Is y=2x-8 and 2x-y=8 a dependent independent or inconsistent

Answers

Answer 1
Note that 2x-y=8 can be solved for y:  y=2x-8.  This is identical to the first equation.  The graph of one is exactly the same as the graph of the other.  Thus, the two equations are dependent.
Answer 2

Answer:

dependent

Step-by-step explanation:

[tex]y=2x-8[/tex] and [tex]2x-y=8[/tex]

First equation is already solve for y

LEts solve the second equation for y

[tex]2x-y=8[/tex]

Subtract 2x on both sides

[tex]-y=-2x+8[/tex]

Divide the whole equation by -1

[tex]y=2x-8[/tex]

After solving for y, both equation are same

When both the system of equation are same then  it has infinite solutions.

They are said to be dependent.


Related Questions

the tangent line to the curve y=x^3-6x^2-34x-9 has slope 2 at two points on the curve. find the two points

Answers

[tex]\bf y=x^3-6x^2-34x-9\implies \cfrac{dy}{dx}=3x^2-12x-34 \\\\\\ \stackrel{\textit{slope of 2}}{2}=3x^2-12x-34\implies 0=3x^2-12x-36 \\\\\\ 0=x^2-4x-12\implies 0=(x-6)(x+2)\implies x= \begin{cases} 6\\ -2 \end{cases}\\\\ -------------------------------\\\\ \stackrel{y}{f(6)}=(6)^3-6(6)^2-34(6)-9\implies f(6)=-213\\\\\\ (\stackrel{x}{6}~,~\stackrel{y}{-213}) \\\\\\ \stackrel{y}{f(-2)}=(-2)^3-6(-2)^2-34(-2)-9\implies f(-2)=27\\\\\\ (\stackrel{x}{-2}~,~\stackrel{y}{27})[/tex]
Final answer:

To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2. The two points are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

Explanation:

To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2.

First, we find the derivative of the function:

dy/dx = 3x^2 - 12x - 34

Next, we set the derivative equal to 2 and solve for x:

3x^2 - 12x - 34 = 2

3x^2 - 12x - 36 = 0

Using the quadratic formula, we find the solutions for x:

x = (-b ± √(b^2 - 4ac))/(2a)

Substituting the values a = 3, b = -12, and c = -36 into the quadratic formula, we get:

x = (-(-12) ± √((-12)^2 - 4(3)(-36)))/(2(3))

x = (12 ± √(144 + 432))/6

x = (12 ± √(576))/6

x = (12 ± 24)/6

x = 12/6 ± 24/6

x = 2 ± 4

So the two points where the slope of the tangent line is 2 on the curve are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

Learn more about Finding points on a curve with a given slope here:

https://brainly.com/question/30466171

#SPJ2

4 1
__ / ( - __ )
5 15

Answers

4 over 5 divided by (-1 over 15)

that means:

[tex] \frac{4/5}{-1/15} = -\frac{4*15}{1*5} =- \frac{4*3*5}{5}=-4*3=-12[/tex]


I hope you got satisfied



Suppose that a large mixing tank initially holds 700 gallons of water in which 50 pounds of salt have been dissolved. another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. if the concentration of the solution entering is 4 lb/gal, determine a differential equation for the amount of salt a(t) in the tank at time t > 0. (use a for a(t).)

Answers

Final answer:

The differential equation for the amount of salt a(t) in the tank at time t > 0 is dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t).

Explanation:

To find the differential equation for the amount of salt a(t) in the tank at time t > 0, we need to consider the rate of change of the salt concentration in the tank.

Let A(t) represent the amount of salt in the tank at time t. The salt entering the tank each minute is given by the concentration (4 lb/gal) multiplied by the rate of inflow (3 gal/min), which is 12 lb/min.

The salt leaving the tank each minute is given by the concentration in the tank (A(t)/V(t)) multiplied by the rate of outflow (2 gal/min), which is 2A(t)/(35 + (3 - 2)t).

Therefore, the rate of change of the salt in the tank is given by the difference between the rate of inflow and the rate of outflow: dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t). This is our differential equation for the amount of salt in the tank.

Learn more about Differential equation here:

https://brainly.com/question/33433874

#SPJ2

Graph a line passing through the point left (−3,6) and having the slope one third. Give the​ slope-intercept form of the equation of the line if possible.

Answers

slope = 1/3
passing through the point left (−3,6)

y = mx + b
6 = 1/3(-3) + b
b = 6 +1
b = 7

equation
y = 1/3(x) + 7

hope it helps
Final answer:

The equation of the line passing through the point (-3,6) with a slope of a third is y = 1/3x + 7. The graph of this line can be drawn by plotting the y-intercept at (0,7) and using the slope to plot other points.

