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Zarrin [17]
2 years ago
11

AE is an angle bisector of BAC if the measure of BAE = x + 30 and masure of angle EAC = 3x-10 determine Measure of angle EAC

Mathematics
1 answer:
TEA [102]2 years ago
5 0
The measure of angle EAC is equivalent to 50 degrees.
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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
If 3 boxes weigh 10 pounds, how much do 4 boxes weigh?
Nataly_w [17]

Answer:

About 13.32 Pounds

Step-by-step explanation:

First. take the total weight of the three boxes and divide it by the number of boxes.

10/3 = 3.33 and so on

Now we know each box ways 3.33 pounds.

Now multiply 4 boxes by 3.33 pounds.

4 x 3.33 = 13.32

So the answer should be about 13.32 pounds.

8 0
2 years ago
Read 2 more answers
A cash register contains $10 bills and $20 bills with a total value of $520. If there are 32 bills total, then how many of each
ohaa [14]

12 is the number of $10 bills

20 is the number of $20 bills

<u><em>Step-by-step explanation:</em></u>

<u><em /></u>

Hello,

<u>Let's note</u>

a    the number of $10 bills

b    the number of $20 bills

The total value is $520 so we can write the first equation (1)

    \boxed{\sf 10a \ + \ 20b \ = \ 520 }

We know that there are 32 bills in total so we can write the second equation (2)

    \boxed{\sf a \ + \ b \ = \ 32 }

(1) - 10*(2) gives

10a + 20b - 10(a+b) = 520 - 320 = 200

10a + 20b - 10a - 10b = 10b = 200

So b = 200/10=20

and then from (2) a = 32 - 20 = 12

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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At the beginning of the year there were 25 students in our
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The answer is a 12% increase. 
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