The number of millions of visitors that a tourist attraction gets can be modeled using the equation y = 2.3 sin[0.523(x + 1)] + 4.1, where x = 1 represents January, x = 2 represents
February, and so on.
a) Determine the period of the function and explain its meaning.
b) Which month has the most visitors?
c) Which month has the least visitors?
Please explain answers thank you!

Step-by-step explanation:

If x = 6 and y = 4. Substitute x and y in the expression.

4x+y

4(6)+(4)

24+4

28

2y²

2(6)²

2(36)

72

( x - y )²

(6+4)²

(10)²

100

Random sampling methods of assigning probabilities is used when we are dealing with sampling.

Random sampling is a method of assigning probabilities used when dealing with samples of a population. It involves randomly selecting a sample from the population and then using that sample to estimate the probabilities of different outcomes. This is done by calculating the proportion of the sample that falls into each category. For example, if you are trying to determine the probability of a certain outcome, you would randomly select a sample from the population and then count how many of the individuals in the sample fall into that category. The probability of the outcome would then be calculated by dividing the number of individuals in that category by the total number of individuals in the sample.

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There are a total of 212 pounds of berries, and the number of friends sharing the berries is equal to 4.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

The total amount of berries = 212 pounds

The number of berries received by each one = 54 pounds

Then, the number of friends sharing the berries is:

212/54 = 3.92 ≈ 4 friends.

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xy + xz is an even integer & x is even and y + xz is an odd integer &  either (x-1) is even or (y-z) is even .

1. xy + xz is an even integer - SUFFICIENT

Given:

xy + z is odd ...(i)

xy + xz is even ...(ii)

subtracting (ii) from (i)

we get xz - z, which should be odd (* since odd - even = odd)

=> z(x-1) is odd

=> both z and (x-1) is odd

=> since (x-1) is odd, x must be even.

2. y + xz is an odd integer -INSUFFICIENT

Given:

xy + z is odd ...(i)

y + xz is odd ...(ii)

subtracting (ii) from (i)

we get xy + z - y - xz

= (x-1)(y-z) , which should be even

=> either (x-1) is even or (y-z) is even ....insufficient to determine

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Answer:

27

Step-by-step explanation:

every 30 men = 9 men with beards

you have 30 3 times in 90 so you get 27

60÷2=30

18÷2=9

30 men normal = 9 men with beards

90÷30=3

3×9=27

Answer:

27 is correct

Step-by-step explanation:

18 out of the last 60 men who walked by had a beard.

based on the given condition formulate

\(\boxed{\frac{18}{60}=\frac{x}{90} }\)

\(\boxed{60x=18(90)}\)

\(\boxed{\frac{18~x~90}{60} }\)

\(\boxed{x=27}\)

60÷2=30

18÷2=9

30 men normal = 9 men with beards

90÷30=3

how many of the next 90 men who walk by

you have 30 × 3  = 90 so you get 27

3 × 9 = 27

Therefore the correct answer is 27

Hope this helps!

if you have any queries please ask.

Answer:

d'accord est-ce moi ou pas la même chose que j'ai fait

Answer:

29.33333... feet per second

Step-by-step explanation:

20×5280=105600 Because 1 mi=5280ft, you multiply 20 by 5280

105600÷60=1760  You divide 105600 by 60 because there are 60 minutes in an hour

1760 ÷ 60  You divide it by 60 again because there are 60 seconds in a minute

Your answer is 29.33333...

The approximate probability that the baggage limit will not be exceeded on the particular airplane is approximately 0.033, or 3.3%.

To calculate this probability, we need to use the concept of the standard normal distribution. We can convert the given mean and standard deviation of the individual passengers' checked-in baggage weight into a standard normal distribution by applying the formula:

Z = (X - μ) / σ

where Z is the standard score, X is the individual baggage weight, μ is the mean weight, and σ is the standard deviation.

In this case, the maximum allowable weight of the checked baggage for the airplane is 6,000 pounds, and the capacity of the airplane is 125 passengers. So the maximum allowable weight per passenger is 6,000 / 125 = 48 pounds.

