Mathematics College

What is the solution to the following system of equations? 3x-2y=12 and 6x-4y=24

Answers

Answer 1

Answer:

A. It has infinitely many solutions

Step-by-step explanation:

I took the Solving Linear Systems By Substitution Quiz on Edge

Answer 2

The given system of equations 3x-2y=12 and 6x-4y=24 has no solution.

As per the question, we have to determine the solution to the following system of equations, 3x-2y=12 and 6x-4y=24

What is the equation?

The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.

Here,
Given a system of the equation,
3x-2y = 12
x = 12 + 2y / 3 - - - - -(1)
6x - 4y =24 - - - - -(2)
Put the value of equation 1 in the equation
6 (12 + 2y / 3) - 4y = 24
2 (12 + 2y) - 4y = 24
24 +4y - 4y = 24
24 = 24

Thus, the given system of equations 3x-2y=12 and 6x-4y=24 has no solution.

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Related Questions

Javier By 48 cards at a yard sale. Of the cards 3/8 were basketball cards how many cards were baseball card

Answers

The answer is 18, Hope you get it right!

The sum of three numbers is 45 the second of the three numbers is three more than twice the first number, ×. The thurd number is two more than the first number, ×. Which equation can be used to solve the first number

Answers

Answer:

Step-by-step explanation:

We know that the 1st equation + 2nd equation + 3rd equation = 45.  Now we just need to identify from the infor given what these equations are, then set them to equal 45.

It has already been determined that the 1st equation is x.

The second equation is "3 more than twice the first".  Twice the first is 2x, and 3 more is +3; therefore, the second equation is: 2x + 3.

The third equation is "2 more than the first".  2 more than is +2, so the third equation is x + 2.

Now we have all 3:

1st:  x

2nd:  2x + 3

3rd:  x + 2

Add them all up and set them equal to 45:

x + 2x + 3 + x + 2 = 45.

You don't have choices listed, so it's either that one above, or simplified down to:

4x + 5 = 45

After that, any simplification done will be solving the equation.

100.6 - 30.06 show me it in vertically form (show work)so I can understand how to regroup it.

Answers

Final answer:

To vertically subtract 30.06 from 100.6, start by borrowing 1 from the tens place and adding it to the ones place. Then, borrow 10 from the hundreds place and add it to the tens place. Finally, combine the result to get 70.54.

Explanation:

To vertically subtract 30.06 from 100.6, you'll need to line up the decimal points vertically. Start by subtracting the hundredths place (0.06) from the hundredths place (0.00). Since 6 is bigger than 0, you'll need to regroup. Borrow 1 from the tens place by making it 9, and add it to the ones place, making it 10. Then, you can subtract 6 from 10, which gives you 4. Next, subtract the whole number part (30) from the whole number part (100). Since 0 is smaller than 3, regroup again by borrowing 10 from the hundreds place and adding it to the tens place, making it 20. Then, subtract 3 from 10, which gives you 7. Finally, combine the result by placing the decimal point in the correct position, which gives you the answer: 70.54.

Hamza bought 8 gallons of brown paint to paint his kitchen and dinning room. Unfortunately, when hamza started painting, he thought the paint was too dark for his house,so he wanted he wanted to make it lighter. The store manager would not let hamza return the paint but did inform that if he used 1 4 of a gallon of white paint mixed with 2 gallons of brown paint, he would get the shade of brown he desires. If hamza decided to take this approach, how many gallons of white paint would hamza have to buy to lighten the 8 gallons of brown paint?

Answers

I believe he would need 56 gallons of white paint.
Is that supposed to be 1, 4 or 14 gallons of white paint? There is a space between the 1 and the 4, but I went with 14 originally.

ANSWER: 56 gallons of white paint

Why?

14 gallons of white paint for every 2 gallons of brown paint
8 divided by 2 = 4 times the amount of white paint needed for 2
4 x 14 = 56 gallons of white pains

IF it was supposed to be 1 or 4 gallons of white paint per 2 gallons of brown

For 1 gallon of white paint for every 2 gallons of brown the answer would be
4 x 1 = 4.

If it should say 4 gallons of white for every 2 gallons of brown the answer would be 4 x 4 = 16.

