For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each. The sellers collected $3,570 from 512 tickets sold. If c is the number of student tickets sold, which equation can be used to find the amount of tickets sold of each type?
10(512 – c) + 5c = 512
10(512 – c) + 5c = 3,570
5(512 – c) + 10c = 3,570
5(512 – c) + 10c 512

Answer:   " 7√6 " .

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                →   The answer is:  " 7√6 units " .

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Step-by-step explanation:

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Method 1:

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This will be a "45-45-90" triangle;

which means that in:

(two sides for triangle will be the same).

which is consistent with the information give:

(the two side of the triangle are sides of a "square" ,

 and ALL sides of a square have the "square length" ;

and one side with be 90 degrees (a right triangle);

and the other angles will be 45 degrees (which is 1/2 of 90 degrees because the will cut into "1/2" of each of the "two other 90 degree angles" when a diagonal is drawn to form the "hypotenuse".

So, for "45-45-90" triangles, the side lengths, are:  

     "x, x, x√2 " ;  in which "x√2" represents the side length of the "hypotenuse" ;  and the two "x" values represent the equal values for the other 2 (two) side lengths.,

We are asked to find the "diagonal" of the square;  in which:  "x = 7√3" ;

 That is, we are ask to find the hypotenuse:  "x√3"  ;

 Note:  We are given:  " x = 7√3 " ;

So:  " x√3 " =  " 7 *√3 *√2 = 7 *√6 = " 7√6 ".

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The answer is:  " 7√6 units " .

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Method 2:

__________________________________________________

Use the Pythagorean theorem (for right triangles):

 "  a² + b² = c² " ;  

      in which: "c" represents the "side length" of the "hypotenuse" ;

                or:  the "diagonal" of the "square" ; for which we shall solve.

                      "a" and "b" represent the other sides of the right triangle.

                     In this case, "a" and "b" are equal;

                            since "a" & "b" are the side lengths of a square.

                    We are given:  a = b = " 7√3 " .

                      We are to find "c" .

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"  a² + b² = c²  " ;  

↔   " c²  = a² + b²  " ;

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 →  c²  = (7√3)² + (7√3)²  ;

 →  c²  = (7²) * (√3)² + (7²) (*√3)²  ;

 →  c²  = ( 49*3)    +  (49*3) ;

 →  c²  = (147) + (147) ;

 →  c²  = 294 ;

Take the "positive" square root of each side of the equation;

    to solve for "c" ;

 →  ⁺ √(c²) = ⁺ √294 ;

→  c = ⁺ √294

⁺ √294 =  ⁺ √3 ⁺ √98 ;

                         →   √98 = ⁺ √49⁺ √2 ;

⁺ √294  =  7√3√2  =  7√6 .    

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  c = 7√6

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The answer is:  " 7√6 units " .

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The values obtained by using "both" methods/ match!

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Hope this helps!

 Best wishes in your academic pursuits

          — and within the "Brainly" community!

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Answer:

The function is:

21000 * (1 - [tex]\frac{16}{100}[/tex])[tex]^{n}[/tex]

The price after 3 years would be D) $12,447

Step-by-step explanation:

Because the value is depreciating, the price will decrease.

The function formula is:

Amount x (1 ± [tex]\frac{percentage}{100}[/tex])[tex]^{n}[/tex]

Where n is the amount of years and the ± is a + if the value is increasing, and a - if the value is depreciating.

So plug the values in, with a minus:

21000 * (1 - [tex]\frac{16}{100}[/tex])[tex]^{n}[/tex]

The price after 3 years would simply be the following equation:

21000 * (1 - [tex]\frac{16}{100}[/tex])[tex]^{3}[/tex]

Which gives the result 12446.7 or 12447 to 1.d.p

This means that the answer is D) $12,447!

Answer:

d= 10.44030651

Step-by-step explanation:

The diameter is the length  between the endpoints.  We can find it using the distance formula.

d= sqrt((x2-x1)^2+(y2-y1)^2 )

d = sqrt((-6-4)^2+ (-1-2)^2)

d = sqrt((-10)^2+(-3)^2)

d= sqrt(100+9)

d = sqrt(109)

d= 10.44030651

Answer:

The y-intercept is at y = 10.

