3) x2+ y2 - x + 3y - 42 = 0
X+y=4

Answers

Answer 1

The solution is [tex](-1,5)[/tex] and [tex](7,-3)[/tex]

Step-by-step explanation:

The expression is [tex]x^{2} +y^{2} -x+3y-42=0[/tex] and [tex]x+y=4[/tex]

Using substitution method we can solve the expression.

Let us substitute [tex]x=4-y[/tex] in [tex]x^{2} +y^{2} -x+3y-42=0[/tex]

[tex](4-y)^{2} +y^{2} -(4-y)+3y-42=0[/tex]

Expanding and simplifying the expression, we get,

[tex]\begin{array}{r}{16-8 y+y^{2}+y^{2}-4+y+3 y-42=0} \\{2 y^{2}-4 y-30=0}\end{array}[/tex]

Let us use the quadratic equation formula to solve this equation,

[tex]\begin{aligned}y &=\frac{4 \pm \sqrt{16-4(2)(-30)}}{2(2)} \\&=\frac{4 \pm \sqrt{16+240}}{4} \\&=\frac{4 \pm 16}{4} \\y &=1 \pm 4\end{aligned}[/tex]

Thus, [tex]y=5[/tex] and [tex]y=-3[/tex]

Substituting y-values in the equation [tex]x+y=4[/tex], we get the value of x.

For [tex]y=5[/tex] ⇒ [tex]x=4-5=-1[/tex]

For [tex]y=-3[/tex] ⇒ [tex]x=4+3=7[/tex]

Thus, the solution set is [tex](-1,5)[/tex] and [tex](7,-3)[/tex]


Related Questions

The price of an item yesterday was 115. Today the price fell to 69. Find the percentage decrease

Answers

Answer:

Step-by-step explanation:

40%

The formula is

Old-new/old *100

115-69/115*100

The percentage decrease is 40% if the price of an item yesterday was 115. Today the price fell to 69.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

The price of an item yesterday was 115. Today the price fell to 69.

The difference in price = 115 - 69 = 46

Percentage decrease = (46/115)×100 = 40%

Thus, the percentage decrease is 40% if the price of an item yesterday was 115. Today the price fell to 69.

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The total of 3 games is $38.97 . Each game costs the same amount. Write an equation that can be used to determine n , the cost of 1 game

Answers

Answer:

Step-by-step explanation:

3games cost38.97 so you have to divide 38.97divided by 3=12.99 so each game was 12.99 a game

Final answer:

To determine the cost of 1 game, set up an equation: 3n = $38.97. Divide both sides of the equation by 3 to isolate n. The cost of one game is $12.99.

Explanation:

To find the cost of one game, we can set up the equation 3n = $38.97based on the given information. where n represents the cost of one game. Since each game costs the same amount, we can write the equation:

3n = $38.97

Divide both sides of the equation by 3:

n = $38.97 / 3

Dividing both sides of the original equation by 3 is a way to undo the multiplication by 3 on the left side, thereby isolating the variable n.

When we perform this division, we find that n is equal to $12.99.

n = $12.99

Therefore, the cost of one game is $12.99.

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factorise 9f²-12f plus 4​

Answers

Answer:

(3f - 2)²

Step-by-step explanation:

Given

9f² - 12f + 4

Consider the factors of the product of the coefficient of the f² term and the constant term which sum to give the coefficient of the f- term.

product = 9 × 4 = 36 and sum = - 12

The factors are - 6 and - 6

Use these factors to split the f- term

9f² - 6t - 6t + 4 ( factor the first/second and third/fourth terms )

= 3f(3f - 2) - 2(3f - 2) ← factor out (3f - 2) from each term

= (3f - 2)(3f - 2)

= (3f - 2)²

Answer:

9f² - 12f + 4 = (3f - 2)²

Step-by-step explanation:

9f²-12f+4 =

= (3f)²-2×(3f)×(2)+2²

= (3f-2)²

pls help 10 points!!!​

Answers

Answer:

3rd one

Step-by-step explanation:

What is the value of b 3.2 = 4/5 ( b - 5 )

Answers

The value of b in the equation [tex]\( 3.2 = \frac{4}{5}(b - 5) \)[/tex] is 9.

