Solve the following system for all solutions:

(x - 1)^2 + (y + 3)^2 = 13

x + y = -3​

Answers

Answer 1

Answer:

( -4, -1 ) and ( -9, - 6)

Step-by-step explanation:

Given(x - 1)^2 + (y + 3)^2 = 13 x + y = -3​Solution

From the second equation we get

x = - y - 3

Substituting x in the first equation

(- y - 3 - 1)^2 + (y + 3)^2 = 13(-y - 4)^2 + (y + 3)^2 = 13(y+4)^2 + (y+3)^2 = 13y^2 + 8y + 16 + y^2 + 6y + 9 = 132y^2 + 14y + 12 = 0y^2 +7y +6 = 0(y+1)(y+6) = 0y = - 1y = - 6

Then

x = -4x = - 9

Answer

( -4, -1 ) and ( -9, - 6)

Related Questions

For the function, f(x) = x - 2, find x if f(x) = -1.

Answers

f(x)=x-2=-1
-1=x-2
+2 +2
-1=x

The circumference of a circle can be found by multiplying Pi by the diameter True False

Answers

Answer:

True

Step-by-step explanation:

You can find the circumference by multiplying Pi and the diameter.

Answer:

True. And if you only know the radius, multiply the radius by two to get the diameter.

what place does the three sit at in 43,628,698,591

Answers

Answer:

Billion

Step-by-step explanation:

In 43,628,698,591 the three is in the Trillion spot.

One, Ten, Hundred, Thousand, Ten Thousand, Hundred Thousand, Million, Ten Million, Hundred Million, Billion.

There are 9 #’s after the 3 which means it is billions :)

write an equation for g(x) given the following transformations, translation right 3, vertical shift up 5, vertical compression/shrink 1/4.

Answers

у вас всё правильно вы молодцы

A child needs to take 1/2 tablespoons of medicine per day in 4 equal doses. How much medicine is in each dose?
PLEASE HELP​

Answers

Answer:

1/8 tablespoons

Step-by-step explanation:

Since the child needs to take 1/2 tablespoons off medicine per day in 4 equal doses, you will divide the 1/2 tablespoons into 4 equal doses, so you need to divide by 4.

You can do this by multiplying 1/2 by 1/4.

[tex]\frac{1}{2} * \frac{1}{4} = \frac{1}{8}[/tex]

Answer:

it would be 1/8

Step-by-step explantion:

simply divide

1/2÷4

=1/8

(that should be right)

I need help? I don’t know what to dooooooo

Answers

Your suppose to graph where the line is

which is more , 1 gallon or 7 pints ,

a. 1 gallon
b. 7 pints
c. nethier ; they are equal

Answers

Answer:A

Step-by-step explanation: 1 Gallon is equal to 8 pints.

Answer:

A

Step-by-step explanation:

pint=1/8 of a gallon

therfor 7 pints = 7/8

7/8<1gal

4x - 10 = p+ 3x - 2x what is the value of x

Answers

Answer: if you need more let me know

1)
What number is 4 times as many as 25?

Answers

Answer:

100

Step-by-step explanation:

Suppose Sine (x) = negative three-fifths and cos(x) < 0. What the value of cos(2x)?

Answers

Answer:

[tex]-\frac{7}{25}[/tex]

Step-by-step explanation:

Value of given trigonometric ratio is equals to  [tex]cos (2x) = \frac{7}{25}[/tex].

What is trigonometric ratio?

" Trigonometric ratio is defined as in the right triangle the ratio which represents the relation between sides of a triangle with acute angle of a triangle."

Identity used

[tex]sin^{2} x +cos^{2} x =1\\ \\cos (2x) = cos^{2} x - sin^{2} x[/tex]

According to the question,

Given value of trigonometric ratio,

[tex]sin x = \frac{-3}{5} \\\\cosx < 0[/tex]

Substitute the value of [tex]sin x[/tex] in the above identity of trigonometric ratio,

[tex](\frac{-3}{5} )^{2} + cos^{2} x=1\\\\\implies cos^{2}x = 1- \frac{9}{25}\\ \\\implies cos x = \sqrt{\frac{16}{25} } \\\\\implies cos x = \frac{-4}{5} , cos x < 0[/tex]

Substitute the value of [tex]sin x[/tex] and [tex]cos x[/tex]  the trigonometric identity ,

[tex]cos (2x) =( \frac{-4}{5})^{2} - ( \frac{-3}{5})^{2}\\\\\implies cos (2x) = \frac{16}{25}- \frac{9}{25} \\\\\implies cos (2x) = \frac{7}{25}[/tex]

Hence ,  value of given trigonometric ratio is equals to  [tex]cos (2x) = \frac{7}{25}[/tex].

