Using f(x)=5x^2, identify the graph of f(x) and g(x)=2f(x)

Answer:

Step-by-step explanation:

Slant height s = 12

Radius r = 8

Lateral area of cone = πrs = 96π units²

Base area of cone = πr² 64π units²

Surface area = 96π + 64π = 160π units²

Divide 21 boxes into two groups so the ratio is 2:5 is 6 boxes and 15 boxes.

In this section, the terms ratio and percentage are defined. Many examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.

Sum of the ratio given is=2+5=7

Now to divide 21 into two groups in the ratio 2:5 , we have to use sum of the ratio.

first group is =\(\frac{2}{7}\)×21

first group is =6

and second group is =\(\frac{5}{7}\)×21=15

Hence the first group will get 6 boxes while other will get 15 boxes.

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Answer:

Well, the circles are split in half so I believe the correct way of doing this will be to shade 5 of the halfs

Step-by-step explanation:

Answer:

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

Shade 1 circle - this is clear.

Shade 5/2 more - how?

It makes two full circles and the half of the third one.

In total we need to shade:

Period of the functions: The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ). The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.

We know that cos (t) is periodic and has a period of 2π.∴ b = 2π∴ The period of the function f(t) =

(7 cos t)² = 2π/b = 2π/2π = 1.

The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ) Hence, the period of the function f(t) =

cos (2φt²/m) is √(4πm/φ).

The function f(t) = (7 cos t)² is a trigonometric function and it is periodic. The period of the function is given by 2π/b where b is the period of cos t. As cos (t) is periodic and has a period of 2π, the period of the function f(t) = (7 cos t)² is 2π/2π = 1. Hence, the period of the function f(t) = (7 cos t)² is 1.The function f(t) = cos (2φt²/m) is also a trigonometric function and is periodic. The period of this function is given by T = √(4πm/φ). Therefore, the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

The period of the function f(t) = (7 cos t)² is 1, and the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

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Answer:

\(10\).

Step-by-step explanation:

See below for a proof of why all but the first digit of this \(N\) must be "\(9\)".

Taking that lemma as a fact, assume that there are \(x\) digits in \(N\) after the first digit, \(\text{A}\):

\(N = \overline{\text{A} \, \underbrace{9 \cdots 9}_{\text{$x$ digits}}}\), where \(x\) is a positive integer.

Sum of these digits:

\(\text{A} + 9\, x= 2021\).

Since \(\text{A}\) is a digit, it must be an integer between \(0\) and \(9\). The only possible value that would ensure \(\text{A} + 9\, x= 2021\) is \(\text{A} = 5\) and \(x = 224\).

Therefore:

\(N = \overline{5 \, \underbrace{9 \cdots 9}_{\text{$224$ digits}}}\).

\(N + 1 = \overline{6 \, \underbrace{000 \cdots 000000}_{\text{$224$ digits}}}\).

\(N + 2021 = 2020 + (N + 1) = \overline{6 \, \underbrace{000 \cdots 002020}_{\text{$224$ digits}}}\).

Hence, the sum of the digits of \((N + 2021)\) would be \(6 + 2 + 2 = 10\).

Lemma: all digits of this \(N\) other than the first digit must be "\(9\)".

Proof:

The question assumes that \(N\!\) is the smallest positive integer whose sum of digits is \(2021\). Assume by contradiction that the claim is not true, such that at least one of the non-leading digits of \(N\) is not "\(9\)".

For example: \(N = \overline{(\text{A})\cdots (\text{P})(\text{B}) \cdots (\text{C})}\), where \(\text{A}\), \(\text{P}\), \(\text{B}\), and \(\text{C}\) are digits. (It is easy to show that \(N\) contains at least \(5\) digits.) Assume that \(\text{B} \!\) is one of the non-leading non-"\(9\)" digits.

Either of the following must be true:

If \(\text{P}\), the digit in front of \(\text{B}\), is a "\(0\)", then let \(N^{\prime}\) be \(N\) with that "\(0\!\)" digit deleted: \(N^{\prime} :=\overline{(\text{A})\cdots (\text{B}) \cdots (\text{C})}\).

