Find all triples of natural numbers (a, b, c) satisfying the system of equations
Answers
9514 1404 393
Answer:
(±7, ±1, ±4)(±13, ±11, ±16)Step-by-step explanation:
Solution of the system by the usual means yields the parametric equations ...
(a², b², c²) = (41 +t, t -7, 2t)
Since we want t-7 to be a perfect square, we can let ...
t -7 = n²
t = n² +7
Then the solutions are ...
(a, b, c) = (±√(n²+48), n, ±√(2(n² +7)))
The only integer solutions are for n=±1 and n=±11. Then the 16 possible triples are ...
(±7, ±1, ±4) and (±13, ±11, ±16) . . . where the signs can have any combination
Related Questions
Find the Perimeter of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
Answers
Adjoa’s gross salary for last month was Ghc4,687.24. If Ghc421.78 was deducted from Adjoa’s salary pay, how much take-home pay did Adjoa earn this past month?
Answers
Adjoa's got 4265.46 Ghc as his take home pay for the past month.
The question gave us his gross salary, which means everything he earned. At the same time, giving us a particular number as deduction. To calculate the net salary, all we have to do is to subtract the deduction from the gross salary, And thus;
4687.24 - 421.78 = 4265.46 Ghc
to learn more, see here https://brainly.com/question/16688602
What are the terms in the expression 4 + 9v + 6w? A. v and w b. 9 and 6 c. 4, 9v, and 6w d. 4, 9, and 6
Answers
Answer:
How do you want me to solve?
Answer:
A po answer jan (20 daw characteristics bago masend sagot)
how would you work out 0.5 is 1/100 of
Answers
0.5% of 100
is equivalent to multiplying them:
0.5% × 100 = 0.5
Given that cos (x) = k
what does cos (2x) = ?
Thanks in advance :)
Answers
Answer:
(2x) = 2k
Step-by-step explanation:
If x = k, then 1x=1k, then 2x=2k
Answer:
2k² - 1
Step-by-step explanation:
cos x =k
cos 2x = 2 cos ² x - 1
= 2k² - 1
Help marking brainliest for who is right
Answers
Answer:
-4,-3 2/3, -1 2/3, -1/2, 2/3, 5 1/2
Step-by-step explanation:
Need help, look at picture
Answers
URGENT HELP I NEED THE ANSWERS TO THIS WORKSHEET
Answers
Answer:
As follows,
Step-by-step explanation:
The sum of the angles of any triangle is 180.
∠U=69
∠D=42
∠E=35
∠F=35
∠G=55
∠H=45
∠I=45
∠J=15
∠M=120
∠K=15
∠L=75
∠Q=55
∠R=55
∠S=42
∠T=42
∠P=21
∠O=69
∠N=21
∠A=60
∠B=60
∠C=60
The cost to mail a first-class letter used to be $0.40 the first ounce. Each additional ounce costs $0.20. Fractions of an ounce are
rounded up to the next whole ounce. How much would it cost to mail a letter that weighs 3.7 ounces?
• $0.60
O $1.00
O $0.90
O $1.20
Answers
Pls help I’ll brainlest
Answers
Answer:
Here are the unscramabled words
Step-by-step explanation:
1. Observation
2. Hypothesis
3. Results
Thank you! Please Brainliest! :)
Can somebody help me as soon as possible?
Answers
Answer:
2400
Step-by-step explanation:
y= -300x + 2400
-300 equals the slope
2400 is the y-intercept
Equation: y = mx + b
Parallelogram BCDE with vertices B(2, -3), C(6,-4), D(7.-6), and E(3.-5):
a) 270° counterclockwise rotation about the point (1,-2)
b) translation along the vector (0,8)
Answers
so (x, y) rotates to (y, -x)
Sadly to change the centre we need to translate the centre to the origin, rotate and the translate back.
In this case that means adding -1, 2 to x,y respectively, rotating, adding 1, -2 to x,y respectively
B(2, 3) translates to (1, 5) which rotates to (5, -1) and translates back to B’(6, -3)
C(6, -4) translates to (5, -2) which rotates to (-2, -5) and translates back to C’(-1, -7)
D(7, -6) translates to (6, -4) which rotates to (-4, -6) and translates back to (-3, -8)
E(3, -5) translates to (2, -3) which rotates to (-3, -2) and translates back to (-2, -4)
The translation is much easier simply moving each point 8 to the right
B’(2, 11), C’(6, 4), D’(7, 2) and E’(3, 3)
Using the grid will everything clear!
a) After 270° counterclockwise rotation about the point (1,-2) the coordinates are B'(-1, -1), C'(-2, -5), D'(-4, -6) and E'(-3, -2).
b) After translation along the vector (0,8) are B''(2, 5), C''(6, 4), D''(7, 2) and E''(3, 3).
Given that, parallelogram BCDE with vertices B(2, -3), C(6, -4), D(7, -6), and E(3, -5).
When rotating a point 270 degrees counterclockwise about the origin our point A(x, y) becomes A'(y,-x). This means, we switch x and y and make x negative.
a) 270° counterclockwise rotation about the point (1,-2)
So, the new coordinates are
B(2, -3)→(1, -1)
C(6, -4)→(5, -2)
D(7, -6)→(6, -4)
E(3, -5)→(2, -3)
After 270° counterclockwise rotation, we get coordinates as
B(1, -1)→B'(-1, -1)
C(5, -2)→C'(-2, -5)
D(6, -4)→D'(-4, -6)
E(2, -3)→E'(-3, -2)
b) Translation along the vector (0,8)
B(2, -3)→B''(2, 5)
C(6, -4)→C''(6, 4)
D(7, -6)→D''(7, 2)
E(3, -5)→E''(3, 3)
Therefore,
a) After 270° counterclockwise rotation about the point (1,-2) the coordinates are B'(-1, -1), C'(-2, -5), D'(-4, -6) and E'(-3, -2).
b) After translation along the vector (0,8) are B''(2, 5), C''(6, 4), D''(7, 2) and E''(3, 3).
