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
Convert .2 to a fraction
shepuryov [24]

.2 converted to a fraction would be 1/5

3 0
3 years ago
Read 2 more answers
2 women and 7 girls can do a peice of work in 4 days.4 women and 4 girls can do the same work in 3 days. How long would it take
svetlana [45]

Answer:

x: work a woman can do in 1 day

y: work a girl can do in 1  day

Then

2x + 7y =1/4

4x + 4y =1/3

4x + 14y =2/4 (1)

4x + 4y  =1/3 (2)

=> Let (1) - (2), 10y =2/4-1/3 <=>10y = 1/6 <=> y = 1/(6x10) = 1/60 (work)

=> From (2),4x = 1/3 - 4x1/60 => 4x = 16/60 => x = 4/60 (work)

=> 1 day, a woman and a girl can do: 1/60+4/60 = 5/60 =1/12 (work)

Then, the day required for a woman and a girl to complete work: 12 days

3 0
3 years ago
Jacky read at the rate of 15 pages per hour. Johnny read at the rate of 1/3 of a pages per minute. Who was reading faster? By ho
o-na [289]
We can compare by converting Johnny's reading time into the same unit of Jacky's, hours.

There are 60 minutes in an hour, so use this:

\frac{1}{3} *  \frac{60}{1} = 20

15 < 20, so Johnny read faster. This is 5 pages faster per hour than Jacky.
3 0
3 years ago
Mr. Barnett’s test is normally distributed with a mean of 65 with a standard deviation of five points what is the probability th
uranmaximum [27]

Answer: 2.5%

Step-by-step explanation:

Mean score = 65

Standard deviation = 5

Score (x) = >75

Z-score = [(score - mean) ÷ standard deviation]

Z - score = [(75 - 65) ÷ 5]

Z - score = 10 ÷ 5 = 2

P(score higher than 75) = 100 - 95 = 5/2 = 2.5%

4 0
2 years ago
pascal wanted the area of the door to be 54 square feet and the width still to be 2/3 the length. what would the dimensions of t
dlinn [17]
The floor wood be 81 dimensions.
8 0
2 years ago
Read 2 more answers
Other questions:
  • Which equation represents the graphed function?
    14·1 answer
  • 0.52 in the simplest form .
    14·2 answers
  • Angelo cuts a piece of wood for a project. The first cut is shown and can be represented by the equation y - 5x-1. The second cu
    10·1 answer
  • You are finding the product of two square roots. Each radicand is the same variable raised to an odd power. Explain why you woul
    15·1 answer
  • What is the square root of 12?
    6·2 answers
  • Ben is paid £9.60 per hour.
    10·2 answers
  • Waht is 2t2 math fir math clas
    8·2 answers
  • Which expression is equivalent to 2x^2 +7x+4
    7·2 answers
  • Write 224% as a fraction or mixed number in the simplest form.
    15·2 answers
  • A skydiver accelerates downward at 8m/s^2 during the first second. Her weight is -540 N. The net force on the skydiver is -290 N
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!