Step-by-step explanation:

It will be between y = 14 and y = 7 because the corresponding x values are -2 and 1.

An increase of 3 units of x  gives a decrease of 6 units of y fro the above values.

Then an increase of 1 ( 1 to 2) in x gives decrease in y of 2 (8 to 6). The other values show the same pattern.

So very unit increase in x,  the y values change by -2.

So  from x = -2 to 0 is +2 units for x and this will be -4 units for y  so the y-intercept ( when x = 0) will be at y = 14-4 = 10

y-intercept  is (0,10).

Answer:

Point slope intercept form: The equation for line is given by; [tex]y-y_1=m(x-x_1)[/tex] ......[1] ; where m is the slope and a point [tex](x_1, y_1)[/tex] on the line.

Let x represents the number of days and y represents the number of friends.

As per the statement:  After day three, he has 25 friends; after day eight, he has 40 friends.

⇒ We have two points i.e,

(3, 25) and (8, 40)

First calculate slope(m);

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given values we get;

[tex]m = \frac{40-25}{8-3}=\frac{15}{5}[/tex] = 3

now, substitute the given values of m=3 and a point (3, 25) in [1] we get;

[tex]y-25=3(x-3)[/tex]

Using distributive property; [tex]a \cdot(b+c) = a\cdot b + a\cdot c[/tex]

[tex]y-25 = 3x - 9[/tex]

Add 25 on both sides, we get;

[tex]y-25+25 = 3x - 9+25[/tex]

Simplify:

y =3x + 16

if  x = 18 days, then;

y = 3(18) + 16 = 54+16 = 70

Therefore, he will have on day 18, if he continues to add the same number of friends each day is, 70 friends.

Answer: Fertilizer A = 20, Fertilizer B = 56

Step-by-step explanation:

Step 1: Set up the equations

[tex]\begin{array}{c|c|c|c}& FertilizerA&FertilizerB&Quantity Required\\Nitrogen&8&5&440\\Phosphorous&2&5&260\\Potassium&4&5&360\\\end{array}[/tex]

Nitrogen: 8x + 5y ≥ 440

Phosphorous: 2x + 5y ≥ 260

Potassium: 4x + 5y ≥ 360

Step 2: Find the vertices

It is easiest to graph the equations to find the vertices. (see attachment).  You can also solve each system of equations to find the intersected points.

The following satisfy the "greater than or equal to" requirement:

Step 3: Use vertices in cost function C(x) to find the minimum

C(x) = $30x + $20y

(0, 88): $30(0) + $20(88) = $1760

(20, 56): $30(20) + $20(56) = $1720    ← This is the minimum!

(50, 32): $30(50) + $20(32) = $2140

(130, 0): $30(130) + $20(0) = $3900

The minimum cost occurs when 20 bags of Fertilizer A and 56 bags of Fertilizer B are purchased.  

This is a linear programming problem. The farmer needs to solve the system of inequalities that define the minimum nutrient requirements for the field and the cost function of the fertilizers to determine the least expensive way to meet the nutrient requirements.

The subject of this problem lies in the realm of linear programming—a mathematical method for determining a way to achieve the best outcome in a given mathematical model.

To solve this problem, we need to find the quantities of Fertilizer A and Fertilizer B that meets the minimum requirements for the field at minimum cost. Let x be the quantity of Fertilizer A and y be the quantity of Fertilizer B. Then, based on the information provided in the problem, we can set up the following inequalities:

Given that a 50-lb bag of Fertilizer A costs $30 and a 50-lb bag of Fertilizer B costs $20, the total cost of the fertilizers can be represented by the equation C = 30x + 20y, where C is the total cost.

The goal is to minimize the cost C = 30x + 20y, subject to the constraints above.
Using graphing or mathematical software, we can construct a graph of these inequalities and find the solution that lies on the feasible region where the cost is minimized.

The farmer needs to solve this system to determine the least amount of each fertilizer to use while still meeting the minimum soil nutrient requirements.

https://brainly.com/question/34674455

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Answer:

∠DBC = 40°

Step-by-step explanation:

We are given a figure where we know that the angle m∠1 = 65°, m∠2 = 60° and m∠6 = 85°. With the help of these given measures of the angles, we are to find the measure of the angle m∠DBC.