To learn more about the rotation of 270° counterclockwise visit:
brainly.com/question/9109065.
#SPJ3
Pls help I’ll brainlest and add extra points
Answers
7-control group- water
8-independent variable- coconut juice
9-dependent variable- green slime
10- homers conclusion would be that neither coconut juice nor water would treat the green slime that had been in his shower.
help me please (I had to write something to ask this question)
Answers
Answer:
-5
Step-by-step explanation:
I think it would be -5 because if Celia had -3, that would take away from Janine, so then it would leave the points at 5. But, it says the team had 0 points all together, so wouldn't it be -5?
maria buys 2 dozen pens at $7.20 a dozen. she then sells the pens at 80c each. calculate her profit
Answers
$7.20•2=$14.40
24 pens • $0.80 =$19.20
$19.20-$14.40=$4.80 profit :)
The prices of a 32-ounce
container of yogurt at three different grocery stores are
$4.49, $3.99, and $4.29, respectively. Find the average
price for the container of yogurt.
Answers
Answer:
9.77 i think
Step-by-step explanation:
add up all prices then subtract by three i think
Answer:
93 is the correct answer
20.99 for a 42 lb-bag of dog food (im pretty sure your supposed to divide the last number to the first number example: 18.5÷11.99)
Answers
Answer:
18.5÷11.99 is correct the answer is most likly option B
what are possible values for a and b in the equation 4^a/4^b=4^-1
Answers
Answer: 11
Step-by-step explanation:The given expression is:
=
=
=
Substituting the value of b=-2 in above expression, we get
=
=
=
Thus, the value of the given expression is -11.
help me asp HELPPPPPPPPP ME
Answers
Answer:
C is the answer
Step-by-step explanation:
Because he have most tresures.
Answer: deep diving dan
Step-by-step explanation: he dived 26 times and found 104 treasure boxes
Question 1 (3 points)
CALCULATOR PERMITTED FOR SUBPART 3
At a bake sale, plates of cookies, p, are sold for $5 each. The amount of money
from the sale of cookies is expressed as dollars, d. Which equation represents the
earnings of the bake sale?
Plates of Cookies (p)
1
2
3
4
Earnings (d)
5
10
15
20
HN
o lol
O a
d = p + 5
Oь
d =P
=
5
Answers
done good job question giy
Your mother drives 60 minutes at a constant speed of 40 miles per hour. She then speeds up, and drives for another 30 minutes at a constant speed of 70 miles per hour. How many miles does your mother travel all together? How long did the trip take?
Answers
Answer: written below
Step-by-step explanation:
1 hour time 40 miles/ hour =1*40=40miles
0.5 *70=0.5*70=35 miles
40+35=75 miles
60 minutes+30 minutes= 90 minutes or 1 1/2hours
Please help me to làm bài
Answers
Answer
Xét f'(x)=0, tìm các giá trị x, lập bảng biến thiên
Đồ thị:
Step-by-step explanation:
The speed of sound in air is 340 m/s. How far , in meters, would a sound of wave travel on 7 seconds?
Answers
Answer:
2 380m
Step-by-step explanation:
very simple just multiply 7×340
6x44
hbgvtfwtydtwftdftwyfdywdwd
Answers
Answer:
264
Step-by-step explanation:
well you could have just used a calculator!
Answer:
Step-by-step explanation:
es 264 como estas
how do you solve -5=4x-8
Answers
Answer:
3.25=x
Step-by-step explanation:
start with -5=4x+8
subtract 8 from each side to get:
-13=4x
divide each side by 4 to get your answer:
-3.25=x-
Answer:
[tex]x = - 3.25[/tex]
Step-by-step explanation:
-5 = 4x + 8
-5 - 8 = 4x + 8 - 8
-5 + (-8) = 4x
-13/4 = 4x/4
Therefore, x = -3.25
-5 + (-8) = 4x
Same Change Change (SCC) rule for integers was applied here.
Colby has a square placemat. The area of the
placemat is 3 square feet
What is the exact perimeter of the placemat?
Use the number pad to enter your answer in the box
The exact perimeter is
ft help please
Answers
Answer:
Step-by-step explanation:
12
5
2
m−
5
4
−
5
3
m
Answers
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
In pic
(Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
Need help with number 10
Answers
Answer:
d
Step-by-step explanation:
the answer is d, tan = (cateto opuesto / cateto adyascente)
Tan is opposite/adjacent
Tan35 = .7002
.7002 = opposite/60
.7002*60=42.012
Opposite = width of river = 42.0
What is the denotation of the word "stealing” in this excerpt?
being deceptive
committing a crime
keeping a secret
taking over
Answers
The word stealing in the given excerpt denotes; taking over
How to find the meaning of the excerpt?
This question is gotten from the excerpt from the Narrative of the Life of Frederick Douglass.
Now, from the given narrative, we see that her frame already racked with the pains of old age, and complete helplessness fast stealing over her once active limbs.
Thus, this means that the word stealing denotes that taking over her active limbs.
Read more about excerpt at; https://brainly.com/question/21400963
#SPJ1
Answer:
Taking over.
Step-by-step explanation:
We know that February has either 28 or 29 days, but there is a year in the future, February will have 30 days
What exactly is this year?
Answers
Answer:
The year 2020 is a leap year, which means February will have 29 days rather than 28, and the overall number of days will be 366 rather than 365. This was also the case in 2016, and the year 2024 will be a leap year once more.
Step-by-step explanation: