1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
e-lub [12.9K]
3 years ago
12

One positive integer is 1 less than twice another. The sum of their squares is 106. Find the integers.

Mathematics
1 answer:
neonofarm [45]3 years ago
8 0
They give us 2 pieces to the puzzle.  Both are positive numbers...x and y.
1.) 1 number is 1 less than twice another number. (x = 2y -1)...and
2.) the sum of their squares is 106.  (x^2 + y^2 = 106).

 substitute the value for x into the second equation.

(2y-1)^2 + y^2 = 106
(2y-1) (2y-1) + y^2 = 106  (use distributive property)
4y^2 - 2y - 2y + 1 + y^2 = 106  (subtract 106 from both sides)
4y^2 - 2y - 2y + 1 + y^2 - 106 = 106 - 106 (combine like terms)
5y^2 - 4y - 105 = 0  (factor)
(y-5) (5y-21) = 0  (set to 0)
y - 5 = 0
y = 5 

substitute the 5 into the equation for y   (x = 2(5) - 1)
           x = 9   if we square 9, we get 81.
subtracted from 106 we have 25...the square root of 25 is 5.

our answers are 5 and 9.
You might be interested in
What is the inverse of the function f(x) = x – 12?
igor_vitrenko [27]
F (x)= x+12 is the inverse of the function
7 0
3 years ago
If Rick buys a remote control car for $29.00, what is his selling price?
Ivahew [28]

Answer:

31

Step-by-step explanation:

31

4 0
3 years ago
9782 divided by 67 step by step Long division
Ipatiy [6.2K]
Here you go . 146 is the answer with the work shown.

8 0
3 years ago
VW | UX. Find UY 20 39 X 26 w​
Lorico [155]

Answer:

39?

Step-by-step explanation:

Because the distance between U and Y is 39.

(I'm sorry if I was wrong)

7 0
2 years ago
Which is an example of a statistical question?
Flauer [41]

Answer:

(A) Question 1

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP!!!<br><br><br><img src="https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7Bx-6%7D%20%3D%20%5Cfrac%7B3%7D%7Bx-10%7D" id="TexFor
    10·2 answers
  • Two questions for 30 points.
    9·1 answer
  • I need help on number 6
    5·1 answer
  • Solve for angle S ? Please help
    15·2 answers
  • If you guys know answer pls
    13·1 answer
  • Find the sale price.<br> Original price: $50<br><br> Discount: 15%<br><br> Sale price: $
    12·2 answers
  • ANSWER QUICK GIVING BRAINIEST!
    11·1 answer
  • 9.) x2 - 6x + 25 = 0 <br> Using the Quadratic Formula
    7·1 answer
  • Acceleration of a runner who goes from 1.4 m/s to 2.2 m/s in 4 s
    13·1 answer
  • Rewrite 3^-4 without negative exponents
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!