The digits of \(N^{\prime}\) would still add up to \(2021\):

\(\begin{aligned}& \text{A} + \cdots + \text{B} + \cdots + \text{C} \\ &= \text{A} + \cdots + 0 + \text{B} + \cdots + \text{C} \\ &= \text{A} + \cdots + \text{P} + \text{B} + \cdots + \text{C} \\ &= 2021\end{aligned}\).

However, with one fewer digit, \(N^{\prime} < N\). This observation would contradict the assumption that \(N\!\) is the smallest positive integer whose digits add up to \(2021\!\).

On the other hand, if \(\text{P}\), the digit in front of \(\text{B}\), is not "\(0\)", then \((\text{P} - 1)\) would still be a digit.

Since \(\text{B}\) is not the digit \(9\), \((\text{B} + 1)\) would also be a digit.

let \(N^{\prime}\) be \(N\) with digit \(\text{P}\) replaced with \((\text{P} - 1)\), and \(\text{B}\) replaced with \((\text{B} + 1)\): \(N^{\prime} :=\overline{(\text{A})\cdots (\text{P}-1) \, (\text{B} + 1) \cdots (\text{C})}\).

The digits of \(N^{\prime}\) would still add up to \(2021\):

\(\begin{aligned}& \text{A} + \cdots + (\text{P} - 1) + (\text{B} + 1) + \cdots + \text{C} \\ &= \text{A} + \cdots + \text{P} + \text{B} + \cdots + \text{C} \\ &= 2021\end{aligned}\).

However, with a smaller digit in place of \(\text{P}\), \(N^{\prime} < N\). This observation would also contradict the assumption that \(N\!\) is the smallest positive integer whose digits add up to \(2021\!\).

Either way, there would be a contradiction. Hence, the claim is verified: all digits of this \(N\) other than the first digit must be "\(9\)".

Therefore, \(N\) would be in the form: \(N = \overline{\text{A} \, \underbrace{9 \cdots 9}_{\text{many digits}}}\), where \(\text{A}\), the leading digit, could also be \(9\).

Therefore, the price of the next model will be $48,297. The decrease in price represents cost savings for consumers, and it may make the sports car more accessible for some buyers.

The price of the next model will decrease by $2,703. The decrease is found by multiplying the current price by 0.053. The price of the next model will be $48,297. This is found by subtracting the decrease from the current price.
To calculate the decrease in price, we need to multiply the current price of $51,000 by the percentage decrease of 5.3%. This gives us a decrease of $2,703. To find the price of the next model, we need to subtract the decrease from the current price.

Therefore, the price of the next model will be $48,297. The decrease in price represents cost savings for consumers, and it may make the sports car more accessible for some buyers.

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Given:

Machine A covers 5/8 square feet in 1/2 hour.

Machine B covers 2/3 square feet in 1/3 hour.

Solution:

The unit rate of the machine A will be as

The unit rate of the machine B will be as

Answer:

Hence, the unit rate of the machine B is greater.

Answer:

Min = 1 4/6

Max = 3

Sum = min + max

=> sum = 1 4/6 + 3

=> sum = 4 /4/6

Answer:

4 4/6

Step-by-step explanation:

Yes, the laws of exponents hold for positive and negative numbers, fractional exponents, and even irrational exponents such as π.

The laws of exponents apply to both positive and negative numbers. For example, when multiplying or dividing numbers with exponents, the exponents can be added or subtracted, respectively, regardless of the sign of the base. Similarly, when raising a number with an exponent to another exponent, the exponents can be multiplied. These rules hold true for positive and negative numbers, allowing consistent manipulation of expressions involving exponents.

Yes, the laws of exponents also hold for fractional exponents. The most common law, the power rule, states that when raising a number to a fractional exponent, the exponent can be expressed as a quotient of integers. This allows us to extend the laws of exponents to include fractional exponents and perform calculations accordingly. For example, we can multiply numbers with fractional exponents by adding the exponents and divide them by subtracting the exponents.

Yes, the laws of exponents also hold for irrational exponents, including numbers like π. Although irrational exponents cannot be expressed as exact fractions or decimals, we can still apply the laws of exponents. When working with irrational exponents, the calculations typically involve approximations or infinite series representations. However, the fundamental rules of exponentiation, such as adding, subtracting, or multiplying exponents, remain valid for irrational exponents as well.

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We can write (15 + 45) as a product of 2 factors using GCF and the distributive property 15(1 + 3).