Explanation:

The provided point through which the line passes is (-3,6) and the slope is a third. The general slope-intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept. That is, it represents the point where the line intersects the y-axis.

Let's use this information to find the equation of the line. We know that y = mx + b. We can substitute the slope (m=1/3) and the point (-3, 6) into this equation: 6 =(1/3)(-3) + b.

Solving this for b gives us b = 6 + 1 = 7. Therefore, the equation of the line in slope-intercept form is y = 1/3x + 7.

To graph the line, you can start by plotting the y-intercept at (0,7) on the y-axis, then rise 1 unit and run 3 units (since the slope = rise/run = 1/3) from the y-intercept point to plot the second point. Connect these points to draw the line.

Learn more about Line Equations and Graphing here:

https://brainly.com/question/2418960

#SPJ12

12-5x-4kx=y solve for x

Answers

[tex]12-5x-4kx=y :x[/tex] 

[tex]-5x-4kx=y-12[/tex] 

[tex]-x(5+4k)=y-12 [/tex] 

[tex]-x= \dfrac{y-12}{5+4k} [/tex] 

[tex]x=- \dfrac{y-12}{5+4k}[/tex]

The apartments in Ericas apartment house are consecutively numbered on each floor. The sum of her and next door neighbor's number is 2409. What are the two numbers?

Answers

Let x be the number of Ericas's apartment, the number of her neighbor will be 
x+1, so

x+ x+1 = 2409

2x = 2408 and x = 1204 and her next door neighbor's is 1205



Ten subtracted from seven times a number is 25 what is the number ?

Answers

x represents the unknown number

7x-10=25
add 10 to both sides

7x=35
divide both sides by 7

x=5

The number is 5.

What number do you subtract from 3 to get 10?

Answers

3 - x = 10
-x = 10 - 3
-x = 7
x = -7 <===
3-10 ( count backwards or use calculator)

= -7

A line can be defined in general form by the equation Ax+By = C where A, B and C are constants. You may assume that both A and B are non-zero. Then the slope of the line is , its x intercept is , and its y intercept is . Of course your answers will depend on A, B, and C. Remember that mathematics, and WeBWorK, are case sensitive, so make sure to use upper case letters A, B and C.

Answers

note: I'm not going to type in case sensitive or correct grammer so it's not my fault if you paste my answer and the program says it's wrong


y=mx+b
m=slope
b=y intercept

the x intercept is where the line crosses the x axis or where y=0
the y intercept is where the line crosses the y axis or where x=0


so

for the slope, solve for y
Ax+By=C
minus Ax both sides
By=-Ax+c
divide both sides by B
[tex]y=\frac{-A}{B}x+\frac{C}{B}[/tex]

the slope is [tex]\frac{-A}{B}[/tex] and the y intercept is at [tex]y=\frac{C}{B}[/tex]

find x intercept
set y=0

Ax+By=C
Ax+B(0)=C
Ax=C
divide both sides by A
[tex]x=\frac{C}{A}[/tex]
the x intercept is at [tex]x=\frac{C}{A}[/tex] or the point [tex](\frac{C}{A},0)[/tex]


slope is [tex]\frac{-A}{B}[/tex]
the x intercept is at [tex]x=\frac{C}{A}[/tex] or the point [tex](\frac{C}{A},0)[/tex]
the y intercept is at [tex]y=\frac{C}{B}[/tex] or the point [tex](0,\frac{C}{B})[/tex]

Final answer:

The slope of a line in general form can be found by rearranging the equation to solve for y. The x-intercept is obtained by setting y = 0 and solving for x, while the y-intercept is obtained by setting x = 0 and solving for y.

Explanation:

The slope of a line defined in general form by the equation Ax+By = C can be found by rearranging the equation to solve for y, resulting in y = (-A/B)x + (C/B). The coefficient of x, -A/B, represents the slope of the line. The x-intercept can be found by setting y = 0 and solving for x, resulting in x = C/A. Similarly, the y-intercept can be found by setting x = 0 and solving for y, resulting in y = C/B.

A post card collector has 1,230 postcards if she displays them on pages that hold 6 cares each how many pages does she need ?

Answers

There are 1230 postcards
each page can hold 6 cards

so your equation is 

1230/6 =x 

where as x is the pages she needs 

x = 205

She needs 205 pages exactly

hope this helps

WILL GIVE THE BRAINLIEST ANSWER!!!

Select the postulate that is illustrated for the real numbers.