To solve for b in the equation [tex]\(3.2 = \frac{4}{5}(b - 5)\)[/tex], we'll first distribute [tex]\(\frac{4}{5}\)[/tex] across b - 5:

[tex]\[3.2 = \frac{4}{5}b - \frac{4}{5} \times 5\]\[3.2 = \frac{4}{5}b - 4\][/tex]

Next, let's isolate the term containing b by adding 4 to both sides:

[tex]\[3.2 + 4 = \frac{4}{5}b\]\[7.2 = \frac{4}{5}b\][/tex]

Now, to solve for b, we'll multiply both sides by [tex]\(\frac{5}{4}\)[/tex] to isolate b:

[tex]\[b = 7.2 \times \frac{5}{4}\]\[b = 9\][/tex]

So, the value of b is 9.

sld;fn;sdlfhs;lfnskfhssf

Answers

PLEASE MARK BRAINLIEST!

Answer:

The best answer is 12.4 units.

Step-by-step explanation:

This is because, when I totaled all of the side lengths, I got an estimated result of 12 units. 12.4 is the next closest answer, so your answer is 12.4

I hope this helps!

- sincerelynini

Step-by-step explanation:

To get the right answer always you can use the save route: Pythagoras' theorem.

[tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]

A student solves the equation StartFraction x + 3 Over 2 EndFraction = StartFraction 3 x + 5 Over 5 EndFraction using the steps in the table.
Original equation
StartFraction x + 3 Over 2 EndFraction = StartFraction 3 x + 5 Over 5 EndFraction
Cross multiplication
5 (x + 3) = 2 (3x + 5)
Distributive property
5 x + 15 = 2 (3 x + 5)
Subtraction property of equality
5 = x

Which method of solving for the variable could be used instead of cross multiplication?
distributing x + 3 and then 3x + 5 to both sides of the equation
distributing x – 3 and then 3x – 5 to both sides of the equation
using the multiplication property of equality to multiply both sides of the equation by 10
using the multiplication property of equality to multiply both sides of the equation by One-tenth

Answers

using the multiplication property of equality to multiply both sides of the equation by 10

Step-by-step explanation:

Given equation is:

[tex]\frac{x+3}{2} = \frac{3x+5}{5}[/tex]

One method to solve this equation is cross-multiplication which the student has used.

One of the alternate method can be multiplying both sides by the LCM of numerators of fractions on both sides

So multiplying both sides by 10 (multiplication property of equality)

[tex]\frac{x+3}{2} * 10 = \frac{3x+5}{5} * 10\\5(x+3) = 2(3x+5)\\5x+15 = 6x+10\\5x+15-10 = 6x\\6x = 5x+5\\6x-5x = 5\\x = 5[/tex]

The alternate method of LCM produces the same answer so the correct answer is:

using the multiplication property of equality to multiply both sides of the equation by 10

Keywords: Linear equations, variables

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Answer:

using the multiplication property of equality to multiply both sides of the equation by 10

Step-by-step explanation:

F(x)=-5x
G(x)=8x^2-5x-9
Find (f•g)(x)
A.-40x^4+25x^3+45x^2
B.-40x^3-5x-9
C.-40x^2+25x+45x
D.-40x^3+25^2+45x

Answers

Answer: D. -40x^3 + 25x^2 + 45x

Step-by-step explanation:

-5x(8x^2 - 5x - 9)

-40x^3 + 25x^2 + 45x

Point slope form. (9,-2) and (4,2)

Answers

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (9, -2) and (4, 2).

Substitute:

[tex]m=\dfrac{2-(-2)}{4-9}=\dfrac{2+2}{-5}=-\dfrac{4}{5}[/tex]

Put the value of a slope and coordinates of first or second point to the equation of a line:

[tex](9,\ -2),\ m=-\dfrac{4}{5}\\\\y-(-2)=-\dfrac{4}{5}(x-9)\\\\\boxed{y+2=-\dfrac{4}{5}(x-9)}\\\\(4,\ 2),\ m=-\dfrac{4}{5}\\\\y-2=-\dfrac{4}{5}(x-4)}[/tex]

(3x+6)(4x+2) what is the answer

Answers

Answer:

12x^2 + 30x + 12

Step-by-step explanation:

Expand the equation using FOIL (First Outside Inside Last)

Hope this helps! :]

Use the graph method to solve the system of linear equations: y = -2x + 1 and y = x - 2 A) (-1, -1) B) (-1, 1) C) (0, 2) D) (1, -1)

Answers

Answer:

x=1, y=-1. (1, -1).

