Tickets for the front section to a rock concert cost $25 each. The back section tickets sold for $15 each. If 400 tickets were sold for a total revenue of $7,500, how many of each each type of ticket were sold? 1. Front – 145, Back – 255 2. Front – 140, Back – 260 3. Front – 155, Back – 245 4. Front – 150, Back – 250

Answer:

8

Step-by-step explanation:

x+37+x+37+90 = 180

2x + 74 = 90

2x = 16

x = 8

Answer:

x=8°

Step-by-step explanation:

JI is a diameter and K is on the circumference of a circle.

∴∠JKI=90°

also KJ=KI=x(say)

tan (x+37)=y/y=1=tan 45

so x+37=45

x=45-37=8°

Answer:

√137

Step-by-step explanation:

[tex](x_1, y_1) = (6, 0)\\(x_2, y_2) = (-5, 4)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d = \sqrt{(-5-6)^2+(4-0)^2}\\ d = \sqrt{(-11)^2+(4)^2}\\ d = \sqrt{121+16}\\ d = \sqrt{137}\: or \:11.7[/tex]

Answer:

288.4m

Step-by-step explanation:

This track is split into a rectangle and two semi-circles.

We can find the length of the semi-circles by finding its circumference with the formula [tex]2\pi r[/tex].

[tex]2\cdot3.14\cdot30\\188.4[/tex]

However this is half a circle, so:

[tex]188.4\div2=94.2[/tex].

There are two semi-circles.

[tex]94.2\cdot2=188.4[/tex]

Since there are two legs of 50m each, we add 100 to 188.4

[tex]188.4+100=288.4[/tex]m

Hope this helped!

Answer:

Step-by-step explanation:

To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.

For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.

15 * 2π ≈ 94.2477796077

We add that to 100m and get:

194.2477796077

Answer:

1) The ship is closer

2) 675.73 m

Step-by-step explanation:

1) The given parameters are;

The initial angle between the ship's course and the lighthouse = 32°

The final angle between the ship's course and the lighthouse = 72°

The distance traveled by the sip between he two positions = 1500 m

Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b

Where;

a = The initial distance fro the lighthouse

b = The final distance fro the lighthouse

The angles of the triangle are

32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°

By sine rule we have;

1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =

Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m

b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m

Therefore, a  > b

The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer

2) By cosine rule we have

a² = b² + c² - 2× b×c×cos(A)

Where the given measurements by Kendra are;

410 m and 805 m with an included (in between) angle of 57°, we have;

Let b = 410 m, c = 805 m, and A  = 57°, we have;

a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²

a = The length of the stream = 675.73 m.

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

Work Shown:

[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]

Notice how 33*77 = 2541 and 11*231 = 2541

[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.

So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]

Answer:

the answer is 3

Step-by-step explanation:

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.

Answer:

See below.

Step-by-step explanation:

[tex]\cos(20)-\sin(20)=\sqrt{2}\sin(25)[/tex]

First, use the co-function identity:

[tex]\sin(90-x)=\cos(x)[/tex]

We can turn the second term into cosine:

[tex]\sin(20)=\sin(90-70)=\cos(70)[/tex]

Substitute:

[tex]\cos(20)-\cos(70)=\sqrt{2}\sin(25)[/tex]

Now, use the sum to product formulas. We will use the following:

[tex]\cos(x)-\cos(y)=-2\sin(\frac{x+y}{2})\sin(\frac{x-y}{2})[/tex]

Substitute:

[tex]\cos(20)-\cos(70)=-2\sin(\frac{20+70}{2})\sin(\frac{20-70}{2})\\\cos(20)-\cos(70) =-2\sin(45)\sin(-25)\\\cos(20)-\cos(70)=-2(\frac{\sqrt{2}}{2})\sin(-25)\\ \cos(20)-\cos(70)=-\sqrt{2}\sin(-25)[/tex]

Use the even-odd identity:

[tex]\sin(-x)=-\sin(x)[/tex]

Therefore:

[tex]\cos(20)-\cos(70)=-\sqrt{2}\sin(-25)\\\cos(20)-\cos(70)=-\sqrt{2}\cdot-\sin(25)\\\cos(20)-\cos(70)=\sqrt{2}\sin(25)[/tex]

Replace the second term with the original term:

[tex]\cos(20)-\sin(20)=\sqrt{2}\sin(25)[/tex]

Proof complete.

Answer:

Step-by-step explanation:

Let y(t) be the amount of salt in the tank after time t.

