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
Anit [1.1K]
3 years ago
14

How many pairs (a, b), where a and b are positive integers, satisfy the equation a2−b2=105? PLS HELP

Mathematics
1 answer:
Vlad [161]3 years ago
6 0

Answer:

  4

Step-by-step explanation:

The left side of the equation can be factored as the difference of squares:

  (a -b)(a +b) = 105

The right side of the equation can be factored to 4 different pairs of factors:

  105 = 1·105 = 3·35 = 5·21 = 7·15

For each of the factor pairs, we can match factors to get, for example, ...

  a -b = 1

  a +b = 105

The solution to this is a = (105 +1)/2 = 53, b = (105 -1)/2 = 52. Thus, we have ...

  (a, b) = (53, 52)

For the other factor pairs, the solutions are ...

  (a, b) = (19, 16), (13, 8), (11, 4)

There are a total of 4 positive integer solutions.

You might be interested in
You order two tacos and a salad. the salad costs 2.50.you pay 8% sales tax and leave a $3 tip. you pay a total of 13.80 how much
riadik2000 [5.3K]
Given:Price of one taco = x; price of 2 tacos = 2xPrice of salad = $2.50Sales tax = 8% of the combined price of two tacos and a salad, namely .08(2x + 2.50)Tip = constant fee = $3.00Total bill = $13.80 Therefore the equation becomes
2x + 2.50 + .08(2x + 2.50) + 3 = 13.80 Solutions: 2x + 2.50 + .16x + .20 + 3 = 13.80 (using the distributive property to multiply 2x and 2.5 by .08).2.16x + 2.70 + 3 = 13.80 (combining like terms)2.16x + 5.70 = 13.80 (combining like terms)2.16x + 5.70 = 13.80 - 5.70 (subtraction property of equality)2.16x = 8.10x = 8.10/2.16 = 3.75 (division property of equality)
The cost of a single taco is $3.75
3 0
3 years ago
Can someone help me learn to solve this?
kondaur [170]

Answer:

x = 110°

Step-by-step explanation:

Given that AB = AD then Δ ABD is isosceles and the base angles are congruent, that is

∠ ABD = ∠ ADB = 35°

The sum of the 3 angles in the triangle = 180°, that is

x + 35° + 35° = 180°

x + 70° = 180° ( subtract 70° from both sides )

x = 110°

5 0
3 years ago
What's rotational symmetry?<br> Can u give a full on explanation?<br> PLS
prohojiy [21]
There is rotational symmetry if there is a center around the object that is turned or rotated a certain amount of degrees and the shape isn't changed.
4 0
3 years ago
What is an equation of the line that passes through the points (4,-2) and (8,3)?
gladu [14]

the other is the same as the other o li and the other o li and the other o li and the other o li and the other o li and has been the best selling game in my history for a while and it is not the best time for me the whole time I was a new York fan who was so excited to see my new album in my first impres and the next episode I had to get out yet and still haven't had to do anything for a long

5 0
3 years ago
PLEASE ANSWER QUICKLY AND CORRECTLY!!! WILL GIVE BRAINLIEST!!!!
bazaltina [42]

Answer:

B. x^2 + 14x + 45.

Step-by-step explanation:

Length = area / width so we do a

Long division:

x - 3) x3 + 11x2 + 3x − 135(x^2 + 14x + 45 <------ Quotient.

        x3 - 3x2

               14x^2 + 3x

               14x^2 - 42x

                            45x - 135

                            45x - 135.

                            .................

5 0
2 years ago
Read 2 more answers
Other questions:
  • A coin is tossed 6 times. what is the probability that the number of heads obtained will be 2? express your answer as a fraction
    10·1 answer
  • Patricia is filling a plastic pool with water using a bucket . The plastic pool holds 4 1/2 gallons of water. Each bucket holds
    9·1 answer
  • The swimsuit is on sale for 25% off its original price. If the original price was $58. What is the sale price?
    7·1 answer
  • Kaleb brougt 4.35 pounds of bananas , 3.89 pounds of oranges ,and 2.13 pounds of avocados .what is the total weight fruit kaleb
    11·2 answers
  • Turn into a decimal 10/10 5/10​
    7·1 answer
  • What is the formula for finding the initial value?
    12·1 answer
  • Why is it important to reconcile your checkbook?
    11·2 answers
  • HELP PLSS WHEHHEHEHE PLSSSSS
    13·1 answer
  • Explain answer <br> GIVING BRAINIEST
    9·2 answers
  • I’ll give you the BRAINLYEST answer if you can help me on this question!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!