Find with proof all real number solutions (x, y) of x^4 −4x^3y +
6x^2y^2 + x^2 −4xy^3 + 2xy −4x +
y^4 + y^2 −4y + 4 = 0.
Answers
The given equation is a quartic equation in two variables, x and y. The solutions to these quadratic equations can be obtained by applying the quadratic formula. By solving these equations, we find the real number solutions for (x, y) to be (1, 1) and (1, -1).
To solve the equation x^4 - 4x^3y + 6x^2y^2 + x^2 - 4xy^3 + 2xy - 4x + y^4 + y^2 - 4y + 4 = 0, we can factorize it as (x^2 + y^2 - 2x - 2y + 2)(x^2 - 4xy + y^2 - 2x + 2y + 2) = 0.
From the first quadratic factor, we get (x - 1)^2 + (y - 1)^2 = 0, which implies x = 1 and y = 1.
From the second quadratic factor, we get (x - 1)^2 + (y + 1)^2 = 0, which implies x = 1 and y = -1.
Therefore, the real number solutions for (x, y) are (1, 1) and (1, -1), which satisfy the given equation.
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Related Questions
3 friends ordered 2 pizzas of 6 slices each and ate equal amounts, how many slices did each person eat?
A 1
B 2
C 3
D 4
Answers
Answer:
Option D, 4
Step-by-step explanation:
2 pizzas x 6 slices per pizza = 12 slices of pizza
12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend
Option D, 4, is your answer
Rectangles ABCD and DEFG are congruent
AB=7cm
AD=17cm
Work out the length of CE
Answers
The length of CE is 7cm
How to determine the lengthTo determine the length, we need to consider the properties of a rectangle, we have;
It is a quadrilateralOpposite sides are known to be parallel and congruent to each otherThe interior angles are equal to 90 degreesDiagonals bisect each other at right anglesThe two diagonals have the same lengthRectangle having side lengths of x and y has the perimeter as 2x+2y unitsA rectangle with side lengths x and y has its area as: xy sin 90 = xy square unitsA diagonal of a rectangle is said to be the diameter of its circumcircleFrom the information given, we have that;
AB = 7cm
AD = 17cm
Then, line CE = line AB
But line AB = 7cm
CE = 7cm
Hence, the length is 7cm
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AABC and ADEF are similar. The lengths of AB and AC are 5 units each, and the length of BC is 6 units.
If the length of EF is 3 units, then the length of DE is
units. If m/ABC is 53°, then mZEDF is
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Answers
The length of DE is 3 units, and the measure of ∠ZEDF is 53°.
Let's analyze the given information and use the properties of similar triangles to find the length of DE and the measure of ∠ZEDF.
First, since triangles AABC and ADEF are similar, we know that their corresponding sides are proportional.
Using the given lengths, we have:
AB/DE = AC/EF = BC/DF
Substituting the known values:
5/DE = 5/3 = 6/DF
Cross-multiplying, we get:
5 \(\times\) 3 = 5 \(\times\) DE
15 = 5 \(\times\) DE
Dividing both sides by 5, we find:
DE = 15/5 = 3 units
Therefore, the length of DE is 3 units.
Now, let's find the measure of ∠ZEDF.
Since ∠ABC and ∠DEF are corresponding angles in similar triangles, they have the same measure.
Given that m/ABC is 53°, we can conclude that m/DEF is also 53°.
Hence, the measure of ∠ZEDF is 53°.
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Find the length of the segment JK in the parallelogram below.
Answers
Answer:
24
Step-by-step explanation:
knowing a parallelogram, JK = ML
so,
14 + 2x = 5x – 1
2x – 5x = –14 –1
–3x = –15
3x = 15
x = 5
substitute x=5 into 14 + 2x
14 + 2(5) = 24
Does someone mind helping me with this problem? Thank you!
Answers
Answer:
x=71; y=19
Step-by-step explanation:
x+y = 90 so x =90-y = 14+3y
so 90=14+4y
90-14 = 4y
76=4y
y=19
x=71
Answer:
x = 71
y = 19
Step-by-step explanation:
I solved by graphing and got (71,19) as included in the image. A more mathematical way to solve is by substitution. You try to find x with one of the equations, plug in x and then solve for y.
x + y = 90
x = 90 - y
90 - y = 14 + 3y
90 - y + y= 14 + 3y + y
90 = 14 + 4y
90 - 14= 14 + 4y - 14
76= 4y
19 = y
x + y = 90
x + (19) = 90
x + 19 - 19= 90- 19
x = 71
42,43,44,44,49,40,39 what is the mode
Answers
Answer:
44
Step-by-step explanation:
I hope it's helpful for youSo the answer will be 44.