Learn more about trigonometric ratio here

https://brainly.com/question/1201366

#SPJ2

The variables x and y are related proportionally. When x =6, y = 10. Find y when x = 57.
When X = 57, y =

Answers

x=6 y=10
x=57 y=10
57/6=9.5
10*9.5 =95
y=95

The quadrilateral shown is a rhombus. What is m∠4?

A) 28°
B) 32°
C) 58°
D) 90°

Answers

I think it would be 28

In a rhombus, both pairs of opposite angles are congruent

so m<4=32 degrees

so your answer is 32 DEGREES

Find he percent of change from 1250 to 1,755mi

Answers

28.7749% increase because

1250/1755 = .7122
.7122 *100 = 71.22%
100 - 71.22 = 28.7749

If Kiran solves the equation for p, which equation would result?

Answers

Answer:  i have a answer but it is not up there srry

Step-by-step explanation:  

In February, you have a balance of $135 in your bank account. Each month you deposit $45. Write an equation to describe the situation.

Answers

Answer:

135+45x

Step-by-step explanation:

6666666666666666666666666666666

expresa en lenguaje algebraico lo siguiente​

Answers

Answer:

i dont speek Spanish sorry

yoooo can someone help meeee thanks In advance

Answers

Answer:

The slope of F = 5.

Not 100% sure.

Solve the following system of equations. y + 5x = 30 2y = 5x + 15

Answers

Answer: Solve   2y-5x-30  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2y-5x-30  = 0 and calculate its properties

Step-by-step explanation:

Answer:

x = 3, y = 15

Step-by-step explanation:

Given the 2 equations

y + 5x = 30 → (1)

2y = 5x + 15 → (2)

Subtract 5x from both sides in (1)

y = 30 - 5x → (3)

Substitute y = 30 - 5x into (2)

2(30 - 5x) = 5x + 15 ← distribute left side

60 - 10x = 5x + 15 ( subtract 5x from both sides )

60 - 15x = 15 ( subtract 60 from both sides )

- 15x = - 45 ( divide both sides by - 15 )

x = 3

Substitute x = 3 into (3) for corresponding value of y

y = 30 - 5(3) = 30 - 15 = 15

Thus solution is x = 3, y = 15

1 11. What is the constant of proportionality? y = 8x​

Answers

Answer:

-8

Step-by-step explanation:

lere

the answer to this is 8

Look at the table


What is the ratio of cows to horses?

pwease help me ​

Answers

Answer:

5:8 is the ratio of cows to horses.

1 What is the nature of the roots of the quadratic equation if the value of its discrimman
is zero?
The roots are not real
o the roots are rational and not equal
b. The roots are irrational and not equal d the roots are rational and equal
2. Whal is the ans of symmetry of the parabola y​

Answers

Answer:

If d is zero, both roots are rational and equal.

Step-by-step explanation:

Quadratic Equations

The standard representation of a quadratic function is:

[tex]f(x)=ax^2+bx+c[/tex]

where a,b, and c are constants.

Solving with the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

The discriminant is defined as:

[tex]d=b^2-4ac[/tex]

The sign of the discriminant defines the nature of the roots of the quadratic equation as follows:

If d is positive, both roots are real and differentIf d is negative, both roots are imaginary and conjugateIf d is zero, both roots are rational and equal.

Tony wants to build a fence around his rectangular garden that has
dimensions 20 ft by 35 ft. His fence posts need to be placed 5 ft apart.
How many posts will Tony need to buy?
posts

Answers

Answer:

22

Step-by-step explanation:

The side of the rectangle that is 20 feet divide it by 5

[tex]\dfrac{20}{5}=4[/tex]

Now we add one to this as the fence post each required in each 5 feet section.

The same is the case for the opposite side.

So, the number of fence posts for the 20 feet sides is [tex]5+5=10[/tex]

Now for the 35 feet side

[tex]\dfrac{35}{5}=7[/tex]

Remove 1 fence post from the ends as that fence post will be covered by the ones on the 20 feet side.

So, new posts on the 35 ft side is 6.

So, the number of fence posts for the 20 feet sides is [tex]6+6=12[/tex]

Total number of posts is [tex]10+12=22[/tex]

Identify the axis of symmetry of the parabola.

Answers

The axis of symmetry of a parabola is a line about which the parabola is symmetrical. When the parabola is vertical, the line of symmetry is vertical. When a quadratic function is graphed in the coordinate plane, the resulting parabola and corresponding axis of symmetry are vertical.

Answer:

AOS: x = -1

Vertex: (-1, -2)

Step-by-step explanation:

Indentify the turning point of the graph with is x = -1.

You can make groups of 3, 4, or 9 pencils with none left over. What is smallest number of pencils you must have to make these groups?

