Theater tickets sold for $7.50 on
the main floor and $, in the
balcony. The total revenue was
$3250, and there were 100 more
main-floor tickets sold than
balcony tickets. Find the number
of each type of ticket sold.
(in Substitution method)
Cant figure the work out :/

Answer:

x = 5

Step-by-step explanation:

90 - 50 = 40

40/8 = 5

Answer:

[tex]x=\dfrac{\log 6}{\log 23}[/tex]

Step-by-step explanation:

Given exponential equation:

[tex]23^x=6[/tex]

[tex]\textsf{Apply the log law}: \quad a^c=b \iff \log_ab=c[/tex]

[tex]\implies\log_{23}6=x[/tex]

[tex]\textsf{Given change of base formula}: \quad \log_by=\dfrac{\log y}{\log b}}[/tex]

Apply the given change of base formula:

[tex]\implies x=\dfrac{\log 6}{\log 23}[/tex]

Answer:

64(ab÷c²)

step by step:

(when you multiply two similar bases you can add their exponents but when dividing similar bases you subtract their exponents)

for example

a³x a= a⁴

a²÷ a= a²-¹= a

so

4a³x 16a⁰b¹÷ 1ac²=

64a³b÷ac²

64a²b/c²

Answer:

b and c

Step-by-step explanation:

b is basically saying flip it up and turning the whole thing left which will put it on top of pnms and c is saying rotate it where line sr and sm would be side by side then flip it right

Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

Given :

At time zero, Kadeesha stepped outside and drove 3 minutes at a speed of 1 block per minute to the store.

after traveling six blocks at her normal speed of three blocks per minute

She spent 5 minutes stopping at the bank as a result. She then sped home at a rate of three blocks per minute.

She therefore begins at (19,8), travels 8 blocks back in 2 minutes, and ends at (21,0).

Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

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Arranging cards with number -4, -2, -1, 5, 6, 8 making pair with the same total. Therefore, the pairs are (8,-4), (6,-2), (5,-1).

A pair is a hand that has two cards of same rank and three other cards that do not match any of these or each other. When comparing two similar hands, the hand with the higher pair wins – therefore 6-6-4-3-2 defeats 6-6-4-3-2. 5-5-A-K-Q.Some things, such as a pair of pants or a pair of scissors, contain two major sections that are the same size and form.

A 55-card deck with one 1, two 2s, three 3s, and so on up to ten 10s is used in the game. Shuffle the deck at the start of the game, then remove five cards from play without looking. Give each player one face-up card.

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Answer:

As [tex]x \to 2^-[/tex], [tex]f'(x)=1[/tex].

Step-by-step explanation:

See the attached image for the graph of f .

As [tex]x\to 2^-[/tex], the important part of the definition of f is the first part, valid for [0, 2). On the interval [1, 2),  [x] = 1, so [tex]f(x)=x\cdot 1=x[/tex], and the slope is 1.

Interestingly, on the interval [2, 3), [tex]f(x)=x(x-1)=x^2-x[/tex], making [tex]f'(x)=2x[/tex]. As [tex]x \to 2^+[/tex], the value of f ' approaches 4.  That accounts for the sudden change in direction at the point (2, 2) where the two pieces of the graph connect.

So although the pieces meet at (2, 2) -- f is continuous -- f  does not have a (two-sided) derivative at that point because the left-hand derivative and right-hand derivative have different values.  There's a "bend" in the graph.

We want to find an equation and the sixth term of the given geometric sequence.

The equation is: [tex]a_{n} = 4*a_{n}-1[/tex] and the sixth term is equal to 512

In a geometric sequence, each term is a constant times the previous term, so the general relation is:

[tex]a_{n} = k*a_{n}-1[/tex]

Here we can use any pair of consecutive terms to find the value of the constant, for example, if we use the first two, we have:

[tex]8 = k*2\\8/2 = 4 = k[/tex]

Now we know the value of the constant, then the general formula is: [tex]a_{n} = 4*a_{n}-1[/tex]

Now we can use this to get the sixth term:

[tex]a_{6} = 4*a_{5}-1=4*128 = 512[/tex]

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Answer:

Yes, it would be 225%.

Step-by-step explanation:

If 20/20= 100% you can evenly take out 200% because there is 45/20.

That leaves you with the 5/20.

5/20= 25%.

If we add those two percentages 200% + 25%= 225%.

I hope that made sense lol, have a great day!

Answer:

0.38

Step-by-step explanation:

When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

given

The grocery store is 31.92 wide overall, with 10 equally wide parking spaces.

If you assume that the width of these 10 parking spaces is equal to the width of the grocery store as a whole, you will have:

10x=31.92

on both sides of the equation, multiply by 10.

10x/10 = 31.92/10

x = 3.192

When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.