Simplify 7x+3y-2+6x-1-y^2

Answers

-y² +13x + 3y - 3

is your answer

hope this helps

write words to match the expression
3+(4×12)

Answers

3 plus the quotient of 4 and 12. Hope this helps!

Algebraically determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry.

Answers

[tex]\bf y=x^3-4x \\\\\\ \textit{check for y-axis symmetry}\\\\ \stackrel{x=-x}{y=(-x)^3-4(-x)}\implies y=(-x)(-x)(-x)+4x\implies \boxed{y=-x^3+4x} \\\\\\ \textit{checking for x-axis symmetry}\\\\ \stackrel{y=-y}{(-y)=x^3-4x}\implies -y=x^3-4x\implies \boxed{y=-x^3+4x} \\\\\\ \textit{checking for origin symmetry}\\\\ \stackrel{x=-x\qquad y=-y}{(-y)=(-x)^3-4(-x)}\implies -y=(-x)(-x)(-x)+4x \\\\\\ -y=-x^3+4x\implies y=\cfrac{-x^3+4x}{-1}\implies \boxed{y=x^3-4x}\quad \checkmark[/tex]

notice, if you replace x = -x and y = -y accordingly for each test for symmetry, if the resulting function, is equal to the original function, then it has that type of symmetry.

Final answer:

Algebraically, the relation y = x^3 - 4x is not symmetric to the x-axis or y-axis but is symmetric with respect to the origin when both x and y are replaced with their negatives.

Explanation:

To determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, or the origin, we perform a series of tests substituting -x for x (to test y-axis symmetry), -y for y (to test x-axis symmetry), and both -x for x and -y for y (to test origin symmetry).

Y-axis symmetry test:

Replace x with -x:

y = (-x)3 - 4(-x)

y = -x3 + 4x ≠ x3 − 4x (not symmetric to y-axis)

X-axis symmetry test:

Replace y with -y:

-y = x3 - 4x ⇒ y = -x3 + 4x ≠ x3 − 4x (not symmetric to x-axis)

Origin symmetry test:

Replace both x with -x and y with -y:

-y = (-x)3 - 4(-x)

-y = -x3 + 4x

y = x3 − 4x (symmetric to origin)

the formula of the area of a triangle is A=1/2bh what is the length of the base if the area is 22cm and the height is 8cm

Answers

The length of the base is 5.5
Put the numbers into the equation. 22=.5(b)8 The right hand side should read 4b, and the left should read 22. Divide both sides by 4 to get b=5.5

WILL GIVE BRAINEST
Costumers can pick their own berries at the gooseberry farm....

Answers

y = 2.5x + 3

answer is
C. y = 2.5x + 3
I think its C. but im not so sure...

a 204 inch board is cut into two pieces. one piece is five times the length of the other.find the lengths of the two pieces

Answers

Solution along with work is included in attachment.

1/4x + 1/3 = 1/6x - 1/4

Answers

1/4x + 1/3 = 1/6x - 1/4

We simply want to isolate x.

So, we must get x onto it's own side of the equal sign.

To do that, we subtract 1/3 from both sides.

1/4x = 1/6x - 1/4 - 1/3


Then, subtract 1/6x from both sides.

1/4x - 1/6x = -1/4 - 1/3

Simplify.

1/4x → 3/12x  ; -1/6x → -2/12x   ; -1/4 → -3/12  ; -1/3 → -4/12

Plug these into our equation.

3/12x - 2/12x = -3/12 - 4/12 

Simplify.

1/12x = -7/12

Multiply everything by 12.

12 · 1/12x = -7/12 · 12

Simplify.

x = -7

~Hope I helped!~



Describe two situations in which opposite quantities combine to make zero

Answers

When one number is negative and the other is positive. 

In the situation, x + (-x) is combined making zero and other y + (-y) is making zero.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers with each other called subtraction.

Division = divide any two numbers or variable called division.

Multiplication = to multiply any two or more numbers or variables called multiplication.

If we combine any two opposite quantities then their summation must be zero.

For example,

if you combine 5 and -5 then it will be 0.

If you combine 10 and -10 then it will be 0.