We are given the following expression-

15 + 45

Now, we can factorize 15 into prime factors as follows -

= 3 × 5 (15 × 1)

Similarly, we can factorize 45 into prime factors as follows -

= 3 × 3 × 5 (15 × 3)

Thus, the greatest common factor of 15 and 45 is 15, so we can

= 15 × 1 = 15 and 15 × 3 is 45

Hence, we can write (15 + 45) as 15(1 + 3).

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The finite correction factor should be used in the computation of the standard deviation of the sample mean and the standard population when n/N is less than 0.05. The correct option is less than 0.05.

The finite correction factor is a statistical adjustment that is applied when the sample size (n) is relatively small compared to the population size (N).

When n/N is less than 0.05, it indicates that the sample size is significantly smaller than the population size, and the finite correction factor helps to account for the potential bias that can arise from this imbalance.

By applying the correction factor, the standard deviation of the sample mean and the standard deviation of the population are adjusted to provide more accurate estimates of the true variability in the data.

This correction is necessary to ensure the validity of statistical inferences and to account for potential errors in estimation.

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Approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.

To find the proportion of customers who take more than 10 minutes to check out, we need to calculate the cumulative distribution function (CDF) of an exponential distribution at 10 minutes and subtract it from 1. The CDF for an exponential distribution with mean (lambda) 5 minutes is given by:

CDF = 1 - e^(- λ * x)

Plugging in λ = 0.2 (1/mean) and x = 10, we get:

CDF = 1 - e^(-0.2 * 10) = 1 - e^(-2) = 1 - 0.135 = 0.865

So, approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.

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Answer:

4 hours

Step-by-step explanation:

Distance covered = 30 km

Usual Speed of both = 10km/hr

Justin's speed = 1/2 * 10 = 5km/hr

Ari's speed = 3/2 * 10 = 15 km/hr

Time taken = distance / speed

Justin's time = 30 / 5 = 6 hours

Ari's time = 30 / 15 = 2 hours

Time difference = (6 - 2) = 4 hours

To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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Answer:

-3 < x \(\leq\) 4

Step-by-step explanation:

A closed circle means that you are including that number in the solution and an open circle means that you are not including that number in the solution.  In this situation 4 is a solution, but -3 is not.

Helping in the name of Jesus.

Answer:

x=7/3

Step-by-step explanation:

8 ^ (x - 1 ) = 16

We need to rewrite 8 as 2^3  and 16 as 2^4

2^3 ^ (x - 1 ) = 2^4

We know that a^b^c = a^(b*c)

2^(3(x-1)) = 2^4

The bases are the same so the exponents are the same

3(x-1) = 4

Distribute

3x-3 = 4

Add 3 to each side

3x-3+3 = 4+3

3x = 7

Divide by 3

3x/3 = 7/3

x=7/3

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

start with -29, multiply each term by 3

start with 90, multiply each term by 0.2

start with 67 and multiply each term by 2

The colony has 8576 cells after 7 minutes

Step-by-step explanation:

The pattern for the first part of Q2 is multiply each term by 3.

-29, -87, -261, -783... start with -29, multiply each term by 3

The pattern for the second part of Q2 is multiply each term by 0.2.

90, 18, 3.6, 0.72... start with 90, multiply each term by 0.2

The pattern for the third part of Q2 is multiply each term by 2

start with 67 and multiply each term by 2

The colony has 67×2×2×2×2×2×2×2= 8576 cells after 7 minutes

52 students passed only one subject

Let's use the following variables to represent the number of students who passed each subject:

P(Ga): the number of students who passed Ga

P(Fante): the number of students who passed Fante

From the problem statement, we know that:

P(Ga) = P(Fante) + 6, since the number of students who passed Ga is 6 more than the number who passed Fante

P(Ga ∩ Fante) = 8, since 8 students passed both subjects

P(Ga ∪ Fante) = 60, since every student passed at least one subject

We want to find the number of students who passed only one subject, which is equal to the total number of students who passed Ga minus the number of students who passed both subjects, plus the number of students who passed Fante but not Ga. In symbols:

P(Ga) - P(Ga ∩ Fante) + (P(Fante) - P(Ga ∩ Fante))

Substituting the values we know:

(P(Fante) + 6) - 8 + (P(Fante) - 8)

Simplifying:

2P(Fante) - 10

We also know that P(Ga) + P(Fante) - P(Ga ∩ Fante) = P(Ga ∪ Fante) = 60.

Substituting the values we know:

P(Ga) + P(Fante) - 8 = 60

P(Ga) + P(Fante) = 68

Substituting P(Ga) = P(Fante) + 6:

2P(Fante) + 6 = 68

2P(Fante) = 62

P(Fante) = 31

Therefore, the number of students who passed only one subject is:

2P(Fante) - 10 = 2(31) - 10 = 52

Therefore, 52 students passed only one subject.

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Hakeem bought 8 apples and 4 bananas worth 11.60 at the grocery store.

Let's assume the number of bananas that Hakeem bought is x.

Since Hakeem bought twice as many apples as bananas, the number of apples he bought would be 2x.

The cost of each apple is 1, so the total cost of apples would be 2x dollars.

The cost of each banana is 0.90, so the total cost of bananas would be 0.9x dollars.

According to the given information, the total cost of apples and bananas is

\($11.60.\)

Therefore, we can set up the equation:

2x + 0.9x = 11.60

Combining like terms:

2.9x = 11.60

Dividing both sides by 2.9:

x = 11.60 / 2.9

x = 4

Hence, Hakeem bought 4 bananas and twice as many apples, which would be

2 (4) = 8 apples.

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Hakeem bought 8 apples and 4 bananas worth 11.60 at the grocery store.

Let's assume the number of bananas that Hakeem bought is x.

Since Hakeem bought twice as many apples as bananas, the number of apples he bought would be 2x.

The cost of each apple is 1, so the total cost of apples would be 2x dollars.

The cost of each banana is 0.90, so the total cost of bananas would be 0.9x dollars.

According to the given information, the total cost of apples and bananas is 11.60.

Therefore, we can set up the equation:

2x + 0.9x = 11.60

Combining like terms:

2.9x = 11.60

Dividing both sides by 2.9:

x = 11.60 / 2.9

x = 4

Hence, Hakeem bought 4 bananas and twice as many apples, which would be.

2 (4) = 8 apples.

To know more about Hakeem bought 8 apples and 4 bananas worth 11.60 at the grocery store.

Therefore, we can set up the equation:

2x + 0.9x = 11.60.

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Answer:

This is really simple, look:

Step-by-step explanation:

If you want to find the unit prize for a dozen cupcakes, and the dozen is 27.00 dollars, you only have to do this:

27 divided into 12

because the unit prize is just basically the price of 1 cupcake

the answer would be 2.25 each

Answer:

\(g=2\)

Step-by-step explanation:

So we have the equation:

\(2g+6+5g=20\)

Combine like terms on the left:

\(7g+6=20\)

Subtract 6 from both sides:

\(7g=14\)

Divide both sides by 7:

\(g=2\)

And we're done!

Step-by-step explanation:

2g+5g=20-6

7g=14

g=2

:)))

The percent of the ship's passengers held round-trip tickets is 50/100 = 50%.

Since the number of passengers on the ship is immaterial, let the number of passengers on the ship be 100 for convenience.  

Let x be the number of passengers that held round-trip tickets.  

Then, since 20 percent of the passengers held a round-trip ticket and took their cars aboard the ship, 0.20(100) = 20 passengers held round-trip tickets and took their cars aboard the ship.  

The remaining passengers with round-trip tickets did not take their cars aboard, and they represent 0.6x (that is, 60 percent of the passengers with round-trip tickets).  

Thus, 0.6x + 20 = x, from which it follows that 20 = 0.4x, and so x = 50.  

The percent of passengers with round-trip tickets is, then, 50/100 = 50%

A roundtrip flight is a flight itinerary that includes one flight to a vacation spot and some other flight lower back from that destination, which include flying from NYC to Paris after which Paris lowers back to NYC. The direction might also include layovers or connections, however, the beginning and endpoint are equal.

Ask the enterprise to alter the round-trip ticket for one-way usage. although airways exercise a varying degree of flexibility, many airlines will regulate a round-ride fare to permit one-manner use, though a few airlines might also charge a penalty or charge for this provider.

also known as “return air tickets,” round-journey tickets are flights from and again to the equal place beginning. A one-manner price tag, then again, simplest lets you to fly your destination, now not back from it.