Now, we need to find the probability that the baggage weight of a randomly selected passenger is less than or equal to 48 pounds. We can convert this value into a standard score by substituting the values into the formula:

Z = (48 - 42) / 25 = 0.24

We can then look up the probability associated with this standard score in the standard normal distribution table or use a statistical calculator to find that the probability is approximately 0.590.

Since there are 125 passengers on the plane, we need to calculate the probability that all of them have baggage weights less than or equal to 48 pounds. This is done by raising the individual probability to the power of the number of passengers:

P = 0.590^125 ≈ 0.033

Therefore, the approximate probability that the baggage limit will not be exceeded on the particular airplane is approximately 0.033, or 3.3%.

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It is more likely that the distance across a circular field is the diameter rather than the circumference.

To determine whether the distance across a circular field is the diameter or the circumference, we can use some formulas that relate these parts of a circle. The formulas are:

Circumference = π * diameter

Diameter = 2 * radius

Radius = diameter / 2

If we plug in the given distance of 98.638 meters into these formulas, we can see which one gives a reasonable value for the other parts of the circle. For example, if we assume that the distance is the diameter, then we can find the radius and circumference as follows:

Radius = diameter / 2

Radius = 98.638 / 2

Radius = 49.319 meters

Circumference = π * diameter

Circumference = π * 98.638

Circumference ≈ 310.05 meters

These values seem reasonable for a circular field. However, if we assume that the distance is the circumference, then we can find the diameter and radius as follows:

Diameter = circumference / π

Diameter = 98.638 / π

Diameter ≈ 31.39 meters

Radius = diameter / 2

Radius = 31.39 / 2

Radius ≈ 15.695 meters

These values seem too small for a circular field. Therefore, it is more likely that the distance across a circular field is the diameter rather than the circumference.

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Complete question:

The distance across a circular field is 98.638 meters. Is it a diameter, a radius or a circumference?

Answer:

$12,088

Step-by-step explanation:

Value = $28,000

Rate, r = 14% = 0.14

Time = 6 years

Using an exponential function :

A = Pe^-rt

P = initial value

A = final worth

A = 28000*e^-(0.14*6)

A = 28000 * e^-0.84

A = 28000 * 0.4317105

A = 12087.894

Worth after 6 years = $12,088

The series   \($\sum_{n=1}^{\infty} \frac{n^2 + 1}{n^{10}}$\) converges. The given series converges.

To test this series for convergence  \($\sum_{n=1}^{\infty} \frac{n^2 + 1}{n^{10}}$\) You could use the Limit Comparison Test, comparing it to the series

\($\sum_{n=1}^{\infty} \frac{1}{n}$\)  

where \(p=1 > 0$.\)

Now, we will use the Limit Comparison Test to determine if the given series converges or diverges.According to the Limit Comparison Test,

if \($\lim_{n\to\infty} \frac{a_n}{b_n}\)  =\(c$\) where \($c > 0$\),

then both \($\sum_{n=1}^{\infty} a_n$\)

and \($\sum_{n=1}^{\infty} b_n$\) converge or both diverge.

That is  , \($\bullet$\) If  \($\sum_{n=1}^{\infty} b_n$\) converges,

then  \($\sum_{n=1}^{\infty} a_n$\)  converges\(.$\bullet$\)

If \($\sum_{n=1}^{\infty} b_n$\) diverges,

then \($\sum_{n=1}^{\infty} a_n$\)  diverges.

Let \($a_n = \frac{n^2 + 1}{n^{10}}$\) and

\($b_n = \frac{1}{n}$\)

Then, \($\lim_{n\to\infty} \frac{a_n}{b_n}\) =  \(\lim_{n\to\infty} \frac{n^2 + 1}{n^{10}} \cdot \frac{n}{1}\)

= \(\lim_{n\to\infty} \frac{n^3 + n}{n^{10}}\)

=\(\lim_{n\to\infty} \frac{1}{n^6}+ \lim_{n\to\infty} \frac{1}{n^9}\)

=\(0$.\)

Since \(\lim_{n\to\infty} \frac{a_n}{b_n} = 0$,\)

which is a finite positive number.