25 + 0 = 25

The commutative postulate for multiplication

Multiplication by one

The addition inverse postulate

Commutative postulate for addition

The distributive postulate

Additive identity

The multiplication inverse

Answers

The answer for this question would be F) Additive identity or the sixth option.

The answer is additive identity because you're adding a number plus 0 and the result is the number u added.
F) Additive identity or number 6 
hope that helps 

the length of a rectangle is 6 units shorter than 1/4 of the width x. Write an expression for the perimeter of the rectangle.

Answers

L=x/4 -6

Perimeter= Length x Width
Width=x
Length= x/4 -6

P=LxW
P=(x/4-6)x(x)
[tex]\bf \textit{perimeter of a rectangle}\\\\ P=2l+2w\quad \begin{cases} l=length\\ w=width\\ -----\\ l=\frac{1}{4}w-6 \end{cases}\implies P=2\left( \frac{1}{4}w-6 \right)+2w \\\\\\ P=\cfrac{1}{2}w-12+2w\implies P=\cfrac{w}{2}-12+2w\implies P=\cfrac{w-24+4w}{2} \\\\\\ P=\cfrac{5w-24}{2}\implies P=\cfrac{5}{2}w-12[/tex]

Ratio of the number of students in art class to the number of students in gym class was 2:7, however art class is small, and gym class is large, students changed for the second semester. Now the students in art class to the number students in gym class is 5:4. If 75 students are in art class in second semester, how many were in art class and gym class first semester?

Answers

semester 1:

let the number of students in the art class be 2a, and the number of the students in the gym class be 7a. (check: the ratio is 2a:7a = 2:7)

so the total number of students is 9a.


semester 2:

the 9a students are go to the art class and gym class at a a ratio of 5: 4, 

so 5a students go to the art class, and 4a students go to the gym class.



75 students are in art class in second semester means that 5a=75

so a=75/5=15.


In the 1st semester the number of students was: 

art class: 2a=2*15=30

gym class: 7a=7*15=105

Evaluate the numerical expression
[18 Divided by (2 x 3)] x 4

Answers

P: parenthesis
E: exponents
MD: multiplication or division (whichever comes first left to right)
AS: addition or subtraction (whichever comes first left to right)

This is the order of operations. We will use this to solve the equation correctly.
We will start with the parenthesis. 2x3=6.
[18/6]x4
Next, we will do the rest of the parenthesis.
18/6=3.
This gets rid of the parenthesis (or brackets.) We will now do the rest of the problem, which is multiplying 3 and 4.
3x4=12.
12 is your final answer.

Wich is bigger two thirds of 30 or one fifth of 25?

Answers

two-thirds of 30 is bigger

two-thirds of 30 = 20
one-fifth of 25 = 5

two-thirds of 30 is bigger

hope this helps

A city's sales tax is 0.07write this decimal as a fraction and tell how many cents of tax are on each dollar

Answers

its 7/100 is the fraction and for a dollar its 7 pennies

A composite number can be written as the product of prime numbers

Answers

A composite number is one that has other factors besides 1 and itself.
Since it is not prime, it has a prime factorization, making this statement true.

Final answer: True

She has given recently are different length one is 3 4/5 feet long and the other is 3 1/2 feet long how much would she have to cut so it will be the same length

Answers

Final answer:

To make the lengths the same, she would have to cut 0.3 feet from the longer piece.

Explanation:

To find the amount she would have to cut to make the two lengths the same, we need to subtract the smaller length from the larger length.

The first length is 3 4/5 feet, which can also be written as 3 + 4/5 = 3 + 0.8 = 3.8 feet.

The second length is 3 1/2 feet, which can also be written as 3 + 1/2 = 3 + 0.5 = 3.5 feet.

Subtracting the smaller length (3.5 feet) from the larger length (3.8 feet), we get:

3.8 feet - 3.5 feet = 0.3 feet.

So she would have to cut 0.3 feet from the longer piece to make the lengths the same.

I need to know how to solve this in order correctly and the answers well

Answers

use order of operations

8^2 = 64

4(64+4*4*8)

4(64+128)

4(192)

768

Caecillia can run 3 over 20 of a Marathon in 2 over 3 of an hour compute the unit rate

Answers

3/20 marathon in 2/3 hour

we want to find per 1 hour

(3/20marathon)/(2/3hour)
multiply it by (3/2)/(3/2)
(3/20marathon times (3/2)/(6/6hour)
(9/40marathon)/(1hour)
9/40marathon per hour

the point (4,7) is on the graph of y=x^2+c. what is the value of c?

