Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x, y, and z in terms of the parameter

a) x + 2y − 7z = −8
b) 2x + y + z = 23
c) 3x + 9 y − 36 z = −63

Answer:

The answer to your question is AC = 14

Step-by-step explanation:

To solve this problem, we must use trigonometric functions.

And we must look for a trigonometric function that relates the opposite side and the hypotenuse.

This trigonometric function is the sine

   [tex]sin\alpha = \frac{opposite side}{hypotenuse}[/tex]

solve for Opposite side = AC

  AC = hypotenuse x sin α

- Substitution

  AC = 25 x sin 34

- Simplification

  AC = 25 x 0.56

- Result

  AC = 14

To know how much of Hillary's payments are deductible as alimony in 2019, we first need to figure out how old her son was when Hillary got divorced in 2016.

Given that Hillary has to pay until her son turns 18 and this occurs 7 years after the divorce, this means that her son was 18 - 7 = 11 years old in 2016.

Therefore, he will be turning 18 in 2025 (2016 + 9 years).

In 2019, which is 3 years after 2016, her son would be 11 + 3 = 14 years old. As her son has not yet reached 18 years old, Hillary is still making $200 payments per month in 2019.

Given there are 12 months in a year, the total amount of alimony payments that Hillary made in the year 2019 is 12 * $200 = $2400.

So, the amount of her 2019 payments that are deductible as alimony is $2400.

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Answer: True.

Step-by-step explanation:

The total number of possible digits in the number system :  10  (from 0 to 9)

If there are 6 randomly selected digits in an automobile license tag, and each digit must be one of the 10 integers (0-9), then the choices for each digit in license tag = 10

Fundamental counting principle , the total number of ways to make 6-digits license tag where the choices for each digit in license tag is 10 will be :

[tex]10\times10\times10\times10\times10\times10=10^6[/tex]

Hence, there are [tex]10^6[/tex] possible license tags.

Therefore , the given statement is correct.

Final answer:

The statement is True because for each of the 6 digits in a license tag, there are 10 possible integers, giving us a total of 10^6 possible combinations.

Explanation:

The question relates to probability and combinatorics, which are branches of mathematics that deal with the likelihood of certain outcomes and the combination of different elements, respectively. If an automobile license tag consists of 6 randomly selected digits and each digit must be one of the 10 integers (0-9), then we must consider every digit independently.

Since there are 10 options for each digit, and there are 6 digits, we calculate the total number of possible license tags by multiplying the number of options for each digit. This is done by raising the number of options (10) to the power of the number of digits (6), which gives us: 10^6. Therefore, the statement is True as there are indeed 10^6 possible license tags.

Step-by-step explanation:

Let w be the work of waxing.

Rosita can wax her car in 2 hours or 120 minutes.

Time taken by Rosita = 120 minutes

[tex]\texttt{Rate of Rosita = }\frac{W}{120}[/tex]

Let time taken by Helga be t,

[tex]\texttt{Rate of Helga = }\frac{W}{t}[/tex]

When she works together with Helga, they can wax the car in 45 minutes.

We have

             [tex]\frac{W}{\frac{W}{120}+\frac{W}{t}}=45\\\\120t=45(120+t)\\\\120t=5400+45t\\\\t=72minutes[/tex]

Time taken by Helga to wax the car is 72 minutes

Answer:

The answer to your question is below

Step-by-step explanation:

1.-                           y = 2x - 64

                            x - 2y = 14

Substitution

                            x - 2(2x - 64) = 14

Simplification

                            x - 4x + 128 = 14

                             x - 4x = 14 - 128

                            -3x = - 114

                               x = 114/3

                               x = 38

                             y = 2(38) - 64

                             y = 76 - 64

                             y = 12

Solution (38, 12)

2.-                            y = x - 6

                               3x + 2y = 8

Substitution

                               3x + 2(x - 6) = 8

Simplification

                              3x + 2x - 12 = 8

                              5x = 8 + 12

                              5x = 20

                              x = 20 / 5

                            x = 4

                             y = 4 - 6

                             y = -2

Solution (4 , -2)

3.-                           x - y = 12

                            27 + 3y = 2x

                            x = 12 + y

                            27 + 3y = 2(12 + y)

                            27 + 3y = 24 + 2y

                            3y - 2y = 24 - 27

                                     y = -3

                             x = 12 - 3

                             x = 9

Solution y = -3

4.-                          y = 2x + 14

                           -4x - y = 4

                            -4x - (2x + 14) = 4

                            -4x - 2x - 14 = 4

                            -6x = 4 + 14

                            -6x = 18

                                x = 18/-6

                                x = -3

                            y = 2(-3) + 14

                            y = -6 + 14

                           y = 8

Solution   y = 8

Answer:

There is no solution.

Step-by-step explanation:

Answer:

her weekly allowance is $16

Step-by-step explanation:

Let x represent Joan's weekly paycheck.

Joan spent half of her paycheck going to the movies. This means that the total amount that she spent at the movies is x/2. The amount that she is left with would be

x - x/2 = x/2

She washed the family car and earned 7 dollars. This means that the total amount left with her is

x/2 + 7

if she ended with 18 dollars, it means that

x/2 + 7 = 18

x/2 = 18 - 7 = 11

x = 2 × 11 = $22

Answer:

see the explanation

Step-by-step explanation:

we know that

To determine the rate per pretzel or unit rate, divide the total paid by the number of pretzel

so

[tex]\frac{126}{42}=\$3\ per\ pretzel[/tex]

Jaimie's error

He subtracted 42 from $126 when he should have divided $126 by 42

Answer:

a) [tex] \frac{dx}{dt}= kx (M-x) -hx[/tex]

[tex] \frac{dx}{dt}= kx (M -x- \frac{h}{k})[/tex]

b) [tex] M -\frac{h}{k}>0 [/tex]

Let's say that [tex] a=M -\frac{h}{k}>0[/tex]

If we multiply the woule equation by k we got:

[tex] kM -h >0[/tex]

So then we satisfy that the equation is also logistic since the parameter [tex] a>0[/tex]

c) If we assume that [tex] kM <h[/tex] then we have that [tex] a<0[/tex]

And then [tec] kx (a -x) <0[/tex] for any value of [tex] x>0[/tex]

And if that hhapens then the population will tend to 0 for any initial condition established/

Step-by-step explanation:

For this case we have the following logistic equation [tex] \frac{dx}{dt}= kx (M-x)[/tex]

Part a

We want to modify our harvesting for this case, so we harvest hx per unit of time for some [tex] h>0[/tex]

So then the model with harvesting who is proportional is given by:

[tex] \frac{dx}{dt}= kx (M-x) -hx[/tex]

And we can write like this:

[tex] \frac{dx}{dt}= kx (M -x- \frac{h}{k})[/tex]

Part b

For this case we assume that [tex] kM>h[/tex]and we need to show that the equation is still logistic. So we need that the sollowing quantity higher than 0

[tex] M -\frac{h}{k}>0 [/tex]

Let's say that [tex] a=M -\frac{h}{k}>0[/tex]

If we multiply the woule equation by k we got:

[tex] kM -h >0[/tex]

So then we satisfy that the equation is also logistic since the parameter [tex] a>0[/tex]

Part c

If we assume that [tex] kM <h[/tex] then we have that [tex] a<0[/tex]

And then [tec] kx (a -x) <0[/tex] for any value of [tex] x>0[/tex]

And if that hhapens then the population will tend to 0 for any initial condition established/

Answer:

Step-by-step explanation:

You swim at 3 km/hr with your body perpendicular to a stream with a current of 5 km/hr.

If your actual velocity is the vector sum of the stream's velocity and your swimming velocity, it means that your actual velocity is the resultant velocity. Let R represent the resultant velocity. It means that

R² = 3² + 5² = 9 + 25

R² = 34

Taking square root of the left hand side and the right hand side of the equation, it becomes

R = √34 = 5.83 km/hr.

Final answer:

To find the swimmer's actual velocity in a stream where the swimmer's velocity is 3 km/hr and the stream's velocity is 5 km/hr, we use the Pythagorean theorem, resulting in an actual velocity of approximately 5.83 km/hr.

Explanation:

The question involves calculating the actual velocity of a swimmer moving in a stream. The swimmer swims at a rate of 3 km/hr perpendicular to the stream, while the stream itself has a current of 5 km/hr.

To find the swimmer's actual velocity when these two vectors are combined, we use the Pythagorean theorem, as the velocities are perpendicular to each other.

Let the swimmer's velocity be represented by Vswimmer = 3 km/hr and the stream's velocity by Vstream = 5 km/hr.

The actual velocity (Vactual) is the vector sum of these two velocities. Since they are at right angles to each other, Vactual can be calculated as [tex]\sqrt{((Vswimmer)^2 + (Vstream)^2)[/tex] .

Substituting the values gives Vactual =[tex]\sqrt{(3^2 + 5^2)} = \sqrt{(9 + 25)} = \sqrt{(34),[/tex] which approximately equals 5.83 km/hr.

Therefore, the actual velocity of the swimmer, taking into account the stream's current, is approximately 5.83 km/hr.

Answer:Sam has 29 movies.

Sam has 11 TV shows.

Step-by-step explanation:

Let x represent the number of movies that Sam has.

Let y represent the number of TV shows that Sam has.

Sam has a total of 40 dvds, movies and tv shows. This means that

x + y = 40 - - - - - - - - - - -1

The number of movies is 4 less then 3 times the number of tv shows. This means that

x = 3y - 4 - - - - - - - - - - -2

Substituting equation 2 into equation 1, it becomes

3y - 4 + y = 40

4y - 4 = 40

4y = 40 + 4 = 44

y = 44/4 = 11

x = 3y - 4 = 3 × 11 - 4

x = 33 - 4

x = 29

By creating a system of equations from the given problem, m + t = 40 and m = 3t - 4, and solving it through substitution, it was determined that Sam has 29 movies and 11 TV shows in his DVD collection.

To solve the given problem, we need to use a system of linear equations. The two variables we need to find are the number of movies (m) and the number of TV shows (t).

According to the problem, the total number of DVDs, which includes both movies and TV shows, is 40. This can be written as an equation: m + t = 40. Additionally, we are told that the number of movies is 4 less than three times the number of TV shows. This gives us a second equation: m = 3t - 4.

Now we have the following system of equations:

We can solve this system by substitution. First, substitute the second equation into the first equation:

Now that we have found the number of TV shows (t), we can calculate the number of movies (m):

Therefore, Sam has 29 movies and 11 TV shows in his collection of 40 DVDs.

Approximately 97.72% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg.

To find the percentage of 18-year-old women with a systolic blood pressure between 96 mmHg and 144 mmHg, we need to calculate the z-scores for the given values using the formula z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

For X = 96 mmHg, z = (96 - 120) / 12 = -2.

For X = 144 mmHg, z = (144 - 120) / 12 = 2.

Using a standard normal distribution table, we can find that approximately 0.9772 (97.72%) of the values fall within 2 standard deviations from the mean. Therefore, approximately 97.72% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg.

https://brainly.com/question/36602693

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Final answer:

Approximately 95% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg, as calculated using Z-scores and the standard normal distribution.

Explanation:

The question asks us to determine the percentage of 18-year-old women who have a systolic blood pressure between 96 mmHg and 144 mmHg, given that the systolic blood pressure is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg.

We will use the concept of Z-scores to find this probability. A Z-score represents the number of standard deviations a data point is from the mean. We can calculate the Z-scores for the systolic blood pressure values of 96 mmHg and 144 mmHg and then use the standard normal distribution table to find the percentages. The calculations are as follows:

Z-score for 96 mmHg = (96 - 120) / 12 = -2
Z-score for 144 mmHg = (144 - 120) / 12 = 2

Looking at the Z-score table, we find that the area between Z = -2 and Z = 2 covers approximately 95% of the data under the normal distribution curve. Therefore, about 95% of 18-year-old women will have a systolic blood pressure between 96 mmHg and 144 mmHg.

Answer:

Last week she work  [tex]3\frac{54}{78}\ hours[/tex].

Step-by-step explanation:

Given:

Last week Stacy earned $24 for baby sitting for hours in her part time job at Burger city she work 12 hours and earned $78.

Now, to find the total hours she work last week.

As, given she work 12 hours and earned $78.

So, to solve by using unitary method:

If she earned $78 in working 12 hours.

So, she earned $1 in working = [tex]\frac{12}{78}\ hour.[/tex]

Thus, she earned $24 in working = [tex]\frac{12}{78} \times 24[/tex]

                                                        [tex]=\frac{288}{78}[/tex]

                                                        [tex]=3\frac{54}{78}\ hours.[/tex]

Therefore, last week she work  [tex]3\frac{54}{78}\ hours[/tex].

Answer:

Miss Silver stein can serve for 12 guests with amount of cake that she has bought.

Step-by-step explanation:

Given:

Number of cakes she bought = 3

Amount of cakes given to each guest = [tex]\frac{1}{4}[/tex]

We need to find the number of guest cakes can be served.

Solution:

Now we can say that;

the number of guest can have the cake to can be calculated by dividing the  Number of cakes she bought from Amount of cakes given to each guest

framing in equation form we get;

Number of guest can have cake = [tex]\frac{3}{\frac{1}{4}} = 3\times\frac{4}{1} =12[/tex]

Hence Miss Silver stein can serve for 12 guests with amount of cake that she has bought.

Answer:

Company made 63 rods with the given amount of steel.

Step-by-step explanation:

Given:

Radius of each rod =4 cm

height of each rod = 30 cm

Number of steel company used = 94953.6

We need to find how many rods company can make.

Solution:

First we will find the Volume of each rod.

Since rod is in cylindrical shape.

So we will use Volume of cylinder.

Now Volume of cylinder is given by π times square of the radius times height.

framing in equation form we get;

Volume of each rod = [tex]\pi r^2h= \pi \times4^2\times 30 = 1507.96 \ cm^3[/tex]

So we can say that steel used to make each rod = 1507.96

Number of steel company used = 94953.6 (given)

To find the number of steel rod company made we will divide Number of steel company used by number of steel used to make each rod.

framing in equation form we get;

number of steel rod company made = [tex]\frac{94953.6}{1507.96}= 62.96\approx63[/tex]

Hence Company made 63 rods with the given amount of steel.

The number of rods made using given data is approximately 63 rods .

To find out how many steel rods a company made based on the total volume of steel used, we need to calculate the volume of one rod and then divide the total volume of steel by this.

The volume of a cylinder (which is the shape of the rods) is calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

Given that each rod has a radius of 4 centimeters and a height of 30 centimeters, the volume of one rod can be found as follows:

V = π(4²)(30)

   ≈ 3.14(16)(30)

   = 1,507.2 cm³

Given the total volume of steel used is 94,953.6 cm³, the number of rods made can be calculated by dividing the total volume of steel by the volume of one rod:

Number of rods = 94,953.6 cm³ / 1,507.2 cm³

                           ≈ 63

Therefore, the company made approximately 63 steel rods.

Answer: The area of triangle ΔXYZ is 12 square inches.

Step-by-step explanation:

Since we have given that

RS = 3 inches

XY = 2 inches

Area of ΔRST = 27 in²

Since ΔRST is similar to ΔXYZ.

So, using the "Area similarity theorem":

[tex]\dfrac{\Delta RST}{\Delta XYZ}=\dfrac{RS^2}{XY^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{3^2}{2^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{9}{4}\\\\\Delta XYZ=3\times 4=12\ in^2[/tex]

Hence, the area of triangle ΔXYZ is 12 square inches.

The area of triangle XYZ is found by squaring the ratio of the corresponding sides of the similar triangles and multiplying it by the area of the larger triangle RST. With the side length ratio of 2:3, the area ratio is (2/3)², resulting in an area of 12  in² for triangle XYZ.

The student's question involves determining the area of a smaller similar triangle (XYZ) given the area of the larger similar triangle (RST) and the lengths of corresponding sides. To solve, we utilize the property that similar triangles' areas are proportional to the square of the ratio of their corresponding sides.

Given:
Length of RS in triangle RST = 3 inches
Length of XY in triangle XYZ = 2 inches
Area of triangle RST (A1) = 27  in²

We establish the ratio of their sides as 2 inches (XY) / 3 inches (RS), which simplifies to 2/3. The ratio of their areas would then be (2/3)² because the area of similar triangles scales with the square of the ratio of their corresponding linear dimensions. Hence, the Area of triangle XYZ (A2) will be A1 × (2/3)².

A2 = 27 in² × (2/3)2 = 27 × 4/9 = 12 in².

The area of triangle XYZ is 12 in².

Answer: the weight of Jon's pet is

(3v - 25) pounds

Step-by-step explanation:

The weight of Jon's dog is v pounds.

His cat weighs 21 pounds less than his dog. It means that the weight of his cat would be

(v - 21) pounds

His bunny weighs 3 pounds less than his cat. It means that the weight of his bunny would be

(v - 21) - 3 = (v - 24) pounds

Therefore, the weight of Jon's pets would be the sum of the weight of his dog, his cat and his bunny. It becomes

v + v - 21 + v - 24 = (3v - 25) pounds.

Final answer:

Jon's pets' total weight is calculated by adding the weight of the dog (v pounds), cat (v - 21 pounds), and bunny (v - 24 pounds), which results in 3v - 45 pounds.

Explanation:

To find the weight of Jon's pets, we start with the known weight of the dog and calculate the other animals' weights based on the given relationships. Jon's dog weighs ( v ) pounds. His cat weights 21 pounds less than his dog, so the cat weighs v - 21 pounds. The bunny weighs 3 pounds less than the cat, which means the bunny weighs (v - 21) - 3 pounds or v - 24 pounds.

Therefore, to find the total weight of Jon's pets, we add the weights of the dog, cat, and bunny together:

Dog's weight: v pounds

Cat's weight: v - 21 pounds

Bunny's weight: v - 24 pounds

The total weight is v + (v - 21) + (v - 24), which simplifies to 3v - 45 pounds.

Answer:

3/80

Step-by-step explanation:

If one fifth of apricots are split into 4 parts, each bag has 1/5 * 1/4 of the original apricots

1/5 * 1/4 = 1/20

Luke keeps 3/4 of those so that's

3/4 * 1/20 = 3/80

Answer:

The weight of the seventh linebacker is = 214 lb.

Step-by-step explanation:

Given:

Mean of 7 linebackers = 236 lb

The weights of first 6 linebackers are:

215 lb, 305 lb, 265 lb, 196 lb, 221 lb and 236 lb

To find the weight of seventh linebacker.

Solution:

Let the weight of the seventh linebacker be = [tex]x[/tex]

The mean of 7 line backers will be given as:

⇒ [tex]\frac{215+305+265+196+221+236+x}{7}[/tex]

The mean of the 7 linebackers is given = 236 lb

Thus, the equation to find [tex]x[/tex] will be :

[tex]\frac{215+305+265+196+221+236+x}{7}=236[/tex]

Simplifying.

[tex]\frac{1438+x}{7}=236[/tex]

Multiplying both sides by 7.

[tex]7.\frac{1438+x}{7}=236(7)[/tex]

[tex]1438+x=1652[/tex]

Subtracting both sides by 1438.

[tex]1438-1438+x=1652-1438[/tex]

∴ [tex]x=214[/tex]

Thus, the weight of the seventh linebacker is = 214 lb.

Answer: The length x =17.64ft

Step-by-step explanation:

Looking at the diagram,to find x,we ues adj/hyp = cos 25°

16/x=cos25°

Cross multiply

X=16/cos25°

X=17.64ft

Answer:

17 feet 8 in

Step-by-step explanation:

im doing it in class imao

Answer:

a relationship ( model equation)

Step-by-step explanation:

the relationship specifies how the dependent variable relies on the independent variable.This helps in manipulating of the variable to see its effect/outcome.The relationship can be mathematical or logical ; it can also be a set of algorithm (program) which can be worked on using the independent variables as inputs. Usually the independent variables influence the dependent variables.

Final answer:

To find the length of each piece of ribbon, divide the total length of 2.65 feet by 5, resulting in 0.53 feet per piece, or approximately 6 inches after converting to a more convenient measurement.

Explanation:

The student's question involves the division of a length of ribbon into equal pieces. Miss Alvarez has a piece of ribbon that is 2.65 feet long and she cuts it into 5 equal pieces. To estimate the length of each piece, we would divide the total length of the ribbon by the number of pieces.

The calculation would be: 2.65 feet ÷ 5 pieces = 0.53 feet per piece. If we want a more convenient measure, we could convert feet to inches since there are 12 inches in a foot, resulting in approximately 6.36 inches per piece (0.53 feet × 12 inches/foot).

As an estimate and for ease of measurement, we might round this to the nearest whole number, suggesting that each piece of ribbon is approximately 6 inches in length.

Answer:

The number of cookies in each package = 6

Step-by-step explanation:

Given:

Taylor purchased a pack of cookies.

Number of cookies Taylor gave to her friends = 5

Number of cookies she had left = 1

To find the number of cookies 'p' in each package.

Solution:

[tex]p\rightarrow[/tex] Number of cookies in each package.

If Taylor gave away 5 cookies to her friends, then the number of cookies left in the package can be represented as:

⇒ [tex]p-5[/tex]

Number of cookies she had left = 1

So, the equation to solve for [tex]p[/tex] can be given as:

[tex]p-5=1[/tex]

Solving for [tex]p[/tex]

Adding 5 both sides.

[tex]p-5+5=1+5[/tex]

∴ [tex]p=6[/tex]

Thus, number of cookies in each package = 6.

Answer:

A. 1 only.

Step-by-step explanation:

Answer: he earned $344 in all.

Step-by-step explanation:

When he does work outdoors he earns $12 an hour. This means that if he works outdoors for x hours, he would earn $12x

When he works indoors he earns $8 an hour. This means that if he works indoors for y hours, he would earn $8y.

Last month he worked 18 hours outdoors. This means that the total amount that he earned working outdoors is

12 × 18 = $216

He worked 16 hours indoors. This means that the total amount that he earned working indoors is

8 × 16 = $128

Total amount that he earned is

216 + 128 = $344

Answer: 0.60 gallon

Step-by-step explanation:

There are 12pounds in a standard US gallon.

12pounds= 1 gallon

5.2 pounds=?

5.2/12 × 1 gallon

0.624 gallon

Rounding to the nearest tenth =0.60

Answer:

(2x-3)/(x+4)

Step-by-step explanation:

Answer:

(x - 4).

Step-by-step explanation:

(x - 4) is common to to top and bottom of the fraction.

The fraction simplifies to (2x+3)/(x+4).

The expression to represent the total price of the supplies is 1.29n + 0.79w + 2.39b

Solution:

Let "n" be the number of nails

Let "w" be the number of washers

Let "b" be the number of bolts

Given that ,

Price of nail = $ 1.29 per lb

Price of washers = $ 0.79 per lb

Price of bolts = $ 2.39 per lb

To find: Expression to represent the total price of the supplies.

Total price = number of nails x Price of nail per lb + number of washers x Price of washers per lb + number of bolts x Price of bolts per lb

[tex]Total\ price = n \times 1.29 + w \times 0.79 + b \times 2.39\\\\Total\ price = 1.29n + 0.79w + 2.39b[/tex]

Thus the expression to represent the total price of the supplies is found

Answer:

The answer to your question is he sold 47 adult tickets and 37 children tickets.

Step-by-step explanation:

Data

Adult ticket = a = $105

Children ticket = c = $60

Total number of tickets = 84

Total money earn = $7155

Equations

                              a + c      = 84     ------------ (I)

                        105a + 60c = 7155 -------------(II)

Multiply equation I by -60

                           -60a  - 60c = -5040

                          105a   + 60c = 7155

Simplify

                          45a               = 2115

                                           a = 2115 / 45

                                           a = 47 tickets

Substitute a in equation I

                          47 + c = 84

                                  c = 84 - 47

                                  c = 37 tickets

You can form linear equations from the given description then use that system to derive the solution.

The amount of each type of tickets sold are:

Children tickets sold = 37

Adult tickets sold = 47

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on  methods can be used to convert description to mathematical expressions.

Let the amount of adult tickets sold be "a"

Let the amount of children tickets sold be "c"

Since the total amount of tickets sold is given as 84

Thus,

Total tickets = children tickets + adult tickets

84 = c + a

a + c = 84

since 1 adult ticket costs $105,

thus, "a" adult tickets cost [tex]105 \times a = 105a \text{\:\:(Written in short)}[/tex] (in dollars)

Similarly,

since 1 children ticket costs $60

"c" children tickets cost [tex]60c[/tex] (in dollars)

Since the price obtained by selling those tickets is $7155

thus,

total amount earned = amount earned by children tickets + amount earned by adult tickets

$7155 = $60c + $105a

Thus, we got the system of equations as:

[tex]a + c = 84\\105a + 60c = 7155[/tex]

Multiplying first equation with -105 to make a's coefficient equal and opposite to make the addition of them eliminate "a":

[tex]-105a -105c = -105 \times 84\\105a + 60c = 7155\\\\\text{Addding both equations}\\\\-45c = 7155 - 8820 = -1665\\\\c = \dfrac{1665}{45} = 37[/tex]

Putting this value in first equation, we get:

[tex]a + c = 84\\a + 37 = 84\\a = 84 - 37 = 47[/tex]

Thus,

The amount of each type of tickets sold are:

Children tickets sold = 37

Adult tickets sold = 47

Learn more about system of linear equations here:

https://brainly.com/question/13722693

Answer:

31.67

Step-by-step explanation:

12 2/3 X 2 1/2

we begin by converting this into improper fractions,

= 38/3 * 5/2

= 95/3

= 31.67