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The limit of a(n) / b(n) is infinity, and b(n) is a known convergent series, we can conclude that the original series \(\sum (1/n^2 + 1/n)\) also converges. The statement "Converges" is the correct answer.

To test the series \(\sum(1/n^2 + 1/n)\) for convergence, we can use the Limit Comparison Test.

We will compare it to the series Σ(1/n),

which is a known series that converges.

Let's denote the original series as \(a(n) = 1/n^2 + 1/n\),

and the comparison series as b(n) = 1/n.

We need to calculate the limit of the ratio of the terms of the two series as n approaches infinity:

\(\lim_{n \to \infty} a(n)/b(n)\\ \\ \lim_{n \to \infty} [(1/n^2 + 1/n) / (1/n)]\\\\ \lim_{n \to \infty} (n+1)\)

As n approaches infinity, the limit of (n + 1) is infinity.

Since the limit of a(n) / b(n) is infinity, and b(n) is a known convergent series, we can conclude that the original series \(\sum(1/n^2 + 1/n)\) also converges.

Therefore, the statement "Converges" is the correct answer.

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Answer:

h = 41.25 foot

Step-by-step explanation:

Given that,

Height of a street light = 7.5 feet

It casts a 3-foot-long shadow.

A nearby flagpole casts a 16.5 foot long shadow. We need to find the height of the flag pole. Let the height be h. It can be calculated as :

\(\dfrac{\text{height of street light}}{\text{height of shadow of street light}}=\dfrac{\text{height of flagpole}}{\text{height of shadow of the flag pole}}\\\\\dfrac{7.5}{3}=\dfrac{h}{16.5}\\\\h=\dfrac{7.5\times 16.5}{3}\\\\h=41.25\ foot\)

So, the height of the flag pole is equal to 41.25 foot.

The height of the flag pole is 41.25 feet tall.

Word problems in mathematics are methods used to solve real-life cases. They usually follow a logical approach with the use of arithmetic operations when solving them.

From the parameters given:

Let the height of the flag pole be = x

∴

To determine the height of the flag pole, we have:

\(\mathbf{x = \dfrac{7.5 feet \ tall \times 16.5 \ foot \ long} {3 \ foot \ long} }\)

x = 41.25 feet tall

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To find the expected number of sixes appearing on three die rolls, we can calculate the probability of rolling a six on each individual roll and then multiply it by the number of rolls.

The probability of rolling a six on a single roll of a fair die is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a six.

Since the rolls are independent events, we can multiply the probabilities together to find the probability of rolling a six on all three rolls:

(1/6) * (1/6) * (1/6) = 1/216

Therefore, the probability of rolling a six on all three rolls is 1/216.

To find the expected number of sixes, we multiply the probability by the number of rolls:

Expected number of sixes = (1/216) * 3 = 1/72

So, the expected number of sixes appearing on three die rolls is 1/72.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

D. 797,481

Step-by-step explanation:

So, with the number 653,841, the number that is in the hundreds place is 8, meaning that the number is 800. So now, since you have to find 1/10 of the value, you have to divid it by 10, giving you 80. Now, looking at the answers, you have to find the number with 8 in the tens place, which is D.

Answer:

no i do think so that dose not make sensens

To obtain 3x² + 5xy from 2x² + 2xy², you would need to add the polynomial x² + 5xy to the original expression.

In order to add two polynomials together, the terms must have the same degree and variable. In this case, we see that 2x^2 and 2xy^2 have different degrees and variables. So, we need to find a polynomial that when added to 2x² + 2xy² will give us 3x² + 5xy.

To do this, we can start by looking at the x² term in 3x² + 5xy. We can see that we need to add x² to our original polynomial. Next, we can look at the xy term in 3x² + 5xy. We can see that we need to add 5xy to our original polynomial.

So by adding x² + 5xy to 2x² + 2xy², we get the desired polynomial of 3x² + 5xy.

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What should be added to 2x² + 2xy² to obtain 3x² + 5xy.