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To begin, our game organizer will introduce participants to the escape game instructions and backstory. Teams will have 60 minutes to complete their chosen quest

An escape room, also known as an escape game, puzzle room, exit game, or riddle room is a game in which a team of players discover clues, solve puzzles, and accomplish tasks in one or more rooms in order to accomplish a specific goal in a limited amount of time. The goal is often to escape from the site of the game.

Once you’re ready to start the game, your team will watch a mission video. This video explains the world your team is now a part of, what you’re trying to accomplish, and why you only have 60 minutes to do so!Some missions are about escaping the room, like in a prison break room. Other missions might not be centered around escaping, but instead, you might be completing a heist or launching a martian spaceship.Here’s an example of the type of mission video that plays at the beginning of a game. This one is from The Escape Game’s The Heist!

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Answer:21 teams

Step-by-step explanation:because if you cont the black dots and read the question that would be the answer

The average speed of the falcon to 3 significant figures will be 107.526 m/s

Distance travelled by falcon = 100 meters

Time taken by falcon to travel the distance = 0.93 seconds

As we have the formula for finding the average speed:

Average speed is a pace defined as a quantity divided by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t is used to compute average speed, where S is the average speed, d is total distance, and t is total time.

Average speed can be find by simply dividing the total distance covered by falcon by the total time taken by him to cover the distance.

So, the value of the average speed will be = (100 m/0.93 sec) =107.526 m/s

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The equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12

Given that,

Three of a parallelogram's vertices have the coordinates (-3, 4), (-2, 1), and (2, 6).

We have to find what is the equation for the side of the line that contains the first two vertices' opposite side.

We know that,

The equation of the line is

y=mx+b

Here, we find m and d

Take the points (-3,4) (-2,1)

m = y₂-y₁ / x₂-x₁

m = 1 - 4 / -2-(-3)

m = -3 / 1

m = -3

Now take point (2,6)

6 = -3(2) + b

6 = -6 + b

6 + 6 = b

12 = b

We get m =-3 and b=12

The equation will be y=-3x+12

3x+y=12

Therefore, the equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12

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Answer:

60 inches < 59 inches

Step-by-step explanation:

1 foot = 12 inches

5 feet = 60 inches

60 inches < 59 inches

Answer:

d

Step-by-step explanation:

Answer:

A=16.3 ft²

Step-by-step explanation:

we are given a composite figure, composing of a triangle and a semicircle

first, let's find the area of the triangle

we are given the height (5 ft) and the base of the triangle (4 ft)

the formula for the area of the triangle is given as bh/2, where b is the base and h is the height

substitute the known values into the formula

[tex]A_{triangle}[/tex]=bh/2

[tex]A_{triangle}[/tex]=(5*4)/2

[tex]A_{triangle}[/tex]=20/2=10 ft²

so the area of the triangle is 10 ft²

now to find the area of the semicircle:

the area of a semicircle is half the area of a circle; the area of a circle is given as πr², where r is the radius. Therefore, the area of a semicircle is (πr²)/2

4 ft isn't just the base of the triangle; it's also the diameter of the semicircle

however, we need the radius

the radius is half the diameter value

r=d/2

r=4/2

r=2 ft

so the radius is 4 feet

now find the area of the semicircle. Don't substitute for π just yet.

[tex]A_{semicircle}[/tex]=(πr²)/2

[tex]A_{semicircle}[/tex]=(π*2²)/2

[tex]A_{semicircle}[/tex]=4π/2

[tex]A_{semicircle}[/tex]=2π

π is often substituted as 3.14 or 22/7

so if we used 3.14 for instance:

[tex]A_{semicircle}[/tex]=6.28; rounded to the nearest tenth, that's 6.3 ft²

now add the two areas together to get the area of the composite figure

[tex]A_{compositefigure}[/tex]=[tex]A_{triangle}[/tex]+[tex]A_{semicircle}[/tex]

[tex]A_{compositefigure}[/tex]=10+6.3=16.3 ft²

Hope this helps! Good luck on your assignment!!

The vertex of V' had a preimage of V(0, 3) as V' has a dilation of 3.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, On a coordinate plane, polygon S'T'U'V' has points (- 2, 4), (- 4, 1),

(- 2, - 2), and (0, 1) with a dilation rule  DO,1/3 (x, y) to [(1/3)x, (1/3)y].

Therefore, The coordinates of the vertex V had a preimage of,

3(V'), which is 3(0, 1) = (0, 3).