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Answer:

x = -2/3  x=1

Step-by-step explanation:

We cant solve by substitution with just one equation

-3x^2 + x +2=0

Factor out a negative

-(3x^2 -x-2) = 0

Divide by negative 1

(3x^2 -x-2) = 0

Factor

(3x +2) (x-1)=0

Using the zero product property

3x+2 =0   x-1 =0

3x= -2   x=1

x = -2/3  x=1

Answer:

\(x = \frac{2}{3} \\ x = - 1\)

Step-by-step explanation:

\(x - 3 {x}^{2} + 2 = 0 \\ - 3 {x}^{2} + x + 2 = 0 \\ - 3 {x}^{2} - 3x + 2x + 2 = 0 \\ - 3x(x + 1) + 2(x + 1) = 0 \\ ( - 3x + 2)(x + 1) = 0\)

\( - 3x + 2 = 0 \\ - 3x = - 2 \\ \frac{ - 3x}{ - 3} = \frac{ - 2}{ - 3} \\ x = \frac{2}{3} \)

\(x + 1 = 0 \\ x = - 1\)

hope this helps

brainliest appreciated

good luck! have a nice day!

7Y=-1X

Step-by-step explanation:

Ya me la pusieron a mi y soy muy bueno en matemáticas

Answer:

x = 1; y = 3

Step-by-step explanation:

Get the unknowns on one side of the equal sign and the known numbers on the other:

EQUATION 1: y = 2x + 1 (subtract 2x from both sides)

y -2x = 1

EQUATION 2: y = 6 -3x (add 3x to both sides)

y + 3x = 6

Now we have two simultaneous equations:

y -2x = 1

y + 3x = 6

subtraction gives -5x = -5 so x = 1

Substitute x = 1 into one of the original equations to find y.

y + 3x = 6 becomes y + 3 = 6, so y = 3

The equivalent regular expression for the given DFA using Arden's theorem is (a+b)(a+bb+ba(a+b))*.

1. Start with the given DFA and its transition table:

  State | Input a | Input b

  ------|---------|---------

  1     | 3       | 2

  2     | 1       | 2

  3     | 2       | -

2. Apply Arden's theorem, which states that for a DFA with a single final state, the regular expression for that state can be obtained by substituting the regular expressions for the other states into the equation: R = S + RP, where R is the regular expression for the final state, S is the regular expression for the current state, and P is the regular expression for the next state.

3. Begin with state 1:

  - Substitute the regular expression for state 3 into the equation:

    1 = 3a + ε

  - Since state 3 has no outgoing transition for input b, it is represented as ε (empty string).

4. Move to state 2:

  - Substitute the regular expression for state 1 into the equation:

    2 = 1(a + b) + 2a + 3b

  - State 1 is represented as (a + b) from the previous step.

  - Note that 1 is substituted because it is the regular expression for the state itself.

5. Move to state 3:

  - Substitute the regular expression for state 2 into the equation:

    3 = 2b

  - State 2 is represented as b from the previous step.

6. Substitute the obtained regular expressions back into the previous equations until no new substitutions are made:

  - In this case, there are no new substitutions to be made.

7. The resulting regular expression for state 1 is (a + b)(a + bb + ba(a + b))*.

Therefore, the equivalent regular expression for the given DFA using Arden's theorem is (a + b)(a + bb + ba(a + b))*.

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The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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The phrase which describes the linear relationship between x and y is; Choice B

The given mathematical form of the expression is; y = x/2.

From the expression above;

On this note, the phrase which represents the linear relationship between x and y is; x is 2 times y.

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Answer:

Step-by-step explanation:

1           |          3

2          |          4

3          |          5

Y  i s  2  m o r e  t h a n  X

The number of tickets sold will be equal to 29.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Let x represent the number of child tickets that were sold

Let y represent the number of adult tickets that were sold

5.30x +9.40y= 1206

The number of adult tickets sold was three times greater than the number of child tickets,

y= 3x

Substitute 3x for y in the equation,

5.40x + 9.40y= 974.40

5.40x + 9.40(3x)= 974.40

5.40x + 28.2x= 974.40

33.6x= 974.40

Divide both sides by the coefficient of x which is 33.5,

x= 974.40/33.6

x = 29

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