Step-by-step explanation:

y=-2x+1

y=x-2

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

-2x+1=x-2

-2x-x=-2-1

-3x=-3

3x=3

x=3/3

x=1

y=1-2=-1

PLEASE ITS MY LAST QUESTION ON THIS ASSIGNMENT PLS PLS

The ratio of the angle measures of a triangle are 1:2:2. What type of triangle is this?

acute triangle
right triangle
obtuse triangle
equiangular triangle

Answers

Answer:

The answer is NOT D, because clearly the angle measurements are not EQUAL. So cross that off. My best guess would be A, acute triangle. Usually for that the two angles are shown as the same and the top angle is usually smaller. That's just from picturing it in the head.

Step-by-step explanation:

Can I have brainliest

Answer: The Answer is acute triangle

What is the equivalent of 20/100

Answers

many fractions including 1/5, 2/10, 3/15, 4/20 and up.
1/5 is the choice most simplified!

On a recent day 8 euros were worth 9 dollars and 24 euros were worth 24 dollars write an equation of the form y = kx

Answers

Question:

On a recent day, 8 euros were worth $9 and 24 euros were worth $27. Write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars.

Answer:

y = 1.125x is the equation to show the relationship between the number of euros and the value in dollars.

Solution:

Given that On a recent day 8 euros were worth 9 dollars and 24 euros were worth 24 dollars

Let "y" be the value in dollars

Let "x" be the number of euros

We have to write a equation in form of y = kx

8 euros were worth 9 dollars

"k" is found as follows:

[tex]k = \frac{\text{value in dollars}}{\text{number of dollars}}[/tex]

[tex]k = \frac{9}{8}[/tex]

Therefore, equation of y = kx is given as:

[tex]y = \frac{9}{8}x[/tex]

[tex]y = 1.125x[/tex]

To check the equation, use the another given value

24 euros were worth $27

[tex]y = 1.125 \times 24\\\\y = 27[/tex]

Hence the equation y = 1.125x is correct    

Evaluate the expression 24/b+8 when b=9

Answers

Final answer:

To evaluate the expression 24/b+8 for b=9, substitute 9 for b to get 24/9 + 8, which simplifies to approximately 10.67.

Explanation:

To evaluate the expression 24/b+8 when b=9, we substitute the value of b into the expression and perform the arithmetic operation.

First, we replace b with 9:

24/9 + 8

Then, we divide 24 by 9:

2.666... + 8

Next, we add 8 to the quotient:

2.666... + 8 = 10.666...

The result of evaluating the expression 24/b+8 for b=9 is approximately 10.67.

Which statements are true about the ordered pair (-3, 1) and the system of
equations?
(x - 4y = 6
| 3x + y = -8
Select each correct answer.
The ordered pair
is a solution to the first equation because it
makes the first equation true.
The ordered pair (-3, 1) is a solution to the second equation
because it makes the second equation true.
The ordered pair
is not a solution to the system because it
makes at least one of the equations false.
is a solution to the system because it
The ordered pair
makes both equations true.

Answers

The ordered pair (-3, 1) is not a solution to system because it makes at least one of the equations false

Solution:

Given system of equations are:

x - 4y = 6 ------- eqn 1

3x + y = -8 ------------ eqn 2

Given ordered pair is (-3, 1)

We have to check if the options are true

Let us substitute (x, y) = (-3, 1) in eqn 1

[tex]-3 - 4(1) = 6\\\\-3 - 4 = 6\\\\-7\neq 6[/tex]

Thus the given ordered pair (-3, 1) did not satisfy the first equation

Substitute (x, y) = (-3, 1) in eqn 2

[tex]3(-3) + 1 = -8\\\\-9 + 1 = -8\\\\-8 = -8[/tex]

Thus the given ordered pair (-3, 1) satisfied the second equation

But for a ordered pair to be a solution to system of equations, it must satisfy both the equations

Thus the ordered pair (-3, 1) is not a solution to system because it makes at least one of the equations false

Mrs. Evans drove 24 miles on 3 gallons of gas. What is her unit rate in miles per gallon??