Answers

Answer:

=36

Step-by-step explanation:

Step-by-step explanation:

for this we has to take the LCM of 3,4 and 9 to find the least common factor in between these three numbers.....

so we have to multiply 3×3×4

=36

so if we divide 36 by 3 ,4 OR 9

we will not find any remainder

What do I put in those blank spaces? Been doing this for hours

Answers

Answer: okay so this is what I think is the answer I used a calculate so

Step-by-step explanation:

$12.05

$24.08

$36.12

$48.16

$60.20

Step-by-step explanation:

1 hour        2 hours         3 hours        4 hours          5 hours  

$12.04       $24.08          $36.12         $48.16            $60.20

2y + 4 = x + 2
Plz help solve for x in terms of y

Answers

Answer:

x=2y+2

Step-by-step explanation:

Answer:

2y + 2 = x

Step-by-step explanation:

Treat is like a normal equation and solve with inverse operations:

2y + 4 = x + 2

    -2         -2

2y + 2 = x

2x+3=17 and x =7



It’s for algebra class please help my teacher is really strict but okay please thank u a lot

Answers

Answer:

The equation is true/ or an identity

Step-by-step explanation:

Plug in 7 for x, you get

2(7)+3=17

14+3=17

17=17

Answer:

14+3=17or(2*7) +3=17basically 17=17

Step-by-step explanation:

2x+3=17 and x =7

Let's Substitute:(Because the variable is x and we have a value for it which is 7)(Bold and underlined is where the variable is in the equation)

Since x is equal to 7 we are going to substitute it in the equation.

So: (2*7) +3=1714+3=17

I think this is the answer since already having the value of x is an answer please let me know if I am wrong or answered incorrectly so I can change my answer or let everyone know its wrong so it can be deleted. I only want to spread truthful information and assistance so let me know how I did by rating the answer, saying thanks or reporting it so I can improve.

Everyone Can Learn and will never stop learning!

Thank you! Hope this helps!

What is the best first step to solve the inequality 5x – 3 ≥ 2?

Answers

Do the Math is Easy man!!!

Answer:

add 3

Step-by-step explanation:

trust me

Find the distance between the two points rounding to the nearest tenth (if necessary). (8,-9) and (2,-7)

Answers

Answer: 6.32 units

Step-by-step explanation: You count the distance and get 6.32 units.

Please help me answer this question 17

Answers

Answer:

∠AEC = 139°

Step-by-step explanation:

EC bisects ∠BED. This means that the line EC cuts the angle in half, so        ∠BEC = 4x + 1

Other Questions
Someequationshave the formy=kxy=kx, wherekkis a number.WhichequationCANNOT be written in the formy=kxy=kx? An example of mitosis at work is a leaf...turning yellow.growing.taking in carbon dioxide.performing photosynthesis. K^2+k=0 what does k= Alex prepares goody bags for his guests. He has 30 Minifigures and 24 spinners. How many goody bags can he make if he wants to put the same number of Minifigures in each bag and the same number of spinners in each bag with no toys left over? 3 examples of situations where a force is a nuisance have this done correctly for brainliest What causes the change within every twenty four hours from day to night on Earth?A)Earth's rotation on its axisthe tilt of Earth on its axisTarth's revolution around the sunthe distance from Larth to the SunTamashenomena on the top of the sun that appear as dark spots comparPlease answer Please help!What is the inverse of f(x)=x2 - 11 if the domain is x > 0 A customer complains that the network connection on the laptop is intermittent. The customer states that they are using a wireless PC card for network connectivity. The customer believes that the laptop may be too far from the wireless access point; however, he does not know where the wireless access point is located.As a technician, you need to be able to ask questions that will be recorded on a work order. What are 5 closed-ended questions and 5 opened-ended questions that you would ask a customer. 100% A coin is tossed 100 times. Which is the best estimate for the number of times the coin will land heads up? A 10 B. 20 c. 50 D. 80 E. 100 100 points please solve fast! Brainliest please! EasyHeart disease is the number 1 killer in the U.S. Write a letter to the US department of health explaining how heart disease is such a problem in our country What to write about: 1. Why heart disease happens or how it is caused. 2.How many people die every year from heart disease. 3.Come up with a solution to solve the problem how was the impeachment of Andrew Johnson and test of the nation's system of checks and balances? Can i get some help im really confused and im in the test 8(3x-2)-8x=9(2x-6) find x Which sentence contains a dangling modifier?A: Leftover pudding, regardless of the flavor, does not last long in our house.B: Worn out from a hard day at work, Dad took a nap on the couch before we ate dinner.C: With a shrug of disappointment, no more available tickets could be purchased by the fans in line.D: Few people enjoyed the new breakfast cereal, which had an odd smell to it. Describe the role of a pharaoh as well as priests of Mesopotamia more - English Practice Book - 6j: (Sipping his tea). What about your family? 3Rewrite the equation y= 3/7x + 4 in standard form. PLEASE HELP Will give brainliest! Write the equation in y=mx+b form for the line on the graph. PLEASE