So,

The first situation ⇒

Combining x and -x

x + (-x) = 0

The second situation ⇒

Combining y and -y

y + (-y) = 0

Hence, In the situation, x + (-x) is combined making zero and other y + (-y) makes zero.

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Kyra typed 140 words in 5 minuets. Then, she typed 196 words in 7 minutes. Was her rate of words per minute constant? If so, what is the constant of proportionality?

Answers

Hello lamdravenox! There are a few ways to tell if the rate of words per minute are constant but we can divide 140/5 and 196/7 to tell if the rate of words per minute are constant.

First divide 140 / 5 = 28 words per min
Second divide 196 / 7 = 28 words per min

So we can see the rate of words per minute is constants and her rate is at 28 words per min so the constant of proportionality is 28 words per minute.

The circular base of a cone has a radius of 5 centimeters. The height of the cone is 12 centimeters, and the slant height is 13 centimeters. What is the approximate surface area of the cone? Use 3.14 for π and round to the nearest whole number. 267 cm2 283 cm2 456 cm2 487 cm2

Answers

Answer:

Option B. is the correct option.

Step-by-step explanation:

The circular base of a cone has a radius of 5 cm. The height of the cone is 12 cm. Slant height of the cone is 13 cm.

We have to calculate the approximate surface area of the cone.

Since we know Surface area of a cone = Area of circular base + lateral area of the cone

Now Surface area of a cone = πr² + πrl = πr(r + l)

By putting the values of the dimensions of a cone in the formula.

S.A. = π (5² + 5×13) = 3.14×(25 + 65) = 3.14×(90) = 282.60 ≈ 283 cm²

Therefore, Option B is the correct option.

Enter the correct unit of measurement to complete the conversion
10,000 grams equals 10 what
1/5000,000 liter eqaul 2 what
1 nanosecond equal one what of a what
1 hectometer equal what meters
1 milliampere equl one waht of an ampere
1 megaton equal 1 what tons
THANK YOU SO MUCH

Answers

Hi. Here you go, hope it helps.

10,000 grams = 10 kilograms
1/500,000 liters equal = 2 microliters
1 nanosecond = 1 billionth of a second
1 hectometer = 100 meters
1 milliampere = 0.001 ampere
1 megaton = 1,000,000 tons

Take care,
Diana

Answer:

As per list given

Step-by-step explanation:

Given are some measurements and we have to convert them into suitable units.

i) 10,000 grams = 10 kilograms

1/500,000 liters equal = 2 microliters

1 nanosecond = 1 billionth of a second

1 hectometer = 100 meters

1 milliampere = 0.001 ampere

1 megaton = 1,000,000 tons

Number of solutions to equations -2+10+7z=16z+7

Answers

The given equation resulting in one solution, which is z = 1/9.

To find the number of solutions to the equation -2 + 10 + 7z = 16z + 7, we first simplify and solve for z. Start by combining like terms on the left side:

-2 + 10 = 8, so the equation becomes 8 + 7z = 16z + 7.

Next, we get all the terms with z on one side and the constants on the other:

Subtract 7z from both sides:

8 = 16z - 7z + 7

Combine z terms:

8 = 9z + 7

Subtract 7 from both sides:

1 = 9z

Divide both sides by 9:

z = 1/9

At the city park there were 15 blue jays, 6 cardinals, and 9 mockingbirds. For each of the following questions set up a proportion equation and solve for the unknown. 1. If there were 6 mockingbirds, how many cardinals would there be at the park? 2. If there were 5 blue jays, how many cardinals would there be at the park? 3. If there were 20 cardinals, how many mockingbirds would there be at the park?

Answers

1. 4 cardinals because: 6 mockingbirds : x cardinals = 9 mockingbirds : 6 cardinals 6*6 / 9 = 4 2. 2 cardinals because: 5 blue jays : x cardinals = 15 blue jays : 6 cardinals 5*6 / 15 = 2 3. 30 mockingbirds because; 20 cardinals : x mockingbirds = 6 cardinals : 9 mockingbirds 20*9 / 6 = 30

The probability that a dvd player produced by vca television is defective is estimated to be 0.06. a sample of ten players is selected at random. (round your answers to four decimal places.) (a) what is the probability that the sample contains no defective units? correct: your answer is correct. (b) what is the probability that the sample contains at most two defective units?

Answers

Absolute MonarchA monarchial form of government in which the monarch exercises ultimate governmental authority.Divine RightIt is the belief that the ruler's authority comes directly from his, or her, God. (Usually the country's main religion.)Charles V (From Spain)Spanish Emperor who ruled the Holy Roman Empire.Philip II (From Spain)King of Spain from 1556 and of Portugal from 1581.Spanish ArmadaA spanish fleet of warships.Huguenot...

rewrite 4/21 and 2/9 so that they have a common denominator, then use <, > or =

Answers

4/21 = 12/63  and 2/9  =  14/63

12/63 < 14/63
2 over 3.5


which means... 5.5 


hope it helped!

A model for the population in a small community after t years is given by P(t)=P0e^kt.
a)If the initial population doubled in 5 years, how long will it take to have tripled its initial population?
b)In addition, if the population of the community is 10,000 in 3 years, what was its initial population?

Answers

[tex]\bf \textit{Amount of Population Growth}\\\\ A=Ie^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}[/tex]

a)

so, if the population doubled in 5 years, that means t = 5.  So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

[tex]\bf \textit{Amount of Population Growth}\\\\ A=Ie^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\to &2\\ I=\textit{initial amount}\to &1\\ r=rate\\ t=\textit{elapsed time}\to &5\\ \end{cases} \\\\\\ 2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r \\\\\\ \boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\ \textit{how long to tripling?}\quad \begin{cases} A=3\\ I=1 \end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}[/tex]

[tex]\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t \\\\\\ \cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t[/tex]

b)

A = 10,000, t = 3

[tex]\bf \begin{cases} A=10000\\ t=3 \end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I \\\\\\ 6597.53955 \approx I[/tex]

Simplify. Assume that all variables represent positive real numbers. sqrt y^9

Answers

See picture for answer.

Kristin jogs around a park that has a perimeter of 12 mile. Kristin jogged around the park 4 times in 50 minutes.

What is the unit rate of Kristin's speed?


Answers

Kristin jogs 48 miles in 50 minutes, so her unit rate is 48miles/50 minutes

12 *4 = 48 total miles in 50 minutes

48 / 50/60 =  57.6 miles per hour

what is the 3sqaure root of 0.027y^9 = ?

Answers

[tex]\bf \sqrt[3]{0.027y^9}\qquad \begin{cases} 0.027=\frac{0027}{1000}\\ 27=3^3\\ 1000=10^3\\ y^9=(y^3)^3 \end{cases}\qquad \sqrt[3]{\cfrac{27}{1000}y^9}\implies \sqrt[3]{\cfrac{3^3}{10^3}(y^3)^3} \\\\\\ \sqrt[3]{\cfrac{3^3(y^3)^3}{10^3}}\implies \cfrac{\sqrt[3]{3^3(y^3)^3}}{\sqrt[3]{10^3}}\implies \cfrac{3y^3}{10}\implies 0.3y^3[/tex]

Find the mean of the given set of numbers. 3, 3, 8, 6, 7, 3

Answers

The answer is 5. The mean is the average you get when you add up all of the numbers and divide by the number of numbers.

Garrett has deposited $519 in a savings account that earns interest at a rate of 4.2% compounded daily. What will the account balance be in 17 years?

Answers

The formula is
A=p (1+r/k)^kt
A future value?
P present value 519
R interest rate 0.042
K compounded daily 365
T time 17 years
A=519×(1+0.042÷365)^(365×17)
A=1,059.83

Hope it helps!

It is estimated that light takes 110,000 years to travel the full distance across our galaxy

In the picture please read the rest of the question.