Since the sum of angles in a triangle is equal to 180 degrees, so:

∠1 + ∠2 + ∠3 = 180

∠3 = 180 - (65 + 60)

∠3 = 55°

Also ∠6 and ∠B are alternate interior angles so if ∠6 = 85° then ∠B is also = 85°.

Now that we know ∠3 and ∠B, we can find ∠DBC:

∠DBC = 180 - (85 + 55)

∠DBC = 40°

Answer:40

Step-by-step explanation:

See angle 1 = 65°

Angle 2 = 60°

We know in a triangle all angle count 180°

So angle 3 = 55°

Now in a straight line all angle count 180°

So angle DBC + angle 3 + remaining angle along the line m will count 180°

Now angle 6 and remaining angle along the line m will be equal as 'm' ?and 'b' are parallel lines and t is intersecting them so it subtend equal angles.

Angle 6 = 85° so remaining angle along the line m is also 85°

We know angle DBC + angle 3 + rem. angle = 180°

Or 55° + 85° + angle DBC = 180°

Therefore, angle DBC = 40°

Hope it helps!!!

B) 87 feet

The mnemonic SOH CAH TOA reminds you the relationship between angle, adjacent, and opposite sides is ...

... Tan = Opposite/Adjacent

In this geometry, the side adjacent to the angle is marked 150 ft, and the side opposite the angle is the height we want to find. This means ...

... tan(30°) = height/(150 ft)

Multiplying by 150 ft, we get ...

... height = (150 ft)·tan(30°) ≈ 87 ft

Answer:

online

Step-by-step explanation:

insert the subject that is into the search bar on google and look for the pdf document. it will contain all the work and information needed

Answer:

Step-by-step explanation:

2. Conclusion: U is the mid point of RN.

Justification: From the figure, you can see that RU=UN which means U divides the line segment RN in two equal halves, thus by definition of mid point theorem, U is the mid point of RN.

3. From the given figure,

Conclusion: ∠7=∠5

Justification: From the figure, you can see that \overrightarrow{IK} bisects∠MIE. Therefore by the definition of bisector angle property, ∠MIK=∠KIE that is ∠7=∠5.

4. Conclusion: if l║m, and t is the transversal, then ∠3=∠7.

Justification: Since l║m and t is the transversal, then ∠3=∠7 as the alternate angles made by the transversal are equal.

5. Conclusion:    If \overrightarrow{BD} bisects ∠ABC, then ∠ABD=∠DBC

Justification: Since,  \overrightarrow{BD} bisects ∠ABC, then by the bisector angle property,  \overrightarrow{BD} divides ∠ABC in two equal angles that is ∠ABD=∠DBC.

6. Conclusion: If ∠2+∠3= 180°,then ∠2 and ∠3 are supplementary angle pairs.

Justification: Since, ∠2 and ∠3 are supplementary angle pairs which are on the same side of the transversal t, their sum is equal to 180° that is ∠2+∠3= 180°.

Answer: 691

Step-by-step explanation:

There are 3 different ways to find the remainder.  I am not sure which method you are supposed to use, so I will solve using all 3 methods.

Long Division:

         10x³ + 24x² + 77x + 230

x - 3 ) 10x⁴ -  6x³  + 5x²   - x  +  1

      - (10x⁴ - 30x³)   ↓       ↓      ↓

                   24x³ + 5x²     ↓      ↓

               - (24x³ - 72x²)   ↓      ↓

                              77x²  - x       ↓

                         -  (77x² - 231x)  ↓

                                        230x + 1

                                     - (230x - 690)

                                                    691 ← remainder

Synthetic Division:

x - 3 = 0   ⇒  x = 3

3  |  10     -6        5       -1        1

   |   ↓      30     72    231    690

      10      24     77    230   691 ← remainder

Remainder Theorem:

f(x) = 10x⁴ - 6x³ + 5x²  - x  +  1

f(3) = 10(3)⁴ - 6(3)³ + 5(3)² - (3)  +  1

     =  810   - 162    + 45    -  3  +  1

     = 691

Answer:

The last graph

Step-by-step explanation: On edge.

Answer:

D or the last graph

Step-by-step explanation:

Edge 2022

Answer:

4000

Step-by-step explanation:

Davila can job 400 feet in 8 min

Answer:

Seth has 21 nickels

Step-by-step explanation:

Let n represent the number of nickels. Since Seth has 8 more nickels than dimes, then (n-8) is the number dimes.

