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
mina [271]
3 years ago
9

2. Suppose (220)_b and (251)_b are the squares of consecutive integers. Determine b.

Mathematics
1 answer:
Andrei [34K]3 years ago
3 0

Let x and x+1 be these consecutive integers. For some base b, we can write

(x_{10})^2=220_b=2b^2+2b

((x+1)_{10})^2=251_b=2b^2+5b+1

If

x^2=2b^2+2b

then

x^2+1=2b^2+2b+1

Now,

x^2+2x+1=2b^2+5b+1

2x+2b^2+2b+1=2b^2+5b+1

\implies2x=3b

Squaring both sides gives

4x^2=9b^2

and so

4(2b^2+2b)=9b^2

\implies8b^2+8b=9b^2

\implies b^2-8b=0\implies\boxed{b=8}

(because the base has to be non-zero)

You might be interested in
Dillon has 4 blue marbles and 3 times as many red marbles.Max has 8 times as many red marbles as Dillon.How much red marbles do
SCORPION-xisa [38]
Dillion has 4 blue marbles and 12 red marbles

And max has 96 red marbles
5 0
3 years ago
The tree diagram represents an
Leviafan [203]

Answer:

0.35

Step-by-step explanation:

.5x.7

6 0
3 years ago
Y = f(x) = 16x Find f(x) when x = 1/2​
Alina [70]

Answer:

The answer depends on what the problem really is.

f(1/2) = 8

or

f(1/2) = 4

See below.

Step-by-step explanation:

This is the problem as it was posted:

y = f(x) = 16x

Let x = 1/2

y = f(1/2) = 16(1/2) = 8

Perhaps the problem is this:

y = f(x) = 16^x

If x is an exponent of 16 and not a factor, then the answer is:

y = f(\frac{1}{2}) = 16^\frac{1}{2} = \sqrt{16} = 4

5 0
3 years ago
What two numbers equal 28?
Drupady [299]
It can be a variety of numbers!
10+18 is 28
8 0
3 years ago
Read 2 more answers
Write the number equal to 2 tens 15 ones
kirza4 [7]
2 tens would be 20 plus 15 ones would be 35.
6 0
3 years ago
Read 2 more answers
Other questions:
  • On the blueprints of Adam's office building, the length of his rectangular office space is
    10·2 answers
  • The graph of was shifted 5 units down and 4 units to the left. What is the equation of the resulting graph?
    7·1 answer
  • Which equation can be used to find the measurement of ∠C? To the nearest degree, what is the measurement of ∠A? A) 5sin∠C = 2; 2
    11·2 answers
  • The snowfall data for Resort A are close to symmetric when they are shown in a box plot. The snowfall data for Resort B are not
    10·2 answers
  • A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution
    6·1 answer
  • Sofia makes and sells stuffed toys. She uses special fabric to cover a foam
    13·1 answer
  • The frequency table shows the height, in inches, of 12 basketball players. What fraction of the players are 70 inches or taller?
    8·2 answers
  • Helllp ASAP!!! I will give you a brainlist
    13·2 answers
  • Joan used 5/6 inch of ribbon to make a bow. How many bows can she make with 15 inches of ribbon? *
    11·2 answers
  • Can anyone please help me with this?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!