Answers

[tex]\bf \stackrel{light~speed}{3.0\times 10^8}ms^{-1}\implies \stackrel{light~speed}{3.0\times 10^8}~\frac{m}{s}\implies 300,000,000~\frac{m}{s}\\\\ -------------------------------\\\\ \textit{how many seconds in a minute?}\qquad 60 \\\\\\ \textit{how many seconds in }\stackrel{1~hr}{60~minutes?}\qquad 60\cdot 60 \\\\\\ \textit{how many seconds in }\stackrel{1~day}{24~hrs}?\qquad 60\cdot 60\cdot 24 \\\\\\ \textit{how many seconds in }\stackrel{1~year}{365~days}?\qquad 60\cdot 60\cdot 24\cdot 365[/tex]

now, it takes 1 second for light to travel 300,000,000 meters.

if we know it takes light 1 second to go 300 million meters, then in 365 days or a year, or 60*60*24*365 seconds, it will then travels

300,000,000 * 60 * 60 * 24 * 365 meters in 1 year,

how about in 110,000 years, how many meters has it travelled?

300,000,000 * 60 * 60 * 24 * 365 * 110,000   that many meters.

we know she travels the Milky Way in 110,000 years  or 60 * 60 * 24 * 365 * 110,000  seconds

and we know that 110,000 years is 3468960000000 seconds, so

if it travels 300000000 meters in only 1 second, in 3468960000000 seconds, it will travel then (300000000) * (3468960000000) meters

or  1040688000000000000000 meters.

What is the factorization of 49b2 − 81? (7b – 9)(7b – 9) (7b – 9)(7b + 9) (7b2 – 9)(7b2 – 9) (7b2 – 9)(7b2 + 9)

Answers

49b^2 − 81 =  (7b + 9)(7b – 9)

answer
(7b – 9)(7b + 9)
Final answer:

The factorization of 49b² - 81 using the difference of squares formula is (7b - 9)(7b + 9).

Explanation:

The question is asking to factorize the expression 49b² - 81, which is a difference of two squares. The difference of squares formula is a² - b² = (a - b)(a + b). In your question, a² is 49b² and b² is 81. Therefore, a would be 7b (since square root of 49b² is 7b) and b would be 9 (since square root of 81 is 9).

Thus, using the formula, the factorization of 49b² - 81 will be (7b - 9)(7b + 9). This provides an explanation of the concepts involved and the steps followed in the solution.

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Kent caught an 8 pound 3 ounce trout in Pike Lake. The season's record catch so far is 129 ounces. Did Kent's fish beat the record?

Answers

Yes Kent Did beat the record. There are sixteen ounces in one pound. 16•8=128+3 sooooo..131

''Please Help!!'' says Kuku and Yaya

A middle-school band holds a car wash to raise money. The sixth-grade band members wash 16 cars. The seventh-grade band members wash 75% as many cars as the sixth-graders. The eighth-grade band members wash half as many cars as the sixth- and seventh-grade band members combined.
If the band charges $5 per car, how much money did the members raise altogether?

Answers

6th grade wash 16 cars
7th grade was 75% as many as 6th grade....0.75(16) = 12 cars washed
8th grade wash half as many as 6th and 7th combined...(12 + 16) / 2 =
28/2 = 14 cars washed

total cars washed : (16 + 12 + 14) = 42 cars
at $ 5 per car.....42 * 5 = $ 210 <===

How is multiplying and dividing numbers in scientific notation different from adding and subtracting numbers in scientific notation?

Answers

When you multiply or divide in scientific notation, you just add or subtract the exponents. When you add or subtract in scientific notation, you have to make the exponents the same before you can do anything else.
Final answer:

In scientific notation, multiplication involves multiplying the numbers before the exponents and adding the exponents, while division involves dividing the numbers before the exponents and subtracting the exponents. Addition and subtraction require the numbers to have the same exponent.

Explanation:

Multiplying and dividing numbers in scientific notation is different from adding and subtracting It's useful to know how to use scientific notation, especially in fields like astronomy where large numbers are common. Numbers in scientific numeration are written with one number to the left of the decimal point. For example, 500,000,000 will be expressed as 5 × 10⁸.

When we multiply two numbers in scientific notation, we multiply the numbers out front and then add the exponents. For instance, if we are multiplying (3 × 10⁵) × (2 × 10¹⁰), our answer will be 6 × 10¹⁵.

On the other hand, to divide two numbers in scientific notation, we divide the numbers out front and then subtract the exponents. For example, if we are dividing 1.2 x 10⁶ by 2 x 10³, our answer will be 0.6 x 10³ or 6 x 10².

When working with addition and subtraction in scientific notation, the numbers must have the same exponent in order for the operation to be performed.

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