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How many solutions does the equation have, x1 + x2 + x3 = 10 , where x1 , x2, and x3 are non-negative integers?

MAVERICK [17]

Non-negative integers are positive integers or zero.

1. When $x_1=0,$ then there are such possible cases for $x_2$ and $x_3:$

$x_2=0,\ x_3=10;$
$x_2=1,\ x_3=9;$
$x_2=2,\ x_3=8;$
$x_2=3,\ x_3=7;$
$x_2=4,\ x_3=6;$
$x_2=5,\ x_3=5;$
$x_2=6,\ x_3=4;$
$x_2=7,\ x_3=3;$
$x_2=8,\ x_3=2;$
$x_2=9,\ x_3=1;$
$x_2=10,\ x_3=0.$

In total 11 solutions for $x_1=0.$

2. For $x_1=1,$ there are such possible cases for $x_2$ and $x_3:$

$x_2=0,\ x_3=9;$
$x_2=1,\ x_3=8;$
$x_2=2,\ x_3=7;$
$x_2=3,\ x_3=6;$
$x_2=4,\ x_3=5;$
$x_2=5,\ x_3=4;$
$x_2=6,\ x_3=3;$
$x_2=7,\ x_3=2;$
$x_2=8,\ x_3=1;$
$x_2=9,\ x_3=0.$

In total 10 solutions for $x_1=1.$

3. This process gives you

for $x_1=2$ - 9 solutions;
for $x_1=3$ - 8 solutions;
for $x_1=4$ - 7 solutions;
for $x_1=5$ - 6 solutions;
for $x_1=6$ - 5 solutions;
for $x_1=7$ - 4 solutions;
for $x_1=8$ - 3 solutions;
for $x_1=9$ - 2 solutions;
for $x_1=10$ - 1 solution.

4. Add all numbers of solutions:

$11+10+9+8+7+6+5+4+3+2+1=66.$

Answer: there are 66 possible solutions (with non-negative integer variables)

8 0

3 years ago

Read 2 more answers

A store prices tapes by raising the wholesale price 50% and adding 25 cents .What must a tape's wholesale price be if the tape s

Andre45 [30]

Let's call the store value as s and the wholesale price as w. A store prices tapes by raising the wholesale price 50%(0.5 in decimals) and adding 25 cents, writing this as an equation, we have

$s(w)=w+0.5w+0.25$

If we invert the equation we're going to find the the wholesale price as a function of the store price.

$\begin{gathered} s=w+0.5w+0.25 \\ s=1.5w+0.25 \\ s-0.25=1.5w \\ w(s)=\frac{s-0.25}{1.5} \end{gathered}$

Now, to find the wholesale price if the sales price is $1.99, we just need to evaluate s = 1.99 on the function we created.

$w(1.99)=\frac{1.99-0.25}{1.5}=1.16$

The wholesale price is $1.16.

5 0

1 year ago

Can you guys and gals help me

professor190 [17]

Answer:

1. B 2. B 3. D 4. A 5. A 6. A 7. B 8. C

Step-by-step explanation:

1. 6 and 8 are right next to each other. Making them 'adjacent angles' as 'adjacent' means 'next to'

2. 2 and 3 are vertically opposite angles, and these angles are equal to each other

3. 3 and 6 are alternate angles. These angles form a 'Z' shape

4. Similar to q2, 1 and 4 are vertically opposite angles

5. Yes they are similar because there are two angles which equal

6. The angles of the big triangle will correlate to the small triangle, therefore x is 40

7. Similar triangles will have the same angles. The top angle of the small triangle is 60, as stated in the big triangle, and 70 is given. The sum of interior angles of a triangle is 180. So, add 60 and 70, then minus from 180

8. Again, same concept as q7, the angles are given to you and you just need to correspond each angle to its respective area, then minus the total of the two given angles from 180

Hope this helped you!!

7 0

3 years ago

A deal is a deal, so here is a good one, let's see who gets it right I had $5.00. My mom gives me $10.00, My dad gave me $30.00.

dimulka [17.4K]

Answer:

$150

Step-by-step explanation:

I feel like this is a trick question

8 0

3 years ago

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Does (0,0) satisfy x+3y>3

PtichkaEL [24]

$\bf x+3y > 3\qquad \qquad (\stackrel{x}{0}~~,~~\stackrel{y}{0})\qquad \qquad 0+3(0) > 3\implies \stackrel{\stackrel{\textit{is this true?}}{\downarrow }}{0>3}\qquad nope!$

4 0

3 years ago