Nickel is worth 5 cents and dime is worth 10 cents.  Thus, n nickels are worth 5n cents and (n-8) dimes are worth 10(n-8) cents. The total value of Seth's coins is $2.35 that is 235 cents, then

[tex]5n+10(n-8)=235.[/tex]

Solve this equation:

[tex]5n+10n-80=235,\\ \\15n=235+80,\\ \\15n=315,\\ \\n=21.[/tex]

Answer:

10.3 units

Step-by-step explanation:

From the given graph, we can see the coordinates of the points B (-2, 4) and D (3, -5).

To use the Pythagorean Theorem, we must have a right angled triangle. So we can select a point X (3, 4) to calculate the distance between B and D using the Pythagoras Theorem.

BX = 5, XD = 9

BD = [tex]\sqrt{BX^2+XD^2}[/tex]

BD = [tex]\sqrt{(5)^2+(9)^2} =\sqrt{106} =10.29[/tex]

Therefore, the points B and D are 10.3 units apart.

[tex](x^{2} +8x+16)(x^{2} -8x+16)\\(x+4)^{2} (x-4)^{2} \\(x^{2}-16)^{2} \\[/tex]

it is true; just work them out, you should get what they got :))

Answer:

True.

Step-by-step explanation:

We have been given an equation [tex][x^2 + 8x + 16]\cdot [x^2- 8x+16] = (x^2-16)^2[/tex]. We are asked to determine whether our given equation is true or false.

To answer our given problem, we will simplify left side of our given equation using distributive property as:

[tex]x^2(x^2- 8x+16)+ 8x(x^2- 8x+16)+16(x^2- 8x+16)[/tex]

[tex]x^4- 8x^3+16x^2+ 8x^3-64x^2+128x+16x^2-128x+256[/tex]

Combine like terms:

[tex]x^4- 8x^3+ 8x^3+16x^2+16x^2-64x^2+128x-128x+256[/tex]

[tex]x^4-32x^2+1256[/tex]

Now, we will expand right side of our given equation using perfect square formula as:

[tex](x^2-16)^2=(x^2)^2-2(x)(16)+16^2[/tex]

[tex](x^2-16)^2=x^4-32x+256[/tex]

Since both sides of our given equation are equal, therefore, our given statement is true.

Answer: Second, third, fifth and sixth options are correct.

Step-by-step explanation:

Since we have given that

[tex]\frac{3}{4}+m=\frac{-7}{4}[/tex]

Now, we will solve it for the value of m :

[tex]\frac{3}{4}+m=\frac{-7}{4}\\\\m=\frac{-7}{4}-\frac{3}{4}\\\\m=\frac{-7-3}{4}\\\\m=\frac{-10}{4}[/tex]

Hence, the value of m is

[tex]\frac{-10}{4}[/tex]

and we can also apply m=[tex]\frac{-5}{2}[/tex]

if [tex]\frac{-5}{4}+m=\frac{-15}{4}\\\\m=\frac{-15}{4}+\frac{5}{4}\\\\m=\frac{-10}{4}\\\\m=\frac{-5}{2}[/tex]

And

[tex]m+2=-0.5\\\\m=-0.5-2\\\\m=-2.5\\\\m=\frac{-5}{2}[/tex]

Therefore, Second, third, fifth and sixth options are correct.

I'm assuming you meant to say "graph" instead of "table".

The function rule is y = x+2 because the y intercept is 2, where the graph crosses the y axis. The slope is 1 meaning we move 1 unit up and 1 unit to the right each time. You can use the slope formula to determine the slope, or simply make this observation of rise vs run.

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

Because this line doesn't go through the origin, and because it's not in the form y = k*x, this means we do not have a direct variation equation.

We do not have an inverse variation equation either because it is not in the form y = k/x or x*y = k. A visual indication of this is that the graph isn't a curved hyperbola.

Therefore, this function is neither direct variation nor inverse variation

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

Plug in y = 10 and solve for x

y = x+2

x+2 = y

x+2 = 10

x+2-2 = 10-2

x = 8

The value of x is 8

So if x = 8, then y = 10 meaning that (x,y) = (8,10) is on this blue diagonal line.