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Answer:

So bassiccalyy the answer is 3344/3 because it is not equivalent to 4

To find the y-intercept of the function k(x) = 3x^4 + 4x^3 - 36x^2 - 10, we evaluate the function at x = 0. The y-intercept is the point where the graph of the function intersects the y-axis. In this case, the y-intercept is -10.

The y-intercept of a function is the value of the function when x = 0. To find the y-intercept of the function k(x) = 3x^4 + 4x^3 - 36x^2 - 10, we substitute x = 0 into the function:

k(0) = 3(0)^4 + 4(0)^3 - 36(0)^2 - 10

= 0 + 0 - 0 - 10

= -10

Therefore, the y-intercept of the function is -10. This means that the graph of the function k(x) intersects the y-axis at the point (0, -10).

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the matching expression to the exponent rules are:

xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾

xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾

x⁰ = 1

(xᵃ)ᵇ = x⁽ᵃ*ᵇ⁾

x⁻ᵃ = 1 / xᵃ

What are the exponent rules?

The power rule of exponents means a number with an exponent raised to another exponent. You will just simply multiply the exponents which are a and b.

xᵃ / xᵇ = ?

When dividing two powers with the same base, you can subtract the exponents.

So:

xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾

In other words, when you divide xᵃ by xᵇ, you can subtract the exponent of x in the denominator from the exponent of x in the numerator. The result is x raised to the difference between the exponents.

xᵃ * xᵇ = ?

When you multiply two powers with the same base, you can add the exponents. So:

xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾

In other words, when you multiply xᵃ by xᵇ, you can add the exponent of x in the numerator to the exponent of x in the denominator. The result is x raised to the sum of the exponents.

x⁰ = ?

Any non-zero number raised to the power of 0 is equal to 1. Therefore,

x⁰ = 1

This is true for any non-zero real number x.

(xᵃ)ᵇ  = ?

(x^a)^b can be simplified using the power of a power rule, which states that when a power is raised to another power, you can multiply the exponents. So:

(xᵃ)ᵇ = x⁽ᵃ*ᵇ⁾

In other words, when you raise xᵃ to the power of b, you can multiply the exponent of x by b. The result is x raised to the product of the exponents.

x⁻ᵃ = ?

x⁻ᵃ can be simplified using the negative exponent rule, which states that when a number has a negative exponent, you can move it to the denominator and make the exponent positive. So:

x⁻ᵃ = 1 / xᵃ

In other words, when x is raised to the power of -a, you can write it as 1 divided by x raised to the power of a.

Hence,  the matching expression to the exponent rules are:

xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾

xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾

x⁰ = 1

(xᵃ)ᵇ = x⁽ᵃ*ᵇ⁾

x⁻ᵃ = 1 / xᵃ

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This is a description of a graphical representation of the labor market, where a line represents the demand curve for labor, showing the relationship between the wage and the quantity of workers demanded, and another line represents the supply curve of labor, showing the relationship between the wage and the quantity of people willing to work. The point where the two lines intersect represents the equilibrium wage and quantity of labor in the market.

The graphical representation of the labor market shows two lines, one representing the demand curve for labor and the other representing the supply curve for labor. The demand curve shows the relationship between the wage offered by firms and the quantity of workers demanded. The supply curve shows the relationship between the wage offered by firms and the quantity of people willing to work. The intersection of these two curves determines the equilibrium wage and quantity of labor in the market.

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Answer:

Step-by-step explanation:

The equation is V = √(20L).

Solve this equation for L and the result is L = V2/20

Since V = 57 mph, putting this value into the equation, L = (57)2/20 = 162.45 ft should be his skid marks

Answer:

  A.  0

Step-by-step explanation:

You want the discriminant of the quadratic 4x²+4x+1.

The discriminant of quadratic ax²+bx+c is ...

  d = b² -4ac

Your given expression has ...

Substituting these values into the formula for the discriminant, we get ...

  d = 4² -4(4)(1) = 16 -16 = 0

The discriminant of the polynomial is 0.

The estimated value of Ay is 1.7.