Answers

Answer:  8 miles

Step-by-step explanation:

24/3=8

can plz someone help me ​

Answers

The ball that reached the highest is Mario's because his reached past 10 whereas Jasmine's was 7.8. The ball that went the farthest is Jasmine's.

What is 6x-5y=22
y= -8

Answers

6x-5y=22

1.) factor the y into the equation So it’ll be 6x-5(-8)=22

2. Solve the equation of -5*-8 = 40

3. The new equation is 6x+40=22

4. Subtract from both sides 22-40 = -18

5. The new equation is 6x=-18

6. Now we have to get x by itself to find its value, so divide by 6 on both sides. 6x/6 = x
And -18/6 = -3

So the value of x is -3

f(x)= x2-5x+2. Find f(-4)

Answers

Answer:

f ( 4 ) = 18

Step-by-step explanation:

Explanation:

f ( x ) = 5 x − 2

Replace  4  instead of  x  to find  f ( 4 )

f ( 4 ) = 5 ( 4 ) − 2 = 20 − 2 = 18

Final answer:

The value of f(-4) for the function f(x) = x^2 - 5x + 2 is 38.

Explanation:

To find the value of f(-4) for the function f(x) = x^2 - 5x + 2, you substitute -4 for x in the function.

It looks like this:

f(-4) = (-4)^2 - 5(-4) + 2

First, you square -4, which is (-4)^2 = 16.

Then, you calculate -5 times -4, which is 20.

Finally, you add 2 to the result.

So, f(-4) is equal to:

f(-4) = 16 - 20 + 2 = 38

The final answer is 38.

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which ordered pair in the form (x,y) is a solution of the equation 7x-5y=28

Answers

Answer:

(4 ,0) is a solution

Step-by-step explanation:

7(4) - 5(0) = 28 - 0 = 28

Step-by-step explanation:

there are more answers.. i get.two answers

x=9:y=7 and x=4;y=0

Samar likes to snack frequently during the day, but he wants his snacks to provide at least 24 grams of protein per day. Each snack pack provides 4 grams of protein and each minibite provides 1 gram. snack pack cost 50 cents each and minibites 12 cents. how many of each snack should he use to minimize his daily cost?

Answers

Answer:

  24 minibites

Step-by-step explanation:

The cost of protein in the snack pack is ...

  $0.50/(4 g) = $0.125/g

The cost of protein in the minibites is ...

  $0.12/(1 g) = $0.120/g

Since the cost of protein is less for minibites, and the only criterion is the amount of protein, the lowest-cost snack mix is 24 minibites.

Answer:

24 minibites

Step-by-step explanation:hoped tt his helped

Which answer represents the series in sigma notation? −5+(−1)+3+7+11

Answers

The series in sigma notation is:  representing terms increasing by 4 starting from -5.

To represent the series in sigma notation, let's first examine the pattern of the terms.

The given series starts with -5 and each subsequent term increases by 4. We can express this pattern using the formula:

[tex]\[ a_n = -5 + (n - 1) \times 4 \][/tex]

Here, [tex]\( a_n \) represents the \( n \)th term of the series[/tex].

Now, let's break down the components of the formula:

-[tex]\( -5 \) is the initial term of the series.- \( (n - 1) \) accounts for the position of each term in the series. When \( n = 1 \), \( (n - 1) = 0 \), so the first term is \( -5 \). As \( n \) increases, \( (n - 1) \) increases by 1, causing the series to increase by 4 each time.- \( 4 \) is the common difference between consecutive terms in the series.[/tex]

Next, we represent the series using sigma notation:

[tex]\[ \sum_{n=1}^{5} (-5 + (n-1) \times 4) \][/tex]

This notation indicates that we sum up the expression [tex]\( -5 + (n-1) \times 4 \) for \( n \)[/tex] ranging from 1 to 5, which covers all the terms of the given series.

