Find a parametric representation of the solution set of the linear equation. (enter your answer as a comma-separated list of equations. use s and t as your parameters.) x + y + z = 2

Answers

Answer 1

Final answer:

The parametric representation of the solution set for the equation x + y + z = 2 is x = t, y = 2 - s - t, z = s, with 's' and 't' as the parameters.

Explanation:

To find the parametric representation of the solution set of the linear equation x + y + z = 2, we first need to express two variables in terms of the third. Let's use 's' and 't' as parameters.

We can express x and y in terms of z. Let's express z as 's'. So, z = s.

The equation x + y + z = 2 thus becomes x + y = 2 - s. We can choose x = t and y = 2 - s - t.

So, the parametric representation of the solution set for the given linear equation is (x = t, y = 2 - s - t, z = s), where 's' and 't' are parameters that can assume any real value.

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Related Questions

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

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]

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

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

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.

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%.

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.

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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

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.

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.

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

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.

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without using a calculator order the numbers from least to greatest square root of 200, 15, and 14

Answers

Least is 14 = 3.7
Next is 15 = 3.8
Largest is 200 = 14. 1

Final answer:

To order the numbers from least to greatest, estimate their square roots: 14 < 14.14 < 15.

Explanation:

To order the numbers from least to greatest, we need to compare their square roots. Without using a calculator, we can estimate the square roots to determine the order.

The square root of 200 is approximately 14.14.The square root of 15 is approximately 3.87.The square root of 14 is approximately 3.74.

Therefore, the order from least to greatest is 14 < 14.14 < 15.

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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

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.

0.8 is 10 times as great as wich decimal?

Answers

I don't know what to say, I've been trying to explain this for like... 10 minutes but I can't think of how to explain it. All I can say is to just divide .8 by 10. The answer is .08.

What is 681,542 rounded to the nearest hundred thousand.

Answers

That would be 700,000

The answer is 700000

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

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

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

Best way to work out planet torrid take 6 years to complete one orbit , planet monde blanc takes 9 years in the year 2035 both planets are lined up perfectly.

How many years will it be before the two worlds are line up again ?

Answers

so... hmmm dunno either planet, I assume they're on the solar system and therefore orbiting the same planet, the sun, or whoever.

but, in short, what I can make out is, when do 6 and 9 have the same LCM, least common multiple, or a factor that's common to both 6 and 9, and therefore meet at such.

well, let's do a prime factoring of 6, is 2 and 3 only, ok,
now a prime factoring of 9, is 3 and 3 only, ok.

now, we have 3 as common to both, so, to get an LCD or LCM, we'll use repeated factors but once only for each instance for each.

therefore [tex]\bf \stackrel{9}{3,3}\qquad \stackrel{6}{2,3}\qquad \stackrel{LCM}{3,3,2}\implies 18[/tex]

so, after 18 years.

[tex]\bf \cfrac{6}{18}\implies \cfrac{1}{3}\impliedby \textit{torrid will be orbiting one-third of the way} \\\\\\ \cfrac{9}{18}\implies \cfrac{1}{2}\impliedby \textit{monde blanc will be orbiting half-way}[/tex]

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.

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

frank finished his history assignment 1/5 hours then he completed his math assignment in 2/3 hours what is the total amount of time Frank's been doing these two assignments write your answer in simplest fraction form

Answers

1/5 = 3/15
2/3 = 10/15
3/15 + 10/15 = 13/15
13/15 cannot be simplified any further

The total amount of time Frank's been doing these two assignments will be 13 / 15 hours.

What is a fraction number?

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Frank finished his history assignment in 1/5 hours then he completed his math assignment in 2/3 hours.

Then the total amount of time Frank's been doing these two assignments will be

⇒ 1/5 + 2/3

⇒ (3 + 2 x 5) / 15

⇒ 13 / 15 hours

The total amount of time Frank's been doing these two assignments will be 13 / 15 hours.

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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.

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]

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.

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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

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.

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]

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