The difference between the upper-class limit and lower class limit of a class interval is called *
2 points
A. Frequency
B. Width
C. Grouped data
D. Ungrouped data
Answers
can u help me with my work pls?
Answers
Given:
\(f(x)=2x^2-12x+24\)The above expression can be expressed as,
\(undefined\)A soda company spends $1200 per day on business expenses plus $1.10 per bottle.
They charge $2.50 for each bottle of soda they produce. How many bottles of soda
must the company sell in one day in order to equal its daily costs?
Answers
Answer: Hi
Step-by-step explanation:
Cost Price per bottle : $1.10
Selling price per bottle : $2.50
2.50 - 1.10 = 1.40
$1200=1.40B
B=858
The company must sell 858 Soda´s in order to equal it daily cost.
Hope this help. Be safe
A
shift worker clocks in at 1730 hours and clocks out at 0330 hours.
How long was the shift?
Answers
To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.
In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.
To calculate the duration of the shift, you can perform the following steps:
1. Calculate the duration until midnight (0000 hours) on the same day:
- The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).
2. Calculate the duration from midnight (0000 hours) to the clock-out time:
- The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).
3. Add the durations from step 1 and step 2 to find the total duration of the shift:
- 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.
Therefore, the duration of the shift was 10 hours.
What is the length of AB?
Round to one decimal place.
Answers
Answer:
5.4
Step-by-step explanation:
"The 'Angle Bisector' Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle."
thus,
DB/AB = DC/AC
2.8/AB = 3/5.8
multiply both sides by AB to make it a numerator
2.8 = 3*AB/5.8
multiply both sides by 5.8/3 to isolate AB
2.8 * 5.8/3 = AB = 5.413 ≈ 5.4
Therefore , the solution of the given problem of triangle comes out to be
AB length = 5.4 units.
Defining a triangleIn a plane, any three points can be joined to form triangles, which have three sides and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.
Here,
According to the "Angle Bisector Theorem," a triangle's opposing side will be divided into two segments that are proportional to the other two sides.
thus,
DC/AC = DB/AB.
2.8/AB = 3/5.8
By multiplying both sides by AB, the numerator is created.
2.8 = 3*AB/5.8
To distinguish AB, multiply both sides by 5.8/3.
2.8 * 5.8/3 = AB = 5.413 ≈ 5.4
Therefore , the solution of the given problem of triangle comes out to be
AB length = 5.4 units.
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A radioactive compound with mass 320 grams decays at a rate of 27% per hour. Which equation represents how many grams of the compound will remain after 7 hours?
Answers
Answer:
320 grams ÷ 27% = 8.3 grams
Step-by-step explanation:
mark brainliest plss
What is the height of the trapezoid?
O 3 units
O 5 units
O 10 units
O 12 units
Answers
Answer:
5 units
Step-by-step explanation:
Height of a trapezoid= 2 × Area/(a+b)
=2 × 40/(6+10)
=2 × 40/16
=5 units
Hope it helps....
Mark me the brainliest....
What is the volume (in cubic units) of a sphere with a radius of 21 units? Assume that =3.14 and round your answer to the nearest hundredth when necessary.
Answers
Answer: \(V=38772.72\ units^3\)
Step-by-step explanation:
Given
radius of sphere \(r=21\ units\)
Volume of sphere can be calculated by this formula
\(V=\frac{4\pi }{3}r^2\)
\(V=\frac{4\pi }{3}\times (21)^3\)
\(V=\frac{4\pi }{3}\times 9261\)
\(V=38772.72\ units^3\)
A ship sails 30km from A on a bearing of 048 degrees and a further 42km on a bearing of 110 degrees to arrive at B. What is the distance and bearing B from A.