Answers

point is (4,7)
So y = 7 = 4^2 + c
c = 7 - 16
c = -9

The value of c in the equation y = x² + c, given the point (4,7) lies on the graph, is found to be -9 after substituting the point's coordinates into the equation and solving for c.

To find the value of c in the equation y = x² + c, where the point (4,7) is on the graph, we substitute the x and y values from the point into the equation. This gives us:

7 = 4² + c

7 = 16 + c

Now, we subtract 16 from both sides to solve for c:

c = 7 - 16

c = -9

Therefore, the value of c is -9.

alyssa received 30,000 from an inheritance and invests in a certificate of deposit paying 5% annual interest and the rest in apple inc. offering an annual return of 11%. if the annual income from her income from her investment is 2220.00, how much did alyssa invest in each?

Answers

Since her annual return is 2220.00 as well as 11% of her investment in Apple, we can divide it by 11 and multiply that by 100 to get her investment in Apple, which would be 20181+81/99. Since she only invested in 2 things, her investment in her certificate of deposit is 30,000-(20181+81/99)=9818+18/99

If the machine has a probability of failure of 0.01, what is the probability of more than 1 failure occurring in a batch of 20 envelopes?

Answers

The Answer is 0.0169
see attachment for full solution

Estimate the quotient 24 3/7÷3 7/13

Answers


Round off the fractions!  3/7 rounds off (down) to 0 and 7/13 (being greater than 1/2) rounds up to 1.  Then we have (24 + 0) / (3+1) = 24/4 = 6.

Unfortunately, this is "quite far" from the actual quotient, 6.9037.

We could experiment:  Let 24 3/7 become 24 1/2 and 3 7/13 become 3 1/2.

(24 1/2) / (3 1/2) = (25/2) / (7/2) = 49/2 / (7/2) = 7 (which is "close" to the actual value, 6.9037.

Let's conclude that the estimation is between 6.9 and 7.0.

Yearly homeowner property taxes are figured at a rate of $1.15 tax for every $100 of home value. Find the property taxes on a townhouse valued at $73,000.

Answers

$100's in the home value = 73,000 / 100
= 730

property taxes = 1.15 X 730
= $839.50
Final answer:

To calculate the property taxes on a townhouse valued at $73,000, divide the value by $100 to find the number of $100 increments, and then multiply this by the tax rate of $1.15.

Explanation:

To find the property taxes on a townhouse valued at $73,000, we need to calculate the tax amount based on the given tax rate. The tax rate is $1.15 for every $100 of home value.

First, we need to find how many $100 increments are there in the home value.

Divide $73,000 by $100:

$73,000 ÷ $100 = $730

Now, multiply the number of $100 increments by the tax rate:

$730 × $1.15 = $839.50

Therefore, the property taxes on a townhouse valued at $73,000 would be $839.50.

Learn more about Calculating property taxes here:

https://brainly.com/question/4891386

#SPJ2

the 400ths power of number is 9^1000 what is the number

Answers

[tex]\bf (9^{1000})^{400}\implies 9^{1000\cdot 400}\implies 9^{400000}[/tex]

What is -9/10 - 7.1?

Answers

The answer would be -8.
Since -9/10 is a fraction, you could turn it into a decimal, which would be -0.9.
Now we have -0.9 - (-7.1)
A negative minus a negative is the same as adding.
 -0.9+(-7.1)=-8


A tank initially contains 200 gallons of brine, with 50 pounds of salt in solution. brine containing 2 pounds of salt per gallon is entering the tank at the rate of 4 gallons per minute and is is flowing out at the same rate. if the mixture in the tank is kept uniform by constant stirring, find the amount of salt in the tank at the end of 40 minutes. the amount of salt in the tank at the

Answers

Final answer:

The amount of salt in the tank at the end of 40 minutes is still 50 pounds.

Explanation:

To find the amount of salt in the tank at the end of 40 minutes, we need to calculate the change in the amount of salt in the tank over that time period.

The tank contains 200 gallons of brine with 50 pounds of salt in solution. Brine containing 2 pounds of salt per gallon is entering and exiting the tank at a rate of 4 gallons per minute.

Since the rate of flow in and out of the tank is the same, the amount of salt in the tank remains constant. Therefore, the amount of salt in the tank at the end of 40 minutes is still 50 pounds.

Sathish is going on a 200020002000-kilometer road trip with two friends. The car consumes 666 liters of gas for every 100100100 kilometers, and gas costs \$1.20$1.20dollar sign, 1, point, 20 per liter. If Sathish and his two friends want to split the cost evenly, how much should they each pay?