Answer:

Use demos it is reaaly helpful with this

To solve the equation 2x-7= 1/3x-2, we multiply both sides by 3, subtract x from both sides, add 21 to both sides, and then divide by 5 to isolate x, resulting in x = 3.

For the given equation 2x-7= 1/3x-2, the goal is to prove x = 3. Here's how to approach it step-by-step:

After solving the equation, it is important to check if the answer is reasonable by substituting x back into the original equation to see if both sides equal.

Answer: Choice B)

an = 15 + a(n-1)

a1 = 250

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

The variable "a" is used to represent the terms. Since we have infinitely many terms to worry about, we won'd use "b, c, d, etc" for the other terms or else we'd run out of letters. So instead, we just stick a number next to "a" to help keep track of the terms

a1 = first term, a2 = second term, a3 = third term, etc

The first term is 250 because Chenoa starts off with $250, so a1 = 250. The answer is between A and B at this point.

The recursive step is how we generate each term. In plain english, the recursive step would be "add 15 to each term to get the next term". In an informal equation, it would look like this

term = (previous term) + 15

So that is why the nth term is

[tex]a_n = 15 + a_{n-1}[/tex]

which means "to get the nth term, we add 15 to the previous (n-1)st term"

This is why choice B is the answer

Answer: If Tara puts 4 pennies in for every one Sam does then after he puts in 10 she would of put 40.

She put in 40 pennies. Hope this helps ;)

Hi there! :)

Answer:

The area of the carpet is 3m².

Step-by-step explanation:

First off, the formula to calculate the area of a rectangle is this: A = L × W

Where "A" is the area, "L" the length and "W" the width.

Now that you have that, replace all the information you know in the equation in order to find the value of "A", which is what we are looking for:

- Just keep in mind that 1 1/2 is the same thing as 1.5

- The term "wide" is used to give the "width"

- The term "long" is used to give the "length"

A = L × W

A = 2 × 1.5

A = 3

There you go! I really hope this helped, if there's anything just let me know! :)

The area of the rectangular flying carpet is [tex]$\frac{15}{4} \text{ m}^2}$[/tex] or [tex]3.75 { m}^2}[/tex]

To find the area of a rectangle, one multiplies the length by the width. The width of the carpet is given as [tex]$1 \frac{1}{2}$[/tex] meters, which can be expressed as a fraction [tex]$\frac{3}{2}$[/tex] of meters. The length of the carpet is given as 2 meters.

Using the formula for the area of a rectangle [tex]A = l \times w$,[/tex] where [tex]$l$[/tex] is the length and [tex]$w$[/tex] is the width, we substitute the given values:

[tex]\[ A = 2 \text{ m} \times \frac{3}{2} \text{ m} \][/tex]

[tex]\[ A = \frac{2 \times 3}{2} \text{ m}^2 \][/tex]

[tex]\[ A = \frac{6}{2} \text{ m}^2 \][/tex]

[tex]\[ A = \frac{15}{4} \text{ m}^2 \][/tex]

[tex]\[ A = 3.75 \text{ m}^2 \][/tex]

Therefore, the area of the carpet is [tex]$\frac{15}{4}$[/tex] square meters or 3.75 square meters.

9514 1404 393

Answer:

  (b)  f(x) = 2^x -3

Step-by-step explanation:

The horizontal asymptote is y=-3, eliminating the first and last choices.

The curvature is upward, eliminating the third choice.

The graph is a representation of ...

  f(x) = 2^x -3

Answer:

The simplest form that represents the difference is ( 2w-3).

Step-by-step explanation:

In this sum after w weeks subscription sold by me = 3w+4

and the subscription sold by my friend =5w+1

so the difference between the numbers of my friend and me

⇒(5w+1)-(3w+4)

⇒5w+1-3w-4

⇒2w-3

So the simplest form is (2w-3).

Final answer:

The difference in the number of subscriptions sold by the friend and the student after w weeks is represented by the simplified expression 2w - 3.