Answers
Answer:
The distance from A to B is approximately 67.5 km
The bearing of B from A is approximately 86.89°
Step-by-step explanation:
i) The distances and the bearing of the motion of the ship is given as follows;
The distance the ship sails on a bearing of 048° = 30 km
The distance further the ship sails on a bearing of 110° = 42 km
From the drawing of the sailing of the ship created with Microsoft Visio, we have;
∠C = 48° + 70° = 118°
By cosine rule, we have;
c² = b² + a² - 2·b·a·cos(∠C)
From which we have;
c² = 30² + 48² - 2 × 30 × 48 × cos(118°) ≈ 4,556.07810082
c ≈ √(4,556.07810082) ≈ 67.5
The distance from A to B = c ≈ 67.5 km
ii) By sine rule, we have;
a/sin(A) = b/sin(B) = c/sin(C)
∴ sin(A) = a·sin(C)/c
Substituting the values of the variables gives;
sin(A) ≈ 48·sin(118°)/67.5
∠A ≈ arcsin(48·sin(118°)/67.5) ≈ 38.89°
Therefore, the bearing of B from A ≈ 48 + 38.89 = 86.89°.
What organelle is found only in eukaryotic cells and contains
DNA?
Answers
Hope this helps :P
Alex scored 40 marks out of 60 in a spelling test pet scored 65% in the same test who did better
Answers
Based on the test by result, Alex did better in the test by scoring 66.67%
PercentageAlex = 40 out of 60Percentage scored by Alex = 40/60 × 100
= 0.66666666666666 × 100
= 66.6666666666666
= 66.67%
my Percentage scored by pet = 65%Therefore, Alex did better in the test
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This needs to be turned in tonight and I need help
Answers
Answer:
Constant is 2
Coefficient is either a 12 or -12 The number of terms is 4 I'm pretty sure. Sorry if I'm wrong :)
Step-by-step explanation:
A house worth £80,000 in January 2012 is set to decrease in value by 7% per year.
A more optimistic forecast suggests that the value of the house will increase by 4% per year. According to this forecast, how much will the house be worth in January 2015?
Answers
Answer:
The house would be worth £89989.12 in January 2015.
Step-by-step explanation:
With respect to the optimistic forecast, the value of the house will increase by 4% per year.
For the first year (January 2012 to January 2013),
4% of £80000 = 0.04 x £80000
= £3200
The cost of the house = £80,000 + £3200
= £83200
For the second year (January 2013 to January 2014), we have;
4% of £83200 = 0.04 x £83200
= £3328
The cost of the house = £83200 + £3328
= £86528
For the third year (January 2014 to January 2015), we have;
4% of £86528 = 0.04 x £86528
= £3461.12
The cost of the house = £86528 + £3461.12
= £89989.12
According to the forecast, the house would be worth £89989.12 in January 2015.
Help me with this plz guys ur my only hope
Answers
Pi = 3.14
Diameter (d) = 86 cm
•°• Radius (r) = 86 ÷ 2 = 43 cm (radius is 1/2 of diameter)
Area of the circle = ?
Formula,
\(\pi( {r})^{2} \)
Substitute the value of 'r' & pi in the formula.
\(\pi(43) {}^{2} \\ = 3.14 \times 43 {}^{2} \\ = 3.14 \times 1849 \\ = 5805.86 \: \: cm {}^{2} \)
⎆ The area of the circle is about 5805.86 cm² (approx.)
Please help thanks I’m so confused
Answers
Answer:
64.93=4.73x+22.36
Step-by-step explanation:
64.93 is how much he paid
22.36 is his constant
4.73 is for 1 call
An almond butter jar label says that it has 30% more almond butter for the same price. Brett knows that the jar is usually 10 ounces, and he wants to find out how much more almond butter is in the larger jar.
Answers
Answer:3
Step-by-step explanation: .03 X 10
convert the angle 0=17 pie/18 radians to degrees
Answers
Answer:
it would be 170°
Step-by-step explanation:
( 17 πover 18 ) ⋅ 180 ° over π
17over18 ⋅ 180
then you cancel the common factors
17 ⋅ 10 mulitply those two and end up with
170°
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!
Answers
n = number of sides
6-2(180) = 720 degrees
the answer is 720
which statement about the angles in the diagram must be true?
A. ∠5 and ∠8 are congruent.
B.∠2 and ∠8 are alternate interior angles. C. ∠4 and ∠7 are corresponding angles.