Answers

First calculate the total amount of liters consumed:

Volume gas consumed = (6 L / 100 km) * 2000 km = 120 L

 

Then calculate the total cost:

Cost = ($1.20 / L) * 120 L = $144

 

Since there are three of them, so each must pay:

Payment of each = $144 / 3 = $48 per person


Answer:

$48 per person

Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?

Answers

total mass of salt in the 2100 grams of solution  = 15 + 0.05 * 210  =     25.5  grams

as a percent this is    (25.5 * 100) / 210  =   12.14% Answer  

Final answer:

Larry's new solution has an approximate salt concentration of 11.33%. This was calculated by adding the initial mass of salt in the solution (10.5 g) to the extra salt added (15 g), resulting in a new total mass of salt (25.5 g), then dividing by the total mass of the new solution (225 g), and finally multiplying by 100%.

Explanation:

To find the percent of salt in Larry's new solution, we first need to calculate the total mass of the solution and how much of that mass is salt. Initially, we have 210 grams of a 5% salt solution. To find out how much salt that is, we use the percentage:

210 g × 0.05 = 10.5 g of salt

Now, Larry adds 15 grams of salt to this solution, so we add that amount to the initial salt mass:

10.5 g + 15 g = 25.5 g of salt

The total mass of the new solution is the sum of the mass of the original solution and the added salt:

210 g + 15 g = 225 g

Finally, to find the mass/mass percent concentration of the new solution, we divide the total mass of salt by the total mass of the solution and multiply by 100%:

((25.5 g / 225 g) × 100% = 11.33%

So, the percent of salt in Larry's new solution is approximately 11.33%.

Other Questions
We use pronouns so that _____.we are not repetitivewe sound more educatedwe can be clear in our writingthey can provide varietythey can provide economy of words Your friend Lana is yawning, rubbing her eyes, and leaning back in her chair. What conclusion can you draw from these details The Changs updated their bedroom by purchasing a new lamp for $89.95 and a comforter set for $239.99. They paid 2007-03-04-00-00_files/i0120000.jpg% sales tax on their purchases. If the Changs paid $351.72 total, determine if they paid the correct amount. a. The Changs family paid $0.33 too much for their purchases. b. The Changs family paid $0.99 too much for their purchases. c. The Changs family paid $5.94 too much for their purchases. d. The Changs family paid the correct amount for their purchases If Dave drives at a steady speed of 50 mph, how long will it take him to drive 10 miles? Which type of electromagnetic radiation has a longer wavelength than visible light? McDonald's has about 210,000 managers and each makes on average 39,000 dollars per year. How much money does McDonald's spend on managers each year? which effect is not caused by rapid growth in china A money box contains only 10-cent and 20-cent coins. There are 27 coins with a total value of $3.60. How many coins of each? No. of 10-cent coins = No. of 20-cent coins = The cable is drawn into the motor with an acceleration of 7 m/s2 determine the time needed for the load at b to attain a speed of 10 m/s, starting from rest. given the functon g(x)= (1/4)^x, determine the y-intercept and the equation of the asymptote.a. the y-intercept is (0, 0.25) and the asymptote is at y=0b. the y-intercept is (1,0) and the asymptote is at y=0. the y-intercept is (1,0) and the asymptote is at y=1c. the y-intercept is (0,1) and the asymptote is at y=0d. the y-intercept is (1,1) and the asymptote is at y= 1. Which text records ancient Hindu religious beliefs? A. Bhagavad-Gita B. Ramayana C. Epic of Gilgamesh D. Torah _____ involves the collection, organization, and analysis of numerical data. Give one example of an equation with variables on both sides that has all real numbers as the solution. Also give an example of an equation with variables on both sides that has no real solutions. 2O POINTS Which of the following was discovered at Catal Huyuk and the purpose of the item discovered is still unknown?pottery.metal smithing.swords.cave drawings. How do you find the answer to a algebraic sum of these like terms 7a, 2a, -3a, 5a, Alfredo is conducting an experiment on the effects of exercise on concentration. the independent variable is (the) ________ and the dependent variable is (the) ________. (select only one answer) 2.4 puzzle time how can you share five apples with seven friends Comment on the structure of the plot. what scene(s) constitute 1) exposition 2) rising action 3) climax 4) falling action 5) denouement? how does the development of the storm correlate with the development of the plot? why is the story called the storm? what is the symbolism of the storm? what circumstances introduced in part i turn out to have a profound effect on events in the story? Jeff prepares meals in the home of his customers. His fixed cost for transportation and supplies is $14.50. The labor and groceries needed for each family meal is $8.80, so the expense function is E=5.7q +8.8True or false? How did lincolns and the unions attitude toward african americans change as the civil war progressed Steam Workshop Downloader