The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $5 and each adult ticket sells for $8. The auditorium can hold at most 150 people. The drama club must make at least $960 from ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.

Inequality 1:
inequality 2:

graph


The drama club could sell ----
student tickets and ----
adult tickets.

Answer:

3(7) + 2* |7 - 8| - 12 = 11

Step-by-step explanation:

3(7) + 2* |7 - 8| - 12

21 + 2* |-1| - 12

21 + 2* 1 - 12

21 + 2 - 12

23 - 12 = 11

Hope this helps! :)

The solutions to the absolute value equations are given as follows:

1. k = -8 or k = 8.

2. x = -7 or x = 7.

3. a = -10 or a = 6.

4. a = -2.5 or a = 2.5.

5. m = -4 or m = 22.

6. x = -4 or x = 6.8.

7. x = -16 or x = 9.

8. a = -2.4 or a = 1.2.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

This means that there are two possible solutions for the equation |x| = a, which are:

x = a or x = -a.

The equation is:

|k| = 8.

Applying the definition of the absolute value function, we have that the possible solutions are:

k = -8 or k = 8.

The equation is:

|x| = 7.

Applying the definition of the absolute value function, we have that the possible solutions are:

x = -7 or x = 7.

The equation is:

|a + 2| = 8.

The possible solutions are that the inside term can be equals to either -8 or 8, hence:

The equation is:

|8a|/10 = 2

In standard format, the equation is:

|8a| = 20

Then the solutions are:

The possible solutions are:

The possible solutions are:

Applying cross multiplication, the expression is:

|2x + 7| = 25

The possible solutions are:

Applying cross multiplication, the expression is:

|-3 -5a| = 9.

The possible solutions are:

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Answer: 5 units

Step-by-step explanation:

\((1,2)\ \ \ \ \ \ (5,5)\ \ \ \ \ L=?\\\\L=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\x_1=1\ \ \ \ \ x_2=5\ \ \ \ \ y_1=2\ \ \ \ \ y_2=5\\\\L=\sqrt{(5-1)^2+(5-2)^2} \\\\L=\sqrt{4^2+3^2}\\\\L=\sqrt{16+9} \\\\L=\sqrt{25} \\\\L=5\ units\)

Answer:

I think it's 1.67 miles

Step-by-step explanation:

24:40    

1 /24 = x/40

24x/24 = 40/24

1 = 1.67 miles

I hope this helps?

For every 1 mile Annabelle drove, Daniel drove 1.67 miles.

I may be wrong.

Probably am...

The output value of f( -3 ) in the function f(x) = x³ + 3x + 17 is -19.

Given the function in the question:

f(x) = x³ + 3x + 17

To evaluate f(-3) for the function f(x) = x³ + 3x + 17, we simply substitute -3 for x in the expression and calculate the result.

f(x) = x³ + 3x + 17

Plug in x = -3

f(-3) = (-3)³ + 3(-3) + 17

First, let's calculate (-3)³, which means raising -3 to the power of 3:

(-3)³ = -3 × -3 × -3 = -27

Next, let's calculate 3(-3):

3(-3) = -9

Now, we can substitute these values into the expression:

f(-3) = -27 + (-9) + 17

Simplifying further:

f(-3) = -27 - 9 + 17

f(-3) = -36 + 17

f(-3) = -19

Therefore, the output value of f(-3) is -19.

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9514 1404 393

Answer:

  55 -2t cars

Step-by-step explanation:

The amount raised is the difference between the revenue and expenses. If c cars and t trucks are washed for a profit of $460 after expenses of $90, the equation can be written ...

  460 = 10c +20t -90 . . . profit equation

  550 = 10c +20t . . . . . . . add 90

  550 -20t = 10c . . . . . . . subtract 20t

  c = 55 -2t . . . . . . . . . . . divide by 10

They have to wash 55-2t cars if they washed t trucks.

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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The gallons of ice cream 4 machines can make is 650 gallons.

Two ice cream machines make a total of 320 gallons in a certain amount of time.

Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:

Therefore,

If 2 ice cream machine = 320 gallons

4 ice cream machine = ?

cross multiply

Hence,

gallons of ice cream made by 4 machines = 320 × 4 / 2

gallons of ice cream made by 4 machines = 1280 / 2\

Therefore,

gallons of ice cream made by 4 machines = 640 gallons

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Answer:

89

Step-by-step explanation:

Answer:

Hence, the smallest interior angle of this octagon is 100

Step-by-step explanation:

Final answer 100

Answer:

A and d

Step-by-step explanation:

because x has a 1 in front of them so add the 3'x and get 3x+2

Using trigonometric ratio, the height of the tree is 70 feet

The angle of elevation is the angle between the horizontal plane and the line of sight when an observer looks upward to see an object. It is typically measured in degrees and is used in geometry and trigonometry to calculate the height of an object or the distance between two objects.

Using trigonometric ratio, we can use the tangent of the angle to find the height of the tree.

tan θ = opposite / adjacent

tan 70 = x / 25

x = 25tan70

x = 68.7 ft≅ 70 feet

The height of the tree is 70 feet

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Answer:

2 19/24 is the simplified answer

Step-by-step explanation:

Hope this helped! :)

Cell notation uses the simplest form of each of the equations, and starts with the reaction at the anode. It is necessary to use an inert electrode, such as platinum, because there is no metal present to conduct the electrons from the anode to the cathode. No concentrations were specified so:

Cell notation uses the simplest form of each of the equations, and starts with the reaction at the anode. It is necessary to use an inert electrode, such as platinum, because there is no metal present to conduct the electrons from the anode to the cathode. No concentrations were specified so:

Cell notation uses the simplest form of each of the equations, and starts with the reaction at the anode. It is necessary to use an inert electrode, such as platinum, because there is no metal present to conduct the electrons from the anode to the cathode. No concentrations were specified so:

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Answer:

54 and 47

Step-by-step explanation:

Lets first number be "x" and second number be "y"

x = y + 7

x + y = 101

(y + 7) + y = 101

2y + 7 = 101

2y = 94

y = 47

x = 47 + 7

x = 54

Answer:

240 feet

Step-by-step explanation:

The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

---------------------------------------------------------

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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Answer:

Step-by-step explanation:

5x = 12x - 20

5x - 12x = -20

-7x = -20

x = 20/7

\(x = \frac{20}{7} \\ \\ x = 2 \frac{6}{7} \).

Step-by-step explanation:

\(5x = 12x - 20\)

Collect like terms and simplify

\(5x - 12x = - 20 \\ - 7x = - 20\)

Divide both sides of the equation by -7

\( \frac{ - 7x}{ - 7} = \frac{ - 20}{ - 7} \)

Simplify

\(x = \frac{20}{7} \\ \\ x = 2 \frac{6}{7} \)

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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In the given similar triangles below, we have to find the measure of Dwrite. Triangle 1, ABC, is similar to Triangle 2, DEF. The two triangles are similar because their corresponding angles are congruent and their sides are proportional.

In order to find the measure of Dwrite, we can use the concept of proportionality. The sides of similar triangles are proportional to each other.

This means that if we know the ratio of the sides of one triangle, we can use that ratio to find the corresponding sides of the other triangle. We can use this property to find the value of Dwrite.

To start, let's write down the ratio of the sides of Triangle 1 and Triangle 2. We can choose any two corresponding sides to do this, but we'll choose AB and DE because they are easiest to measure: AB/DE = 6/8.5We know that the measure of AB is 6, so we can solve for the measure of DE: DE = AB x (DE/AB)DE = 6 x (8.5/6)DE = 8.5Now we know that the measure of DE is 8.5.

We can use this to find the measure of Dwrite. We know that DE and Dwrite are corresponding sides of Triangle 2 and Triangle 1, respectively.

So we can write a proportion using the ratio of DE to Dwrite: DE/Dwrite = 8.5/xWe know that DE is 8.5, so we can substitute that in:8.5/Dwrite = 8.5/Now we can solve for x by cross-multiplying:8.5x = 8.5Dwrite = 1Therefore, the measure of Dwrite is 1.

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Answer:

x >= 9

x <= 32

x > -24

x > -5

x <= 10

x > -6

Step-by-step explanation:

first, write it down as inequalities:

5x >= 45

x/4 <= 8

x/-3 < 8

7x > -35

x/2 <= 5

3x > -18

then, solve the inequalities

5x >= 45

x >= 45/5

x >= 9

x/4 <= 8

x <= 8*4

x <= 32

x/-3 < 8

x > 8 * -3

x > -24

7x > -35

x > -35/7

x > -5

x/2 <= 5

x <= 5*2

x <= 10

3x > -18

x > -18/3

x > -6

The inequality is x < -1

An inequality is a mathematical statement that represents the relation between two expressions that are not equal.

Symbol used to denote inequalities are signs such as

≠ ‘not equal to’,

> ‘greater than’,

< ‘less than’

≥ ‘greater than or equal to’

≤ ‘lesser than or equal to’

From the given diagram, the circle is resting at -1 but the circle is not shaded. This means that -1 is not included in the inequality.

Furthermore, the arrow is pointing towards the left side of the number line which means only numbers lesser than -1 (towards the left of -1) are included. Therefore, the inequality is

x < -1

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Answer:

2580 seconds

Step-by-step explanation:

There are 60 seconds in 1 minute, so you do 43 * 60 = 2580 seconds

Hello!

The best way to solve this is to replace X for Y, and Y for X.

---------------------------------------------

A sample problem to help:

4x +8 = y  

4y +8 = x  (switched X and Y)

Y + 8 = 1/4x (solve for Y)

-8            -8

y = 1/4x -8

(now your almost done, since this is function, we need to change y to be f(x))

f(x) = 1/4 - 8

---------------------------------------------

Now that you have a basic understanding, let's do the ones you listed!

We are looking to see if the equations are inverses of the equation.

---------------------------------------------------------------------------------------------

1. f(x) = 2/3x - 7         g(x) = 3/2x + 7

First: You use equation f(x), and change f(x) to y:

y = 2/3x - 7

Next: You switch x and y:

x = 2/3y - 7

Now solve for y.

x = 2/3y - 7

+7            +7

x + 7 = 2/3y

\(*\frac{3}{2}\)       \(*\frac{3}{2}\)

y = \(\frac{3}{2}x\) + 5

(Set it to f(x) )

f(x) = \(\frac{3}{2}x\) + 5

Now look to see if it matches with the second equation.

f(x) = \(\frac{3}{2}x\) + 5     g(x) = 3/2x + 7

It doesn't, so it is not the inverse of each other.

---------------------------------------------------------------------------------------------

2. f(x) = -2x - 1           f(x) =-1/2x - 1/2

First: You use equation f(x), and change f(x) to y:

y = -2x - 1

Next: You switch x and y:

x = -2y - 1

Now solve for y.

x = -2y - 1

+1        +1

x + 1 = -2y

/-2   /-2

-1/2x + 1/2 = y

(Set it to f(x) )

f(x) = -1/2x + 1/2

Now look to see if it matches with the second equation.

f(x) = -1/2x + 1/2          f(x) =-1/2x - 1/2

It does, so it is the inverse of each other.

---------------------------------------------------------------------------------------------

3. f(x) = \(\frac{x+1}{2}\)               g(x) = 2x - 1

First: You use equation f(x), and change f(x) to y:

y = \(\frac{x+1}{2}\)

Next: You switch x and y:

x = \(\frac{y+1}{2}\)

Now solve for y.

x = \(\frac{y+1}{2}\)

*2    *2

2x = y + 1

-1        -1

y = 2x - 1

(Set it to f(x) )

f(x) = 2x - 1

Now look to see if it matches with the second equation.

f(x) = 2x - 1     g(x) = 2x - 1

It does, so it is the inverse of each other.

---------------------------------------------------------------------------------------------

#Team Trees #Team Seas #PAW #Spread_Positivity

I hope this helps,

-Oceanbreeze24

Answer:

b = √(m+g²)/4f

Step-by-step explanation:

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

Helping in the name of Jesus.

Answer:

\(y = \frac{ - 3 + 4x}{3} \)

Step-by-step explanation:

You can't do much except to move everything to the right side. Which basically will solve for y. If you have the value of x, you can plug into x and you'll get the value for y. Therefore, y is solved

Answer:

65/100 that is the answer to this question