D. ∠1 and ∠5 are alternate exterior angles.
Answers
Answer:
C
Step-by-step explanation:
they r located at the same spot & side of the intersecting line on both parallel lines
Dijdndjfncjfnfnnfjfjdjkakjfbdkhnxjdy business Biden
what is volume of the figure in cubic feet? A. 136 cubic feet B. 6,144 cubic feet C. 9,600 cubic feet D. 11,520 cubic feet
Answers
The box should have inches for its length, width, and height. 2. Divide the result of multiplying the length, breadth, and height by 1,728. In cubic feet, this represents the container's volume.
How do you figure out volume in cubic feet?As such, it is listed here for documents that can simply be destroyed.
1 cubic foot equals a WPS Records Retention box.1 cubic foot equals 1 drawer in a typical filing cabinet.Box of copy paper (10 ream box) equals one cubic foot.5 Reams of Copy Paper =.5 Cubic FeetThe instructions below can be used to calculate a container's cubic foot volume.
Determine the box's inches-long dimensions for width, height, and depth.Divide the result of multiplying the length, breadth, and height by 1,728.In cubic feet, this represents the container's volume.
A case in point
18"L x 11.5"W x 9"H = 1,863 cubic inches
1,863/1,728 equals 1.078 cubic feet.
The aforementioned container has a volume of 1.1 cubic feet (round to the nearest tenth).
The Complete Question.
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compare 3/5 and 5/8 by converting each fraction to a decimal which is larger
Answers
Answer: 5/8
Step-by-step explanation: remember the "/" sign just means divide.
3 divided by 5=0.6, and 5 divided by 8=0.625, so 5/8 is larger
David y Angie tienen dos cartulinas iguales. David corta la suya en 3 trozos iguales y Angie la corta en 7 trozos. Los dos usan 2 de sus trozos para hacer un muñeco. Que fracción de cartulina ha usado David?¿Y Angie?¿Quien ha usado mas cartulina? Alguien me lo dice por fa es que no lo entiendo
Answers
Answer:
(i) David ha empleado \(\frac{2}{3}\) de la cartulina.
(ii) Angie ha empleado \(\frac{2}{7}\) de la cartulina.
(iii) David ha usado más cartulina.
Step-by-step explanation:
El problema indica que David y Angie emplean una cartulina del mismo tamaño cada uno. David corta la suya en 3 pedazos iguales, mientras que Angie obtiene 7 pedazos iguales. Finalmente, cada uno emplea dos de sus pedazos. A continuación, respondemos a las preguntas del enunciado:
(i) ¿Qué fracción de cartulina ha usado David?
La fracción de cartulina empleada por David es igual a los pedazos utilizados divididos por el total de pedazos. Esto es:
\(x = \frac{2}{3}\)
David ha empleado \(\frac{2}{3}\) de la cartulina.
(ii) ¿Qué fracción de cartulina ha usado Angie?
Aplicando el mismo procedimiento del punto anterior, tenemos que:
\(x = \frac{2}{7}\)
Angie ha empleado \(\frac{2}{7}\) de la cartulina.
(iii) ¿Quién ha usado más cartulina?
La persona que ha usado la mayor cantidad de cartulina es aquella que tiene el menor denominador. Por tanto, David ha usado más cartulina.
A gardener made a scale drawing of a lawn with a scale factor of 1:15. The dimensions of his drawing are 6 inches long by 3 inches wide. his partner plans to make another scale drawing of the lawn, but with a scale factor of 1:5. What are the dimensions of his scale drawing?
A. The length is 1 inch and the width is 2 inch
B. The length is 2 inch and the width is 1 inch
C. The length is 9 inch and the width is 18 inch
D. The length is 18 inch and the width is 9 inch
Answers
D. The length is 18 inches and the width is 9 inch
What is a scale factor?
A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.
It is given that the scale factor of the gardener is 1:15.
The dimensions of his drawing are 6 inches long by 3 inches wide.
Therefore the original dimensions are 6*15= 90 inches.
3*15= 45 inches.
The scale of his partner is 1:5.
So, we have to divide the original dimensions by 5.
The dimensions of the scale drawing are 90/5= 18 inches long
45/5=9 inches wide.
Therefore length is 18 inches and the width is 9 inches.
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3x-15=3
what is x in this equation?
Answers
Answer: The answer is 6
Step-by-step explanation: 3x-15=3 Add 15 to both side
3x=18 Divide 3 to both side
3= 3
x=6 The answer