In summary, the series is represented in sigma notation as described above, capturing the pattern of increasing terms starting from -5.

You estimate that a baby pig weighs 20 pounds. The actual weight of the baby pig is 16 pounds. Find the percent of error

Answers

Answer:

U were 20% off

Ure estimate was 80%

Step-by-step explanation:

16/20 is 80%

100%-80% is 20%

The percent of error is 20%

For every 12 boys at the music camp, there are 18 girls. Which is the correct ratio of girls to total number of campers?
A.18 to 12
B.12 to 30
C.3:2
D.3:5

Answers

The ratio is 12:30 or if broken down 2:5

but the answer is 12 to 30 or 12:30

Answer:

The answer is D.

Step-by-step explanation:

There are 30 campers total. The ratio as a fraction is 18/30. If you reduce this, you get 3/5, or 3:5.

Olivia goes shopping with a friend and notices her friend's fashionable winter boots. She thinks about the recent cool weather and realizes she needs to buy a pair. In which stage of the consumer purchase decision process was Olivia when she had this realization?

Answers

Answer:

Problem Recognition Stage (the first stage)

Explanation:

The "Consumer Buying Decision Process" consists of 5 stages. These are: Problem Recognition, Information Search, Evaluation of Alternatives, Purchase Decision and Post-Purchase Evaluation. This information is commonly used by marketing businesses in order to know the habit or behavior of people upon buying goods and services.

Olivia's situation above is in the "Problem Recognition" stage. This is the first stage of the process. She realizes that she needs the winter boots because of the cool weather and thus, she realizes that she has a need or a problem that she wanted to solve. Buyers recognize this problem as a gap in their needs, thus they want to fill it immediately once they recognize it. This will be followed by "Information Search," a time whereby she'll consider some options in buying boots.

Thus, this explains the answer.

PLZZZZZ HELP!!!!
What idea, achievement, or life event is associated with Aristotle?


condemned to death by poison


tutored Alexander the Great


thought philosopher-kings should run the government

Answers

Answer: B) Tutored Alexander The Great

Step-by-step explanation: k12 test 1.12, :)

3X plus 3Y equals -18 and negative 2X plus 2Y equals -4 find a solution set

Answers

Answer:

The vaues to the given equations are x=-2 and y=-4

Therefore the solution set is (-2,-4)

Step-by-step explanation:

Given equations are [tex]3x+3y=-18\hfill (1)[/tex]

[tex]-2x+2y=-4\hfill (2)[/tex]

To solve the given equation to find the solution set :

Multiply the equation (1) into 2 we get

[tex]6x+6y=-36\hfill (3)[/tex]

Multiply the equation (2) into 3 we get

[tex]-6x+6y=-12\hfill (4)[/tex]

Now adding the equations (3) and (4) we get

[tex]6x+6y=-36[/tex]

[tex]-6x+6y=-12[/tex]

________________

[tex]12y=-48[/tex]

[tex]y=\frac{-48}{12}[/tex]

Therefore y=-4

Substitute the value of y=-4 in the equation (1) we get

[tex]3x+3y=-18[/tex]

[tex]3x+3(-4)=-18[/tex]

3x-12=-18

3x-12+12=-18+12

3x=-6

[tex]x=\frac{-6}{3}[/tex]

Therefore x=-2

The vaues to the given equations are x=-2 and y=-4

Therefore the solution set is (-2,-4)

Is the graphed function linear?
400
300
Yes, because each input value corresponds to
exactly one output value.
Yes, because the outputs increase as the inputs
increase
* No, because the graph is not continuous
200
No, because the curve indicates that the rate of
change is not constant.
100
4
6

Answers

to know if something is linear when you graph it it is always going to be in a straight line. if it isn't then it is not linear

Answer:

D

Step-by-step explanation:

i got it right on E2020

What is the equation of a line with a slope of -2 that passes through the
point, (-2, 12)?
O A. y = 4x-2
O B. y = -2x+6
O C. y = -2x+8
O D. y=-2x+4
SUBMIT

Answers

Answer:

O B. y = -2x+6

Step-by-step explanation:

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