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
zaharov [31]
3 years ago
11

How many solutions does the equation x_1 +x_2+x_3+x_4+x_5=21 have where x_1, x_2, x_3, x_4, and x_5 are nonnegative integers and

x_1 >= 1?
Mathematics
1 answer:
omeli [17]3 years ago
4 0

Step-by-step explanation:

x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 21\\     (given)

Let us consider :

x_{1} = t_{1} + 1

x_{2} = t_{2}

x_{3} = t_{3}

x_{4}  = t_{4}

x_{5} = t_{5}

Now, by substituting the above considerations in the above equation, we get:

t_{1} + 1 + t_{2} + t_{3} + t_{4} + t_{5} = 21\\

t_{1}  + t_{2} + t_{3} + t_{4} + t_{5} = 20\\

where,

t_{i} \geq 1

then it follows

n = 20

r = 4

then no. of solutions for the eqn = _{r}^{n + r}\textrm{C}

                                                      = _{4}^{24}\textrm{C}

                                                      = 10626

Answer :

no. of solutions for the eqn 10626

You might be interested in
A card is drawn from a standard 52-card deck. What is the probability that the card is a red 8, given that the card is an 8?
crimeas [40]
<span>probability that the card is a red 8
=
2 out of 52 or 1 out of 26

hope it helps</span>
8 0
3 years ago
Read 2 more answers
Use polynomial division to completely factor y=x^3+3x^2-13x-15 by x+5
Salsk061 [2.6K]

Answer:

(x - 3)(x + 1)(x + 5)

Step-by-step explanation:

I'd use synthetic division instead.  If we were to find the roots of the given polynomial, we could from them write the factors as well.

The divisor x + 5 corresponds to root x = -5.  Setting up synthetic div.,

-5   )   1    3    -13    -15

               -5     10    +15

      -----------------------------

           1   -2     -3      0

Since the remainder is 0, we know that -5 is a root and (x + 5) is a factor.  Moreover, we know that the coefficients of the quotient are 1, -2 and -3.

1x² - 2x - 3 can be factored:  the factors are (x - 3) and (x + 1).

So the end result for this problem is (x - 3)(x + 1)(x + 5).

7 0
2 years ago
The larger of two numbers is 7 times the smaller number. Three times the larger number is 7 more than 4 times the smaller number
Juliette [100K]

Let the smaller number be x.

Given, the larger number is 7 times the smaller number.

So, the larger number = 7x.

Given, 3 times the larger number is 7 more than 4 times the smaller number.

So we can write the equation as,

3(7x) = 4(x)+7

3(7x) = 4x+7

21x = 4x+7

Now we have to move 4x to the left side by subtracting 4x from both sides.

21x-4x = 4x-4x+7

21x-4x = 7

17x = 7

To get x, we will divide both sides by 17. We will get,

\frac{17x}{17} = \frac{7}{17}

x = \frac{7}{17}

So the smaller number = \frac{7}{17}

The larger number = 7(\frac{7}{17} ) = \frac{49}{17}

So we have got the required numbers.

Smaller number = \frac{7}{17} and larger number = \frac{49}{17}.

4 0
3 years ago
If there are 300 seventh graders, and 80% passed the benchmark, how many passed the benchmark
notsponge [240]

Answer:

240 seventh graders passed

Step-by-step explanation:

300 x 0.8 = 240

7 0
2 years ago
Help plsss I’m a little confused<br> We started this today :/
belka [17]
We can’t see the question
3 0
3 years ago
Read 2 more answers
Other questions:
  • Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
    5·2 answers
  • Please I need help . I will brainlist
    6·1 answer
  • Amy and Mary are playing a board game that uses game money if $5 and $10. At the end of the game, Amy has n bills worth $5 each
    7·1 answer
  • I need to know what is the chance the driver still got in an accident
    13·1 answer
  • Write the equation of the line with a slope of 2 that passes through the points -2,-7 and 5,7
    5·1 answer
  • Name the property of real numbers illustrated by the equation.<br><br> -3(x+4)=-3x-12
    10·1 answer
  • The equation for the circle below is x^2+y^2=64 what is the length of the circle’s radius
    14·1 answer
  • Suppose one worker can assemble two machines parts and 30 minutes a customer building a new factory needs 832 parts they want th
    12·1 answer
  • Write all perfect squares between 26 and 125​
    15·1 answer
  • A circle is centered at M(0,0)M(0,0)M, left parenthesis, 0, comma, 0, right parenthesis. The point B(-4,\sqrt{5})B(−4, 5)B, left
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!