Given equation:y = tan(4x + 6)At x = 3 and dx = 0.1

We have to find dy.Using the formula for differential:dy = y′dx

Here, y′ denotes the derivative of y with respect to x.To find y′, differentiate the given equation, we get:y′ = sec²(4x + 6)

On substituting the values of x and dx in the above expressions, we get:dy = y′dx= sec²(4x + 6)dxPutting x = 3 and dx = 0.1, we get:dy = sec²(4x + 6)dx= sec²(4 × 3 + 6) × 0.1= sec²(18) × 0.1= 0.08844 (approx)

Thus, the differential dy is 0.08844 when x = 3 and dx = 0.1.Given equation:y = 4x²At x = 1 and dx = 0.4

We have to find the change in y, Ay.Using the formula for differential:dy = y′dx

Here, y′ denotes the derivative of y with respect to x.To find y′, differentiate the given equation, we get:y′ = 8xOn substituting the values of x and dx in the above expressions, we get:dy = y′dx= 8x × dxPutting x = 1 and dx = 0.4, we get:dy = 8x × dx= 8 × 1 × 0.4= 3.2Thus, the change in y, Ay = dy = 3.2 when x = 1 and dx = 0.4.Given equation:y = 4√xAt x = 3 and dx = 0.4

We have to find the differential dy.Using the formula for differential:dy = y′dx

Here, y′ denotes the derivative of y with respect to x.To find y′, differentiate the given equation, we get:y′ = 2/√x

On substituting the values of x and dx in the above expressions, we get:dy = y′dx= 2/√x × dxPutting x = 3 and dx = 0.4, we get:dy = 2/√x × dx= 2/√3 × 0.4= 0.88445 (approx)Thus, the differential dy is 0.88445 when x = 3 and dx = 0.4.Given equation:y = 3x² + 5x + 4At x = 2 and dx = 0.1

We have to estimate Ay using linear approximation.To estimate Ay using linear approximation:

Step 1: Find the derivative of y, y′.y′ = 6x + 5

Step 2: Find the value of y′ at x = 2.y′(2) = 6(2) + 5= 12 + 5= 17

Step 3: Use the formula for linear approximation:Δy = y′(a)Δx

Here, a = 2 and Δx = dx = 0.1

Substituting the values of a, Δx, and y′(a) in the above expression, we get:Δy = y′(a)Δx= 17 × 0.1= 1.7

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Answer:

False

Step-by-step explanation:

The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

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Answer:

80.95

Step-by-step explanation:

Percentage increase = \(\frac{New Value - Old Value}{Old Value}\) *100

=> (38-21)* 100/21 = 80.9523%

The answer round it to the nearest 100th = 80.95%

Answer:

2(x+21) > -30

Step-by-step explanation:

The "number" is x

The sum of x and 21 times 2

Greater than looks like this: >

-30 less than 2(x+21)

On solving the algebraic expression 4nm^0 × 2m^4n^3, the value is obtained as 10368.

What is algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

The given algebraic expression is -

4nm^0 × 2m^4n^3

The values for n and m is given as 2 and 3 respectively.

Substitute the values of n and m in the algebraic expression.

= 4nm^0 × 2m^4n³

= 4(2)(3)^0 × 2(3)^4(2)³

Use the exponents rule -

= 4(2)(1) × 2(81)(8)

Use the arithmetic operation of multiplication -

= 8 × 1296

= 10368

Therefore, the final value is obtained as 10368.

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If m=3 and n=2. What is 4nm^0 x 2m^4n^3 ?

Answer:

(5, 4 )

Step-by-step explanation:

Given the 2 equations

3x - y = 11 → (1)

- 2x - 4y = - 26 → (2)

Multiplying (1) by - 4 and adding to (2) will eliminate the y- term

- 12x + 4y = - 44 → (3)

Add (2) and (3) term by term to eliminate y

- 14x + 0 = - 70

- 14x = - 70 ( divide both sides by - 14 )

x = 5

Substitute x = 5 into either of the 2 equations and solve for y

Substituting into (1)

3(5) - y = 11

15 - y = 11 ( subtract 15 from both sides )

- y = - 4 ( multiply both sides by - 1 )

y = 4

solution is (5, 4 )