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
Roman55 [17]
3 years ago
11

The sum of the squares of two consecutive positive integers is 41. Find the two

Mathematics
1 answer:
Komok [63]3 years ago
7 0

We have to present the number 41 as the sum of two squares of consecutive positive integers.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

16 + 25 = 41

<h3>Answer: 4 and 5</h3>

Other method:

n, n + 1 - two consecutive positive integers

The equation:

n² + (n + 1)² = 41     <em>use (a + b)² = a² + 2ab + b²</em>

n² + n² + 2(n)(1) + 1² = 41

2n² + 2n + 1 = 41     <em>subtract 41 from both sides</em>

2n² + 2n - 40 = 0     <em>divide both sides by 2</em>

n² + n - 20 = 0

n² + 5n - 4n - 20= 0

n(n + 5) - 4(n + 5) = 0

(n + 5)(n - 4) = 0 ↔ n + 5 = 0 ∨ n - 4 =0

n = -5 < 0 ∨ n = 4 >0

n = 4

n + 1 = 4 + 1 = 5

<h3>Answer: 4 and 5.</h3>
You might be interested in
Which number line represents the solution of 4 - 3x &gt; 13?
Oksanka [162]

Answer:

x

Step-by-step explanation:

Given inequality:

4-3x>13

In order to represent the solution on the number line, we will first solve the given inequality.

We have

4-3x>13

Subtracting both sides by 4.

4-3x-4>13-4

-3x>9

Dividing both sides by -3.

\frac{-3x}{-3} [On dividing both sides by a negative number the sign of the inequality reverses.]

x

So, solution of this inequality will range from -3 to -∞

The number line is represented below.

5 0
3 years ago
Write an equation that is parallel to y = 3x + 5 and passes through the point (-4, -13)
larisa86 [58]
Y equals three x minus one
5 0
3 years ago
Jerry's return trip took 2/5 hour longer. How long did his return trip take?
Vedmedyk [2.9K]
It took him 4 1/5 hours to get home
5 0
3 years ago
Why is everything 1 when raised to the 0th power?
olga_2 [115]
Yeah dang i have no idea. great question tho
3 0
2 years ago
Read 2 more answers
√16+5-√121 can you please help me please
Andreas93 [3]

Step-by-step explanation:

\sqrt{29 }  -  \sqrt{121}  \\  \sqrt{29} - 11 \\  =  - 5.614835193

4 0
3 years ago
Other questions:
  • What is the solution to the system that is created by the equation y=-x+6 and the graph shown below
    12·2 answers
  • The angles of an equilateral triangle are congruent. If x represents the measure of one angle of an equilateral triangle, which
    12·1 answer
  • -25 Points-
    13·1 answer
  • Joseph reads 12 pages in 84 minutes. Assume Joseph reads at a constant speed. Write the number of minutes it takes Joseph to rea
    9·1 answer
  • The dot plot shows the ages of soloists in a orchestra. Answer the following questions below.
    11·2 answers
  • Help me with geometry plzzzzzzzzzzzzzzzzzzzz
    14·2 answers
  • Five Questions FIFTY POINTS...look please don't just get this points I really need help in math rn. tysm for your help really ne
    5·1 answer
  • What is the distance between the points (4, 5) and (4, -3)
    15·2 answers
  • 0.10 x 37.7 explain please
    12·1 answer
  • What is the measure of RCP?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!