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e-lub [12.9K]
4 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]4 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.
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Answer:

x=0

Step-by-step explanation:

1. 0=33.2x  

2. 33.2x=0

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What is the difference written in scientific notation 1.3x10^6 - 6.8 x 10^5
Pavlova-9 [17]

One way to solve this is to revert to integers.

Do this by moving the decimal in 1.3 to the right 6 places (indicated by the positive power value) and then 6.8 move the decimal to the right 5 places (same reason)

Now you have 1,300,000 & 680000. Subtract to get 620,000.

Now convert your product to scientific notation again by moving your decimal to the left until you are left with 6.2 x ? The question mark will be 10 to the number of places you moved the decimal. 10^5

We have 6.2 x 10^5.

It is import to note that when the decimal must be moved to the right for values less than one, the power will be negative.

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3 years ago
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2x+3y=8 9x-3y = 14<br>solve by substitution ​
Olegator [25]

Answer: x=2 and y=4/3

Step-by-step explanation:

To solve by substitution method, you want to solve for one variable, and plug it into the other equation.

Let's solve for y in 2x+3y=8.

2x+3y=8                          [subtract both sides by 2x]

3y=8-2x                           [divide both sides by 3]

y=\frac{8-2x}{3}

Now that we have y, we can plug it into the second equation.

9x-3y=14                         [plug in y]

9x-3(\frac{8-2x}{3} )=14                 [multiply 3 and y to cancel out the 3]

9x-(8-2x)=14                [distribute -1 to 8-2x]

9x-8+2x=14                   [combine like terms]

11x-8=14                          [add both sides by 8]

11x=22                                [divide both sides by 11]

x=2

Since we know the value of x, we can substitute it back into any of the 2 equations to find y.

2x+3y=8                           [plug in x=2]

2(2)+3y=8                        [multiply 2 and 2]

4+3y=8                            [subtract both sides by 4]

3y=4                                  [divide both sides by 3]

y=\frac{4}{3}

Our final answer is x=2 and y=4/3.

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