(A) Incoming rate = 0 (due to Pure water having no salt)

(B) Mixed solution comes out at 150 L/min. Initially the tank has 15,000 L of brine with 24 kg of salt.

concentration of salt at time t  = y(t) / 15000 kg/L

Outgoing rate = y(t)/15000 * 150 = y(t) / 100

(C) we know that,

[tex]\frac{dy}{dx} =(incoming\ rate) - (outgoing\ rate)[/tex]

[tex]\frac{dy}{dx} =0-\frac{y(t)}{100} = \frac{-y(t)}{100}[/tex]

Separate variable and integrate

[tex]\int {\frac{dy}{y} } = - \int {\frac{1}{100} } \, dt[/tex]

[tex]ln|y|=-\frac{1}{100}t + D[/tex]

[tex]y=e^{D} e^{\frac{-t}{100} }[/tex]

[tex]y= Ce^{\frac{-t}{100} }\ [C=e^{D} ][/tex]

At t= 0 , y(0) = 24 kg

[tex]24=C\ e^{0}[/tex]

C= 24

(D) Therefore, the amount of salt in the tank after time t :

[tex]y(t)=24e^{\frac{-t}{100} }\ kg[/tex]

Answer: [tex]y-1=\dfrac32(x+3)[/tex]

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]

Since parallel lines have equal slope . That means slope of the required line would be .

Equation of a line passing through (a,b) and has slope m is given by :_

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]

Required equation: [tex]y-1=\dfrac32(x+3)[/tex]

Answer:

The middle of the sailboat is approximately 268.8 feet from the shore.

Step-by-step explanation:

Let the distance from shore to the middle of the boat be represented by x, the angle of elevation of Sandra from the shore to the top of the boat mast  is 7°. Applying the required trigonometric function to this question, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan 7° = [tex]\frac{23}{x}[/tex]

⇒  x = [tex]\frac{23}{Tan 7^{0} }[/tex]

       = [tex]\frac{23}{0.12279}[/tex]

      = 268.7515

∴ x = 268.8 feet

The middle of the sailboat is approximately 268.8 feet from the shore.

Best way to solve this is by using

[tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]

[tex]where \: s = \frac{a + b + c}{2} [/tex]

s=(12+8+17)/2

=18.5

using the formulae

area =43.5

Answer:

She sold 10 pounds of peaches and 45pounds of grapes

Step-by-step explanation:

X= pounds of peaches

x+35=pounds of grapes

2x+4(x+35)=200

2x+4x+140=200

6x=200-140

6x=60

x=10

She sold 10 pounds of peaches and 45pounds of grapes. (Sorry, can’t help you graph it.)

Answer:

answer is D

Step-by-step explanation:

2^4=16

16+(16-12)=20

over

(6+9)/(7-4)

15/3=5

so the new equation is 20/5=4

Answer:

D. 4

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Exponents

[tex]\frac{16 + (16 -3(4))}{(6+9)/(7-4)}[/tex]

Step 2: Parenthesis

[tex]\frac{16 + (16 -12)}{15/3}[/tex]

Step 3: Parenthesis

[tex]\frac{16 + 4}{15/3}[/tex]

Step 4: Divide

[tex]\frac{16 + 4}{5}[/tex]

Step 5: Add

[tex]\frac{20}{5}[/tex]

Step 6: Divide

4

Answer:

He had a different number of points to the left of the vertical line than to the right of the vertical line.

Step-by-step explanation:

Divide-center method is the method which involves dividing the data on the graph into two equal parts and then fin the line of best fit. The center of each group is approximated and then a line is constructed between two centers which is estimated as line of best fit.

Answer:

(0,3), graph is attached.

Step-by-step explanation:

We know that the first equation will increase 2 points in y for every 1 x, since the constant next to x is 2. We also know it's y-intercept will be 3.

As for the second equation, we know it will have no y and instead run through the y=3 line, crossing every value of x.

Graphing this, we see that these lines intersect at (0,3) so that's the solution to this system.

Hope this helped!

As per the question,

We have to find what's the coefficient.

Let's start to seperate the expression.

Here,

x is the variable,

4 is a number.

-3 is also a number.

4, -3x

The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.

Answer:

Hey there!

Rearrange the expression to: -3x+4

The coefficient would be -3.

Let me know if this helps :)

Answer:

25 + 10h = 50+5h

Step-by-step explanation:

Black Diamond Ski Resort

25 + 10h

Bunny Hill Ski Resort

50+5h

We want when they are equal

25 + 10h = 50+5h

Answer:

10x + 25 = 5x + 50

Step-by-step explanation:

Step-by-step explanation:

Example 1:

a+c=b+c then a=b

First let the value of a and b be different (not equal)

a=5

b=7

c=10

a+c=b+c

5+10=7+10

15≠17

Example 2:

Let the value a and b be equal (the same)

a=5

b=5

c=10

a+c=b+c

5+10=5+10

15=15

So when,

a+c and b+c is equal, a and b are always equal.

Hope this helps ;) ❤❤❤

Answer:

a=b

Step-by-step explanation:

Reason:

a+c=b+c

a-b=c-c

c-c would be 0

if a-b=c-c=0

a-b=0

Only if a=b can a-b=0

You can also take it as:

b-a=c-c (a+c=b+c)

b-a=0=c-c

Therefore b=a

By the way even I am a BTS army

Answer:

1st side: 150

2nd side: 30

Answer:

768 libras de fuerza

Step-by-step explanation:

Tenemos que encontrar la ecuación que los relacione.

F = Fuerza necesaria para evitar que el automóvil patine

r = radio de la curva

w = peso del coche

s = velocidad de los coches

En la pregunta se nos dice:

La fuerza requerida para evitar que un automóvil patine alrededor de una curva varía inversamente con el radio de la curva.

F ∝ 1 / r

Y luego con el peso del auto

F ∝ w

Y el cuadrado de la velocidad del coche

F ∝ s²

Combinando las tres variaciones juntas,

F ∝ 1 / r ∝ w ∝ s²

k = constante de proporcionalidad, por tanto:

F = k × w × s² / r

F = kws² / r

Paso 1

Encuentra k

En la pregunta, se nos dice:

Suponga que 400 libras de fuerza evitan que un automóvil de 1600 libras patine alrededor de una curva con un radio de 800 si viaja a 50 mph.

F = 400 libras

w = 1600 libras

r = 800

s = 50 mph

Tenga en cuenta que desde el

F = kws² / r

400 = k × 1600 × 50² / 800

400 = k × 5000

k = 400/5000

k = 2/25

Paso 2

¿Cuánta fuerza evitaría que el mismo automóvil patinara en una curva con un radio de 600 si viaja a 60 mph?

F = ?? libras

w = ya que es el mismo carro = 1600 libras

r = 600

s = 60 mph

F = kws² / r

k = 2/25

F = 2/25 × 1600 × 60² / 600

F = 768 libras

Por lo tanto, la cantidad de fuerza que evitaría que el mismo automóvil patine en una curva con un radio de 600 si viaja a 60 mph es de 768 libras.

Answer:

5,383,000  / *improvments cost 8,074,500

Step-by-step explanation:

if 2.5 is by 'times' then,

13,457,500 / 2.5 =

5,383,000

Which means the cost of the land is 5,383,000

To check just multiply:

5,383,000 x 2.5 = 13,457,500

*Extra

13,457,500 - 5,383,000

= the cost of improvements =  8,074,500

Hope this helps, and have a good day :)

Answer:

$3,845,000

Step-by-step explanation:

As per given:

Then total is:

Cost of the land alone is  $3,845,000

Answer:

3.03 • 10⁻³ is scientific notation

0.00303 is decimal form

Answer:

C is a function

Step-by-step explanation:

We can use the vertical line test.  If a vertical straight lines passes through the graph more than one, it is not a function

A and B are not functions

C is a function

Answer:

a) 2 h 45 min

b) 2 h 50 min

c) 2 h 20 min

d) 3 h 20 min

Step-by-step explanation:

Answer:

a) hours: 9 hours 15 minutes

minutes: 555

b) hours: 9hours 10 minutes

minutes: 550

c) hours: 2hours 20 minutes

minutes: 140

d) hours: 3 hours 20 minutes

minutes: 200

Step-by-step explanation:

Answer:

Daily pay= $18

5 days pay = $90

Step-by-step explanation:

Archer's daily pay =p

Pay for 5 days= 5p

Gas = 1/2 of 5p

= 1/2 × 5p

= 5p/2

Water = $5

Balance = $40

5p = 5/2p + 5 + 40

5p - 5/2p = 45

10p -5p /2 = 45

5/2p = 45

p= 45÷ 5/2

= 45 × 2/5

= 90/5

P= $18

5p= 5 × $18

=$90

The equation to determine Archer's daily pay is

5p = 5/2p + 5 + 40

Divide both sides by 5

p = 5/2p + 45 ÷ 5

= (5/2p + 45) / 5

p= (5/2p + 45) / 5

Answer:

c

Step-by-step explanation:

The expression (9⁶ x 7⁻⁹)⁻⁴ is equivalent to expression 7³⁶ / 9²⁴. Then the correct option is D.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (9⁶ x 7⁻⁹)⁻⁴

Simplify the expression, we have

⇒ (9⁻⁶ x 7⁹)⁴

⇒ 9⁻²⁴ x 7³⁶

⇒ 7³⁶ / 9²⁴

Then the correct option is D.

More about the equivalent link is given below.

https://brainly.com/question/889935

#SPJ2

Answer:

Step-by-step explanation:

The diagonals of the rhombus divide it into 4 congruent right triangles.

So we can use Pythagorean theorem to calculate side of a rhombus.

[tex](\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17[/tex]

Perimeter:

P = 4s = 4•17 = 68 cm

Answer:

x = 20

Step-by-step explanation:

Intersecting Chords Theorem: ab = cd

Step 1: Label our variables

a = x

b = x - 11

c = x - 8

d = x - 5

Step 2: Plug into theorem

x(x - 11) = (x - 5)(x - 8)

Step 3: Solve for x

x² - 11x = x² - 8x - 5x + 40

x² - 11x = x² - 13x + 40

-11x = -13x + 40

2x = 40

x = 20

Answer: x=20

Step-by-step explanation:

[tex]ab=cd[/tex]

[tex]x(x - 11) = (x - 5)(x - 8)[/tex]

[tex]x^2 - 11x = x^2 - 13x + 40[/tex]

[tex]x^2 - 11x = x^2 - 8x - 5x + 40[/tex]

[tex]-11x = -13x + 40\\2x = 40\\x = 20[/tex]

Answer:

The answer can be interpreted by the distance moved by each gallon :))

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Just took it. Edg 2020. Hope this helps :)