What are two consecutive numbers whose squares differ by 31

Answers

Answer 1

Answer: so 2 consecutive numbers are number that come right after each other so the numbers could be represented as x and x+1 where x represents an unknown umber

squares are the number times itself so
x time x and (x+1) times (x+1)
so therefor the difference is 31
obviously (x+1) times (x+1) is bigger than x times x so
x times x=(x+1) times (x+1)-31
so you multiply to findn the answer
x times x=x^2
pemdas so multiply
(x+1)(x+1)
use distributive property which si a(b+c)=ab+ac so
(x+1)(x+1)=(x+1)(x)+(x+1)(1)
distribute again
(x+1)(x)=x^2+1x
(x+1)(1)=1x+1
(x+1)(x+1)=x^2+1x+1x+1=x^2+2x+1
so we have
x^2=x^2+2x+1-31
add like terms
x^2=x^2+2x-30
subtract x^2 from both sides
x^2-x^2=x^2-x^2+2x-30
0=0+2x-30
0=2x-30
add 30 to both sides
30=2x
divide both sides by 2
15=x
subsitute
x+1 is second number
15+1=16

the numbers are 15 and 16
their squares are 225 and 256

the numbers are 15 and 16

Related Questions

mr. Hightower recorded the amount of each project that had been completed at the end of the week. the line plot describes the information he record ed. what fraction of the projects were 3/4 complete?
you order two servings of Pancakes and a fruit cup. The cost of the fruit cup is one dollar and $1.50. You leave a 15% tip. Your total bill is $11.50. How much does one serving the pancake cost?
170 is 1/10 of 17 true or false 170 is 1/10 of 17 true or false
Solve the system using any method.y = 3x + 2y = 7x - 10
Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?GIVE U MANY POINTS!!!!!!

The four highest scores at a diving meet were 9.08, 9.1, 9.15, and 9.06 points. Which of 3 of these numbers were the lowest out of all 4 of the numbers?

Answers

From lowest to highest:
9.06, 9.08, 9.1, 9.15
3 lowest numbers are 9.06, 9.08, and 9.1

all you have to do is put them in order from least to greatest
9.06, 9.08, 9.1, 9.15
hope i helped you out in some type of way

Find the LCM of 24,36

Answers

Answer:

LCM of 24, 36 = 72

Step-by-step explanation:

24 = 24, 48, 72, 96

36 = 36, 72, 109

Answer:

The LCM of 24 and 36 = 72

Step-by-step explanation:

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 24:

24, 48, (72), 96, 120

Multiples of 36:

36, (72), 108, 144

Hope this helped!

Todd begins piano practices at 4:15 p.m and ends at 5:50 p.m . How long does he practices

Answers

4:15 to 5:00 is 45 minutes; 5:00 to 5:50 is 50 minutes. 50+45=95 minutes = 1 hour and 35 minutes.

an hour would put todd at 5:15 and then 50-15= 35 so 1 hour and 35 minutes

????????????????????

Answers

The answer is A, because:
The dimentions in cm are 5cm by 3cm, so you make that to scale. The page says that 1cm is equal to 5m, so you multiply both numbers by 5 and you get 25 by 15. If you need clarification, let me know.

The answer is a because to get the length of the sides you do 7-4 which is 3 times five is 15m. To find the base you do 2 times 3 times 5 which is 25m. A) 25m. * 5m.

Can you think of 7 ways to make 7 using arithmetic?