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The simplest form   [tex]\frac{2\sqrt{3} }{\sqrt{6} }[/tex] is [tex]\sqrt{2}[/tex]

Step-by-step solution:

[tex]=\frac{2\sqrt{3} }{\sqrt{6} }[/tex]

[tex]=\frac{2\sqrt{3} }{\sqrt{2*3} }[/tex]              (write factors of [tex]\sqrt{6}[/tex] i.e. [tex]\sqrt{2*3}[/tex])

[tex]=\frac{2\sqrt{3} }{\sqrt{2}\sqrt{3} }[/tex]

[tex]=\frac{2\ }{\sqrt{2}\ }[/tex]

[tex]=\frac{2\ }{\sqrt{2}\ } * \frac{\sqrt{2} }{\sqrt{2} }[/tex]        (Rationalize it by [tex]\sqrt{2}[/tex])

[tex]=\frac{2\sqrt{2} }{2}[/tex]

[tex]=\sqrt{2}[/tex]

Therefore, the correct solution to this question is [tex]\sqrt{2}[/tex]

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Answer:

Step-by-step explanation:

2/9 + x = 11/18

x = 11/18 - 2/9

x = 63/162

x = 7/18

2/9 + 7/18 = 11/18

11/18 = 11/18

Answer:

h= (V/πr²)(3)

Step-by-step explanation:

Answer: The scale of a map is a ratio that represents the relationship between distances on the map and distances in the real world. For example, a scale of 1:20 000 means that 1 unit on the map represents 20 000 units in the real world.

In this case, we are given that the area of the forest on the first map is 50 cm² and the area of the forest on the second map is 8 cm². We can use the scale of the first map to find the scale of the second map.

Since the area of the forest on the first map is 50 cm² and the scale is 1:20 000, the area of the forest in the real world is 50 cm² * 20 000 = 1 000 000 cm².

Similarly, since the area of the forest on the second map is 8 cm², the area of the forest in the real world is 8 cm² * x, where x is the scale of the second map.

Setting these two expressions equal to each other, we get:

1 000 000 cm² = 8 cm² * x

Dividing both sides of the equation by 8 cm², we get:

x = 125 000

Therefore, the scale of the second map is 1:125 000.

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

3/5 of 200 = 120

The correct answer is option A: the optimal corner point won't change.

The optimal corner point is the point where the objective function reaches its maximum value, with the constraints of the problem being satisfied. If the slope of the objective function stays between the slopes of the binding constraints, it means that the current optimal corner point will remain unchanged.

This is because if the objective function's slope is within the slopes of the binding constraints, then the set of points where the objective function reaches its maximum value will be the same. Therefore, the optimal corner point will not change.

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Answer:

Emily has 10 nickels, 20 dimes and 12 quarters in her piggy bank

Step-by-step explanation:

The number of dimes in Emily's piggy bank = 2 × The number of nickels

The number of quarters in it = 2 + The number of nickels

Whereby;

The number of quarters = The number nickels

The number of dimes = The number of quarters

The number of nickels = The number of dimes

The total amount = Current amount - $150

Let 'x' represent the number of dimes, let 'y' represent the number nickels, and let 'z' represent the number quarters in Emily's piggy bank, we have;

x = 2 × y

z = 2 + y

The total amount in the piggy bank is therefore;

Total = C = x×0.1  + y×0.05 + z×0.25 = 2·y×0.1 + y × 0.05 + (2 + y) × 0.25 = 0.5·y + 0.5

C = 0.5·y + 0.5

With the second condition, we have;

z = y

x = z

y = x

We get

x × 0.1 + y × 0.05 + z × 0.25 = y ×0.1 + y×0.05 + y×0.25 = 0.4·y = C - 1.5

∴ C = 0.4·y + 1.5

Which gives;

0.5·y + 0.5 = 0.4·y + 1.5

0.1·y = 1.5 - 0.5 = 1

y = 1/0.1 = 10

y = 10

Therefore;

x = 2×y = 2 × 10 = 20

z = 2 + y = 2 + 10 = 12

Therefore;

The number number of nickels in her piggy bank, y = 10

The number of dimes in her piggy bank, x = 20

The number of quarters in her piggy bank, z = 12

Answer:

24 nickles 48 dimes 26 quarters

Step-by-step explanation:

Answer:

0.000000654 kg

Step-by-step explanation:

Answer:

[tex](15 + 2x)(20 + 2x)[/tex]

Step-by-step explanation:

Given

[tex]Length= 15[/tex]

[tex]Width = 20[/tex]

[tex]Deck = x[/tex] --- on both sides

Required

An expression for total area of the pool

Because the deck will be on both sides,

the dimension of the pool will be:

[tex]L = Length + 2 * deck[/tex] --- Length

[tex]L = 15 + 2x[/tex]

[tex]W = Width + 2 * deck[/tex] --- Width

[tex]W = 20 + 2x[/tex]

The total area of the pool is calculated as:

[tex]Area = Length * Width[/tex]

[tex]A = (15 + 2x) * (20 + 2x)[/tex]

[tex]A =(15 + 2x)(20 + 2x)[/tex]

Hence, the expression is: [tex](15 + 2x)(20 + 2x)[/tex]

Answer: Okay this is the formula for slope: y=mx+b 2 would be the slope and -1 would be the y intercept so select b.

Step-by-step explanation: