explanation of two column proofs? (geometry)

Answer:

[tex]\large\boxed{A.\ y^3}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\\dfrac{y^{10}}{y^7}=y^{10-7}=y^3[/tex]

[tex]\text{Other method:}[/tex]

[tex]\text{We know:}\ a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}\\\\y^{10}=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}_{10}\\\\y^7=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}_7}[/tex]

[tex]\dfrac{y^{10}}{y^7}=\dfrac{y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\cdot y\cdot y}{y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup\cdot y\!\!\!\!\diagup}=y\cdot y\cdot y=y^3[/tex]

To find the unit rate representing how many patients each nurse is responsible for with 28 patients and 2 nurses, you divide 28 by 2, resulting in 14 patients per nurse.

Nurse Unit Rate Calculation:

Identify the total number of patients: 28 patients

Determine the number of nurses: 2 nurses

Calculate the unit rate by dividing the total number of patients by the number of nurses: 28 patients ÷ 2 nurses = 14 patients per nurse

If the side lengths of rectangle B are proportional to the side lengths of rectangle A, the possible side lengths of rectangle B, with a ratio of 2, could be 12 cm and 7 cm.

If the side lengths of rectangle B are proportional to the side lengths of rectangle A, it means that the corresponding sides are in the same ratio. The ratio of the side lengths of rectangle B to rectangle A can be expressed as:

Ratio = Side length of B / Side length of A

In this case, you are given the side lengths of rectangle A as 6 cm and 3.5 cm. Let's find the ratio:

Ratio = Side length of B / Side length of A

Now, you can choose any common multiple to scale up the ratio. For example, you could multiply both sides by 2 to get a simpler ratio.

New Ratio = 2 * (Side length of B / Side length of A)

Now apply this ratio to the side lengths of rectangle A to find the corresponding side lengths of rectangle B:

Side length of B = 2 * Side length of A

Side length of B = 2 * 6 cm

Side length of B = 12 cm

Similarly, Side length of B = 2 * 3.5 cm

Side length of B = 7 cm

So, the possible side lengths of rectangle B, if they are proportional to rectangle A with a ratio of 2, could be 12 cm and 7 cm.

Given the ratio of seats in the Circle to the Stalls is 2:5 and knowing the number of filled seats in the Circle, we can calculate that there were 1320 filled seats in the Stalls. This brings the total number of filled seats to 1848. However, without information on the theatre's total capacity, we cannot calculate the percentage occupancy.

The ratio of the number of seats in the Circle to the number of seats in the Stalls is 2:5. This means that for every 2 seats in the Circle there are 5 in the Stalls. Given that there were 528 seats filled in the Circle, we can use this ratio to calculate the number of filled seats in the Stalls.

Divide the number of filled Circle seats by 2 (which is 528/2 = 264) and then multiply by 5, which gives us 1320 filled seats in the Stalls. To calculate the total number of filled seats, we add the filled seats in the Circle and the Stalls together (1320 + 528), which gives us 1848 filled seats.

To work out the percentage of occupancy, we must first find out the maximum capacity of the theatre. All we know is the ratio of seats, we don't know the exact total number of seats. Unless we know the total number of seats in the theatre, we cannot work out the percentage of occupancy for last Friday.

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The number of occupied seats in the theatre, in both Circle and Stalls is summed up and divided by the total number of seats in the theatre. The result in decimal is multiplied by 100% to get the percentage occupancy. In this case, as all seats were occupied, the percentage is 100%.

The subject of your question involves ratio and percentage, which falls under the category of Mathematics, specifically proportions and ratios. We know that the ratio of the number of seats in the Circle to the number of seats in the Stalls is 2:5. This means that for every 2 seats in the Circle, there are 5 seats in the Stalls. If there were 528 seats occupied in the Circle, since the ratio is 2:5, the number of occupied seats in the Stalls would be (528/2)*5 = 1320. The total number of seats in the theatre is the sum of seats in both Circle and Stalls which is 528+1320 = 1848. The proportion of occupied seats is the sum of occupied seats in both levels (528+1320) divided by the total (1848), which gives us the decimal 1. The percentage of this is 1*100 = 100%. So the percentage occupancy of the theatre last Friday was 100%.

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Answer:

The Glee Club sold 90 Adult tickets.

Step-by-step explanation:

Let the number of Student ticket be x.

Let the number of Adult ticket be y.

Total Number of ticket sold is 150.

Hence,

Total Number of ticket = number of Student ticket + the number of Adult ticket

[tex]x+y=150 \ \ \ \ equation\ 1[/tex]

Also Given;

Student tickets cost $5.00 each.

Adult tickets cost $8.00 each.

Ticket Sales is $1,020.

hence,

[tex]5x+8y=1020 \ \ \ \ equation\ 2[/tex]

Now Multiplying equation 1 by 5 we get.

[tex]5\times(x+y)= 5\times150\\5x+5y=750\ \ \ \ equation \ 3[/tex]

Now Subtracting equation 2 from equation 3 we get;

[tex](5x+8y=1020)-(5x+5y=750)\\\\3y = 270\\y= \frac{270}{3}= 90[/tex]

Number of adult ticket sold is 90.

Also [tex]x+y=150\\x+90=150\\x=150-90=60[/tex]

Number of Student ticket sold is 60.

Hence, The Glee Club sold 90 Adult tickets.

By using a system of equations and the elimination method, we determined the Glee Club sold 90 adult tickets.

To help you understand how many adult tickets were sold by the Glee Club, we can use a system of equations to represent the situation. Let x represent the number of student tickets sold, and let y represent the number of adult tickets sold.

We have two equations based on the problem:

We can solve this system using the substitution or elimination method. Here, elimination will be more convenient:

Therefore, the number of adult tickets sold was 90.

Britt will earn more interest after three years due to the compound interest on her account, totaling $788.13 compared to Adam's $750 from simple interest, resulting in a difference of $38.13. The key distinction lies in the interest calculation: Adam's remains constant, while Britt's increases each year due to the compounding effect.

The question involves calculating and comparing simple and compound interest earned on two separate $5,000 deposits over a period of three years at an annual interest rate of 5%.

Adam's account earns simple interest, meaning the interest each year is calculated using the original principal of $5,000, resulting in $250 of interest per year, totaling $750 after three years.

Britt's account, however, earns compound interest, with each year's interest calculated on the growing balance from the previous year.

As we can see from the tables, Britt's first year interest is the same as Adam's ($250), but it increases each subsequent year because it's calculated on the new principal (original plus accumulated interest).

After three years, Britt's total interest is $788.13, earning more interest than Adam's $750. The difference in the total interest earned after three years between Britt (compound interest) and Adam (simple interest) is $38.13.

The main difference in how interest is calculated between Britt and Adam's accounts is that Adam's interest is consistently $250 each year (calculated as $5,000 x 0.05),

while Britt's interest increases each year, demonstrating the effect of compound interest.

By Year 3, Britt earns $275.63 in interest compared to Adam's unchanged $250.

The equation of the line is y = [tex]\frac{2}{3}[/tex] x + 9

Step-by-step explanation:

The equation of a line in slope-intercept form is y = m x + b, where

∵ The line has a slope [tex]\frac{2}{3}[/tex]

∴ m = [tex]\frac{2}{3}[/tex]

∵ The y-intercept is 9

∴ b = 9

- Substitute the values of m and b in the form of the equation below

∵ y = m x + b

∴ y = [tex]\frac{2}{3}[/tex] x + 9

The equation of the line is y = [tex]\frac{2}{3}[/tex] x + 9

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Answer:

Step-by-step explanation:

6*68=408

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

48/10=4.8

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

3.8=x/7.7

x=3.8*7.7x

x=29.26

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

x+5.1=13.4

x=13.4-5.1

x=8.3

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

8x=64

x=64/8

x=8

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

22=m+1

m=22-1

m=21

----------

45-4x for x=5

45-4(5)=45-20=25

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

256, 64, 16, 4

Answer:

6*68=408

Step-by-step explanation:

Answer:

From figure A

The value of ∠ B = 75.74°   ,  ∠ C = 70.26° and  AB = 27.37

From figure B

The value of ∠ A = 42.8°   ,  ∠ B = 106.2° and  AC = 30.04

Step-by-step explanation:

Given first figure as :

AC = 28.2

BC = 16.5

∠ A = 34°

Let AB = c

From law of sines

[tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

Or, [tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex]

or, [tex]\dfrac{16.5}{Sin 34}[/tex] = [tex]\dfrac{28.2}{Sin B}[/tex]

Or,  29.506 =  [tex]\dfrac{28.2}{Sin B}[/tex]

Or, Sin B =  [tex]\dfrac{28.2}{29.5}[/tex]  

Or, Sin B = 0.955

∴  ∠B = [tex]Sin^{-1}[/tex] 0.955

I.e∠ B = 75.74

Now, ∠ C = 180° - ( ∠A + ∠B )

Or, ∠ C = 180° - ( 34° + 75.74° )

Or, ∠ C = 70.26°

Now, Again

[tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

so,  [tex]\dfrac{28.2}{Sin 75.74}[/tex] = [tex]\dfrac{c}{Sin 70.26}[/tex]

Or,   [tex]\dfrac{28.2}{0.9691}[/tex] = [tex]\dfrac{c}{0.9412}[/tex]

Or, c = 29.09 × 0.9412

∴    c = 27.37

I.e AB = 27.37

Hence,  The value of ∠ B = 75.74°   ,  ∠ C = 70.26° and  AB = 27.37

From figure second

Given as :

AB = c= 12

BC = a = 16

∠ C = 31°

let AC = b

From law of sines

[tex]\dfrac{a}{Sin A}[/tex] = [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

Or, [tex]\dfrac{a}{SinA }[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

or,  [tex]\dfrac{16}{Sin A}[/tex] = [tex]\dfrac{12}{Sin 31}[/tex]

or,  [tex]\dfrac{16}{Sin A}[/tex] = [tex]\dfrac{12}{0.51}[/tex]

Or, [tex]\dfrac{16}{Sin A}[/tex] = 23.52

∴ Sin A = [tex]\dfrac{16}{23.52}[/tex]

I.e Sin A = 0.68

Or,  ∠ A = [tex]Sin^{-1}[/tex] 0.68

or,  ∠ A = 42.8°

Now,  ∠ B = 180° - ( 31° + 42.8° )

Or,  ∠ B = 106.2°

Now,  [tex]\dfrac{b}{Sin B}[/tex] = [tex]\dfrac{c}{Sin C}[/tex]

or,  [tex]\dfrac{b}{Sin 106.2}[/tex] = [tex]\dfrac{16}{Sin 31}[/tex]

Or, [tex]\dfrac{b}{0.96}[/tex] = [tex]\dfrac{16}{0.51}[/tex]

or, b = 31.3×0.96

∴ b = 30.04

Hence The value of ∠ A = 42.8°   ,  ∠ B = 106.2° and  AC = 30.04

Answer

Answer:

159

Step-by-step explanation:

Add 99 and 60 to get 159. Now subtract 99 from that and you will have 60.

The negative sign shows that they still owed $5000 to the creditors which shows a loss of money between June and December.

Step-by-step explanation:

Amount owed at the end of June = $3765

Amount owed at the end of December = $8765

As Hightop Roofing owed creditors the amount, therefore, we will consider the amount as negative, therefore,

Amount in June = -3765

Amount in December = -8765

To see the difference, we will subtract the amount owed in June from the amount owed in December.

[tex]Difference=(-8765)-(-3765)\\Difference=-8765+3765\\Difference=-5000[/tex]

The negative sign shows that they still owed $5000 to the creditors which shows a loss of money between June and December.

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Answer:

231

Step-by-step explanation:

Given

[tex]\frac{4}{77}=\frac{12}{x}[/tex]

Cross Multiply

[tex]x \times 4=12\times 77\\x=\frac{12\times 77}{4} \\x= 3\times 77\\x= 231[/tex]

Therefore x=231

Answer:

y=-2x+5

Step-by-step explanation:

Answer:

Domain- [-4,∞)  ; Range-  [-2,∞)

Step-by-step explanation:

[tex]y=\sqrt{x+4} -2[/tex]

For Domain, we need to find the range of value for x,

As the value for x+4 should be positive or 0 because it is under the square root bracket sign.

[tex]x+4\geq 0[/tex]

[tex]x\geq -4[/tex]

x ∈ [-4,∞)

For the range of values, we need to find all the possible value of y

As the value given by the square root will always be greater than equal to 0.

[tex]\sqrt{x+4}\geq 0[/tex]

[tex]\sqrt{x+4} -2\geq -2[/tex]

Therefore ,

y ∈ [-2,∞)

Answer:

An open circle line going passed and from 3 that way --->

Step-by-step explanation:

Add 15 to both sides

12b > 36

Divide 12 to both sides

b > 3

Answer:

It will be an open circle going pass the 3 like this

o---------------------------------------------------------------->

Step-by-step explanation:

12b - 15 > 21

add 15:

12b - 15 > 21

      + 15  + 15

So now it's:

12b > 36

Now divide by 12:

12b > 36

/12     /12

And now your answer is:

b > 3

Answer:

y = 2x-3

Step-by-step explanation:

y-17=2(x-10)

distribute 2 ---> y-17= 2x-20

add 17 to both sides ---> y=2x-3

The equation of the given line will be [tex]y =2x - 3[/tex]

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as: [tex]y = mx+c[/tex]

Since given line has slope = 2, thus its equation will be: [tex]y = 2x + c[/tex]

The other data about the straight line will help us find the value of c.

Since the line passes through (10,17) coordinate, thus this must satisfy the equation. Putting x = 10, and y = 17 will give us:

[tex]y = 2x + c\\17 = 2 \times 10 + c\\17 = 20 + c\\c = 17 - 20 = -3[/tex]

Thus, the value o y-intercept = c = -3

Thus, the equation of considered straight line is  [tex]y =2x - 3[/tex]

The graph of this equation is given below.

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Answer:

The numerator is the first number in a division problem (dividend). The denominator is the second number in a division problem (divisor).

Answer:

Divisor

Step-by-step explanation:

The denominator is the divisor. This is the split apart quantity.

I am joyous to assist you anytime.

Answer: [tex]H_0: p=0.30[/tex]

[tex]H_a: p <0.30[/tex]

Step-by-step explanation:

Definition:

Null Hypothesis : It is a statement about the population parameter that contains = , ≤ and ≥ signs.

Alternative hypothesis : It is also a statement about the population parameter against the null hypothesis that contains ≠  , < and > signs.

For the given situation.

Let [tex]\mu[/tex] be the population proportion of treated patients are uninsured.

A hospital director is told that 30% of the treated patients are uninsured.

Then, Null Hypothesis : [tex]H_0: p=0.30[/tex]

The director wants to test the claim that the percentage of uninsured patients is less than  the expected percentage.

i.e. Alternative hypothesis : [tex]H_a: p <0.30[/tex]

Hence, the set of hypothesis :

[tex]H_0: p=0.30[/tex]

[tex]H_a: p <0.30[/tex]

A nationwide sample of people ages 18 to 25. This option provides a broader representation of the population, ensuring a more comprehensive understanding of young adults' opinions on video games. The correct choice of option is A.

Option A provides a broader representation of the population as it includes individuals from across the country, capturing a diverse range of demographics, backgrounds, and gaming habits. This sample is more likely to reflect the general attitudes and behaviors towards video games among young adults in the country.

Options B, C, and D are less likely to generalize to Matt's population of interest as they target specific subsets of individuals who may have a higher propensity for gaming or different gaming preferences, potentially biasing the survey results.

Option E, while focusing on the correct age range, is limited to Matt's hometown and may not represent the broader population's opinions and behaviors towards video games.

Therefore, option A, a nationwide sample of people ages 18 to 25, is the most likely to generalize to Matt's population of interest.

Question:-

Matt wants to investigate the opinions of young adults in the country, ages 18 years to 25 years, about time spent playing video games. He plans to administer a survey to a sample of people. Which of the following samples is most likely to generalize to his population of interest?

A)A nationwide sample of people ages 18 to 25.

B) A sample of attendees of a gaming convention

c) A sample of people who click on a link in an online gaming site

D) A sample of people who buy video games from an online store

E) A sample of people ages 18 to 25 in Matt's hometown

Based on the analysis above, the most likely sample to generalize to Matt's population of interest is: A nationwide sample of people ages 18 to 25

The correct option is (a).

To determine which sample is most likely to generalize to Matt's population of interest (young adults aged 18 to 25), let's analyze each option:

a. A nationwide sample of people ages 18 to 25:

  This option covers a broad range of young adults across the entire country, which increases the likelihood of representing Matt's population of interest. However, it may still include individuals who do not play video games, as well as those who play video games excessively. Overall, this sample is more likely to generalize to Matt's population compared to options c, d, and e.

b. A sample of attendees of a gaming convention:

  This option would likely include individuals who are particularly interested in gaming, which may not be representative of all young adults aged 18 to 25. Attendees of a gaming convention may have different gaming habits compared to the general population of young adults, making this sample less likely to generalize to Matt's population of interest.

c. A sample of people ages 18 to 25 in Matt’s hometown:

  While this sample may be convenient for Matt to access, it is limited to individuals in his hometown and may not be representative of young adults nationwide. Additionally, individuals in Matt's hometown may have different demographics and gaming habits compared to the entire population of young adults aged 18 to 25.

d. A sample of people who click on a link in an online gaming site:

  This sample is likely biased towards individuals who are already interested in gaming, as they are visiting an online gaming site. Therefore, it may not represent the entire population of young adults aged 18 to 25, especially those who do not regularly visit gaming sites.

e. A sample of people who buy video games from an online store:

  Similar to option d, this sample is biased towards individuals who are interested in video games, as they are purchasing video games from an online store. Therefore, it may not represent the entire population of young adults aged 18 to 25.

Based on the analysis above, the most likely sample to generalize to Matt's population of interest is:

a. A nationwide sample of people ages 18 to 25

complete question given below:

Matt wants to investigate the opinions of young adults in the country, ages 18 years to 25 years, about time spent playing video games. He plans to administer a survey to a sample of people. Which of the following samples is most likely to generalize to his population of interest?

a. A nationwide sample of people ages 18 to 25

b. A sample of attendees of a gaming convention

c. A sample of people ages 18 to 25 in Matt’s hometown

d. A sample of people who click on a link in an online gaming site

e. A sample of people who buy video games from an online store

Answer:

Length = 17, Width = 6

Step-by-step explanation:

Let the length be L and width be W.

L = 3W - 1 , and,

2(L + W) = 46 => L+W = 23  => L = 23 - W, putting this into L = 3W - 1

23 - W = 3W - 1

24 = 4W

W = 6

therefore, L = 23 - W = 17

Answer:

x=-2+sqrt(7)*i, -2-sqrt(7)*i

Step-by-step explanation:

x^2+4x=-11

x^2+4x-(-11)=0

x^2+4x+11=0

Apply the quadratic formula with a=1, b=4 and c=11.

Answer:

amplitude = 3

Step-by-step explanation:

The standard form of a cosine function is

f(x) = a cos(bx + c) + d

amplitude = | a |, period = [tex]\frac{2\pi }{b}[/tex]

phase shift = - [tex]\frac{c}{b}[/tex], d is the vertical shift

Given the above function, then

amplitude = | - 3 | = 3

Answer:

A ) The selling price of radio is $ 81.64

B ) The selling price of microscope is $ 72.94

Step-by-step explanation:

Given as :

A ) Market price of radio = M.P = $ 125.60

Let The selling price of radio = S.P =  $ x

The discount = 35 %

So, Discount %  = [tex]\dfrac{M.P - S.P}{M.P}[/tex]

Or, [tex]\frac{35}{100}[/tex] = [tex]\dfrac{125.60 - x}{125.60}[/tex]

Or, [tex]\frac{x}{125.60}[/tex] = 1 - [tex]\frac{35}{100}[/tex]

Or,  [tex]\frac{x}{125.60}[/tex] =  [tex]\frac{100-35}{100}[/tex]

Or,  [tex]\frac{x}{125.60}[/tex] =  [tex]\frac{65}{100}[/tex]

∴  x = [tex]\frac{125.60\times 65}{100}[/tex]

I.e  x = $ 81.64

So, The selling price of radio is $ 81.64

B ) The market price of microscope = M.P = $ 96.25

    The discount = 20 %

    Tax percentage = 6 %

Let the selling price of microscope = $ y

Now, So, Discount %  = [tex]\dfrac{M.P - S.P}{M.P}[/tex]

Or, [tex]\frac{20}{100}[/tex] = [tex]\dfrac{96.25 - y}{96.25}[/tex]

Or, [tex]\frac{y}{96.25}[/tex] = 1 - [tex]\frac{20}{100}[/tex]

Or,  [tex]\frac{y}{96.25}[/tex] =  [tex]\frac{100-20}{100}[/tex]

Or,  [tex]\frac{y}{96.25}[/tex] =  [tex]\frac{80}{100}[/tex]

∴  y = [tex]\frac{96.25\times 80}{100}[/tex]

I,e y = $ 77

Again Tax of 6% is added

So , $ 77 - 6 % of $ 77

Or, $ 77 × 0.94 = $ 72.38

∴ The final cost of microscope after discount and tax is $ 72.94

Hence A ) The selling price of radio is $ 81.64

And     B ) The selling price of microscope is $ 72.94   Answer

The correct answer is (a) a sheet of wet cardboard, which becomes limp when moistened as the material loses its rigidity and strength, unlike the other items listed which maintain their form and firmness.

Among the options provided, a sheet of wet cardboard is most likely to feel limp. When cardboard absorbs water, the material becomes weak and loses its rigidity, making it bend or flop easily. The other materials listed, such as a sheet of ice, a sleeping child, and a sheet of plywood, retain their form and rigidity better when they are not altered by external factors like moisture.

A sheet of ice remains solid until it melts, a sleeping child is not an inanimate object and doesn't become limp simply because they are asleep, and a sheet of plywood is a construction material designed to remain sturdy even when faced with various environmental conditions. Therefore, (a) a sheet of wet cardboard is the correct answer as it is the one that could be expected to feel limp when wet.

Answer:

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side of a square

We have

[tex]A=1yd^2[/tex]

Therefore

[tex]s^2=1yd^2\to s=\sqrt{1yd^2}=1yd[/tex]

Answer:

8^5

Step-by-step explanation:

8^5

Answer: 3.75 gallons

Step-by-step explanation:

8 fl oz x 60 (minutes)=480 fl oz

480 fl oz ÷ 128=3.75 gallons

Water flow rate is defined as the volume of the fluid passing by some location. The water leaking from the pipe per hour is 3.75 gallons

A pipe is leaking at the rate of 8 fluid ounces per minute.

Water flow rate is defined as the volume of the fluid passing by some location.

As the flow rate is 8 fluid ounces per minute. In a hour there is total 60 minutes. Thus the flow rate of the pipe in fluid ounces per hour is,

[tex]Q=8\times60[/tex]

[tex]Q=480[/tex]

A fluid ounces is the unit of the measurement of the liquid. There is total 128 fluid ounces in a gallons. Thus the flow rate of the water in gallon can be calculated by dividing the 480 by 128. Thus the flow rate of pipe in gallons per hour is,

[tex]Q=\dfrac{480}{128}[/tex]

[tex]Q=3.75[/tex]

Hence the water leaking from the pipe per hour is 3.75 gallons.

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Answer:

x=0, y=2. (0, 2).

Step-by-step explanation:

3x+2y=4

8x-3y=-6

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

3(3x+2y)=3(4)

2(8x-3y)=2(-6)

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

9x+6y=12

16x-6y=-12

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

25x=0

x=0/25

x=0

3(0)+2y=4

0+2y=4

2y=4-0

2y=4

y=4/2

y=2

The solution of the systems of equations by substitution will be;

⇒ x = 0, y = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ 3x + 2y = 4

⇒ 8x - 3y = -6

Now,

Since, The system of equation are,

⇒ 3x + 2y = 4  ..(i)

⇒ 8x - 3y = -6  ..(ii)

Find the value of x from (i) as;

⇒ 3x + 2y = 4

⇒ 3x = 4 - 2y

⇒ x = 1/3 (4 - 2y)

Substitute above value in (ii), we get;

⇒ 8x - 3y = -6

⇒ 8 × 1/3 (4 - 2y) - 3y = -6

⇒ 32/3 - 16y/3 - 3y = - 6

⇒ 32/3 + 6 = 25y/3

⇒ 50/3 = 25y/3

⇒ 50 = 25y

⇒ y = 2

And, From (i),

⇒ 3x + 2y = 4

⇒ 3x + 2 × 2 = 4

⇒ 3x  = 4 - 4

⇒ x = 0

Thus, The solution of the systems of equations by substitution are;

⇒ x = 0, y = 2

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