Explanation:

To find the difference between the number of subscriptions your friend has sold and the number you have sold, you simply subtract your sales from your friend's sales. The expression for your sales is (3w + 4) subscriptions and for your friend's sales is (5w + 1) subscriptions. So, the expression representing the difference will be:

(5w + 1) - (3w + 4)

Distributing the negative sign across the terms in the second set of parentheses gives us 5w + 1 - 3w - 4. Combining like terms, which are the 'w' terms and the constant terms separately, we get:

(5w - 3w) + (1 - 4) which simplifies to 2w - 3.

This expression 2w - 3 is the simplified form representing the difference between the number of subscriptions sold by your friend and you after w weeks.

Answer:

[tex]\frac{40}{19}\text{ or }2\frac{2}{19}[/tex] cases per hour.

Step-by-step explanation:

We are told that Jerry hears 5 cases every [tex]2\frac{3}{8}[/tex] hours.

To find the number of cases that Jerry hears per hour let us divide 5 by [tex]2\frac{3}{8}[/tex].

[tex]\text{Jerry hears cases per hour}=5\div 2\frac{3}{8}[/tex]

Let us convert our mixed fraction into improper fraction.

[tex]\text{Jerry hears cases per hour}=5\div \frac{19}{8}[/tex]

Since dividing a number by a fraction is same as multiplying the number by the reciprocal of the fraction.

[tex]\text{Jerry hears cases per hour}=5\times \frac{8}{19}[/tex]

[tex]\text{Jerry hears cases per hour}=\frac{40}{19}[/tex]

[tex]\text{Jerry hears cases per hour}=2\frac{2}{19}[/tex]

Therefore, Jerry hears [tex]\frac{40}{19}\text{ or }2\frac{2}{19}[/tex] cases per hour.

When a 20-foot length of wire is cut into 6 pieces of equal length, each piece would be approximately 3.33 feet long. Rounding to the nearest whole numbers, this means the length of each piece will fall between 3 feet and 4 feet.

To find the length of each piece of wire when a 20-foot length of wire is cut into 6 pieces of equal length, you divide the total length by the number of pieces. So, you calculate:

Since we're looking for whole-number lengths that the length of each piece falls between, we can round 3.33 feet down to the nearest whole number (3 feet) and up to the next whole number (4 feet). Thus, the length of each piece will fall between 3 feet and 4 feet.

Final answer:

To set up a profitable computer repair business, assuming $50 for parts per repair and a service fee of $150, the weekly expenses equation is y = 50x + 500, and income equation is y = 150x, where x is the number of repairs.

Explanation:

When starting a computer repair business with estimated expenses of $500 per week, it's crucial to set average costs for replacement parts and fees for services to ensure profitability. Let's assume an average cost of $50 for parts per computer repaired and a service fee of $150 per repair. If x represents the number of computers you repair each week, your total weekly expenses for parts would be 50x plus the fixed expenses of $500, resulting in a total expense equation of y = 50x + 500. Your total weekly income can be modeled by the equation y = 150x, with each repair contributing $150 to the income.

To break even or make a profit, the total income must exceed total expenses, leading to an analysis based on the number of repairs done weekly. This practical application of linear equations in a business setting helps in budgeting, pricing strategies, and understanding economic principles behind running a service-based business. Monitoring these variables is key to achieving sustainability.

Answer:

Option D is correct.

as the particle always moves to the right

Step-by-step explanation:

Given the function:  [tex]s(t) = \frac{t^3}{3} - \frac{12t^2}{2} + 36t[/tex] , 0<t<15;

where

s(t) represent the distance in feet.

t represents the time in second.

Since, when the particle is moving to the right,

⇒ s(t) is increasing.

so, [tex]v(t) =\frac{ds}{dt} > 0[/tex]

Find the derivative of s(t) with respect to t;

Use derivative formula:

[tex]\frac{dx^n}{dx} = nx^{n-1}[/tex]

[tex]\frac{ds}{dt} = \frac{3t^2}{3}-\frac{24t}{2}+36[/tex]

Simplify:

[tex]\frac{ds}{dt} = t^2-12t+36[/tex]

As [tex]\frac{ds}{dt} > 0[/tex]

⇒[tex] t^2-12t+36 > 0[/tex]

[tex](t-6)^2 >0[/tex]               [[tex](a-b)^2 = a^2-2ab+b^2[/tex] ]

⇒ this is always true because square of any number is always positive

Therefore, it means that the particle always moves to the right.