage of tip paid by the Ming = 18%

To Find:

Total amount Ming pays the cab driver=?

Solution:

The total amount of the tip paid by the Ming to the cab driver be x

then

x = car fare + 18% of cab fare

substituting the values we get

x = 22 + 18% of 22

x = 22 +  [tex]\frac{18}{100} \times 22[/tex]

x = 22 +  [tex]\frac{18}{100} \times 22[/tex]

x = 22 +  [tex]0.18 \times 22[/tex]

x = 22 + 3.96

x = 25.96

Answer:

The new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).

i.e. [(-4,0)→(4,0)]

Step-by-step explanation:

The rule for rotation a point 180° counterclockwise about the origin states that when a point (x, y) is rotated 180° counterclockwise about the origin, the new position of the coordinates of point P(x, y) becomes (-x, -y).

Hence,

So, when the given point  (-4,0) is rotated 180 degrees counterclockwise using center (0,0), the new coordinates of the image will be:

Therefore, the new coordinate of the image will be (4, 0) when the point (-4,0) is rotated 180 degrees counterclockwise using center (0,0).

i.e. [(-4,0)→(4,0)]

Keywords: rotation, origin, image

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x+y≤525 and 9x+5y≤1200 represents the scenario.

Step-by-step explanation:

Given,

Room for people at summer camp = 525 people

Maximum budget = $1200

Cost per adult = $9

Cost per camper = $5

It means that there cannot be spent more than $1200.

x represents the number of adults.

y represents the number of campers.

x+y≤525      

9x+5y≤1200

x+y≤525 and 9x+5y≤1200 represents the scenario.

Keywords: inequality, budget

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Answer:  

x+y≤525      

9x+5y≤1200

Step-by-step explanation:

Answer:

13/14 is greater

Step-by-step explanation:

Find the lcm for both:

9 x 7     = 63

10 x 7        70

13 x 5    = 65

14 x 5        70

so therefore 13/14 is greater since it has a greater value when finding the lcm