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weqwewe [10]
2 years ago
6

50 POINTS! By using shadows, Tatiana wants to find the height of a building. At a certain time of day, her shadow is 2.4 feet lo

ng and the building’s shadow is 16 feet long. Her height is 5.8 feet. How tall is the building?
Mathematics
1 answer:
vagabundo [1.1K]2 years ago
6 0
The building is 16 feet tall
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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
I really need help with this and how you got it please 10 points!!
Kamila [148]

Answer:

1 and 7  are congruent

2 and 5 are supplementary

4 and 6 are congruent

3 and 8 are supplementary

8 0
2 years ago
Tell whether it is possible to draw a triangle with the given side lengths.
expeople1 [14]

Answer:

A.

Step-by-step explanation:

Since the 2 shorter sides are greater than the longest side when added, it meet the triangle inequality thoerem. Triangle Inequality Theorom: The longest side of a triangle is less then the 2 shorter sides added.

4 0
3 years ago
Simplify using appropriate property: 5/7 X 1/5 + 5/7 X 3/5Simplify using appropriate property:
chubhunter [2.5K]

Answer:

4/7

Step-by-step explanation:

5/7 x (1/5+3/5) = 5/7 x 4/5 = 4/7

8 0
3 years ago
Use complete sentences to describe why √-1≠-√1
Salsk061 [2.6K]

Answer: because √-1 complex number ; and -√1 real number

Step-by-step explanation:

because √-1 complex number ; and -√1 real number or                                         \displaystyle\ (\sqrt{-1})^2 \neq(- \sqrt{1} )^2 \\\\-1\neq 1                                              

7 0
3 years ago
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