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
Setler79 [48]
3 years ago
10

A, b, c and d are positive integers, such that a+b+ ab = 76, c+d+ cd = 54. Find (a+b+c+d)·a·b·c·d.

Mathematics
1 answer:
lutik1710 [3]3 years ago
6 0

Notice that

(1 + <em>x</em>)(1 + <em>y</em>) = 1 + <em>x</em> + <em>y</em> + <em>x y</em>

So we can add 1 to both sides of both equations, and we use the property above to get

<em>a</em> + <em>b</em> + <em>a b</em> = 76  ==>  (1 + <em>a</em>)(1 + <em>b</em>) = 77

and

<em>c</em> + <em>d</em> + <em>c d</em> = 54  ==>  (1 + <em>c</em>)(1 + <em>d</em>) = 55

Now, 77 = 7*11 and 55 = 5*11, so we get

<em>a</em> + 1 = 7  ==>  <em>a</em> = 6

<em>b</em> + 1 = 11  ==>  <em>b</em> = 10

(or the other way around, since the given relations are symmetric)

and

<em>c</em> + 1 = 5  ==>  <em>c</em> = 4

<em>d</em> + 1 = 11  ==>  <em>d</em> = 10

Now substitute these values into the desired quantity:

(<em>a</em> + <em>b</em> + <em>c</em> + <em>d</em>) <em>a</em> <em>b</em> <em>c</em> <em>d</em> = 72,000

You might be interested in
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. she
Orlov [11]

Answer:

B. H1= b1=0

Step-by-step explanation:

the alternative hypothesis is correct

7 0
3 years ago
I need to find the slope for these lines please help
geniusboy [140]

Answer:

-3/1 for both

Step-by-step explanation:

the slope of a parallel line is the same

pls mark brainliest

8 0
3 years ago
Serafina is solving a number puzzle that involves three integers. Integers, e, f, and g, where e is negative. The product of e a
Alex73 [517]

Answer:

a

Step-by-step explanation:

3 0
3 years ago
|2x-3|=2 please answer this by Wednesday. I have no idea how to solve this. I wasn't paying attention
Sholpan [36]

Answer:

x=2.5

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Michael wrote the system of equations below, but he accidentally left out the coefficient of x in the first equation.
Art [367]

Your answer would have to be 2

6 0
2 years ago
Read 2 more answers
Other questions:
  • Can you help me on number 11 and 13?
    9·1 answer
  • You have 3/5 of an apple pie . you divide the remaining pie into 5 equal pieces. what fraction of the original pie is each slice
    10·1 answer
  • Which setof numbers could all be reasonably rounded to. 33,100​
    6·2 answers
  • Ggfhfsbdhdjhddhdhbdbdgdhbdbdhd
    8·1 answer
  • Margot has 21 1/2 pounds of flour 8 pounds of butter and 18 1/2 ponds of sugar to make shortbread cookies if she makes 12 batche
    14·1 answer
  • What is the answer for (3s-4) (2s-2)​
    6·1 answer
  • HELP I NEED TO FINISH THIS ASAP!!!
    13·2 answers
  • A chapter takes 65 min to read Express 65 as a improper factor of an hour in simplelest form
    8·1 answer
  • The probability of getting broccoli and fish for dinner is:
    12·2 answers
  • What is specific heat of solid lead shots explained process​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!